Feedback linearization for control of air breathing engines

NASA Technical Reports Server (NTRS)

Phillips, Stephen; Mattern, Duane

1991-01-01

The method of feedback linearization for control of the nonlinear nozzle and compressor components of an air breathing engine is presented. This method overcomes the need for a large number of scheduling variables and operating points to accurately model highly nonlinear plants. Feedback linearization also results in linear closed loop system performance simplifying subsequent control design. Feedback linearization is used for the nonlinear partial engine model and performance is verified through simulation.

Adaptive nonlinear control for autonomous ground vehicles

NASA Astrophysics Data System (ADS)

Black, William S.

We present the background and motivation for ground vehicle autonomy, and focus on uses for space-exploration. Using a simple design example of an autonomous ground vehicle we derive the equations of motion. After providing the mathematical background for nonlinear systems and control we present two common methods for exactly linearizing nonlinear systems, feedback linearization and backstepping. We use these in combination with three adaptive control methods: model reference adaptive control, adaptive sliding mode control, and extremum-seeking model reference adaptive control. We show the performances of each combination through several simulation results. We then consider disturbances in the system, and design nonlinear disturbance observers for both single-input-single-output and multi-input-multi-output systems. Finally, we show the performance of these observers with simulation results.

A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

NASA Astrophysics Data System (ADS)

Mamehrashi, K.; Yousefi, S. A.

2017-02-01

This paper presents a numerical solution for solving a nonlinear 2-D optimal control problem (2DOP). The performance index of a nonlinear 2DOP is described with a state and a control function. Furthermore, dynamic constraint of the system is given by a classical diffusion equation. It is preferred to use the Ritz method for finding the numerical solution of the problem. The method is based upon the Legendre polynomial basis. By using this method, the given optimisation nonlinear 2DOP reduces to the problem of solving a system of algebraic equations. The benefit of the method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, compared with the eigenfunction method, the satisfactory results are obtained only in a small number of polynomials order. This numerical approach is applicable and effective for such a kind of nonlinear 2DOP. The convergence of the method is extensively discussed and finally two illustrative examples are included to observe the validity and applicability of the new technique developed in the current work.

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input.

PubMed

Yu, Jinpeng; Shi, Peng; Dong, Wenjie; Lin, Chong

2017-09-01

In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.

Parametric Stiffness Control of Flexible Structures

NASA Technical Reports Server (NTRS)

Moon, F. C.; Rand, R. H.

1985-01-01

An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.

Indirect learning control for nonlinear dynamical systems

NASA Technical Reports Server (NTRS)

Ryu, Yeong Soon; Longman, Richard W.

1993-01-01

In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control

NASA Astrophysics Data System (ADS)

Ma, Tiedong; Li, Teng; Cui, Bing

2018-01-01

The coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, two novel sufficient conditions for achieving the cooperative control of a class of fractional-order nonlinear multi-agent systems are derived. Finally, two numerical simulations are verified to illustrate the effectiveness and feasibility of the proposed method.

A nonlinear control method based on ANFIS and multiple models for a class of SISO nonlinear systems and its application.

PubMed

Zhang, Yajun; Chai, Tianyou; Wang, Hong

2011-11-01

This paper presents a novel nonlinear control strategy for a class of uncertain single-input and single-output discrete-time nonlinear systems with unstable zero-dynamics. The proposed method combines adaptive-network-based fuzzy inference system (ANFIS) with multiple models, where a linear robust controller, an ANFIS-based nonlinear controller and a switching mechanism are integrated using multiple models technique. It has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system. Moreover, it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance. As a result, the controller has the following three outstanding features compared with existing control strategies. First, this method relaxes the assumption of commonly-used uniform boundedness on the unmodeled dynamics and thus enhances its applicability. Second, since ANFIS is used to estimate and compensate the effect caused by the unmodeled dynamics, the convergence rate of neural network learning has been increased. Third, a "one-to-one mapping" technique is adapted to guarantee the universal approximation property of ANFIS. The proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system, respectively, where its effectiveness has been justified.

Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation

NASA Astrophysics Data System (ADS)

Balcerzak, Marek; Dąbrowski, Artur; Pikunov, Danylo

2018-01-01

This paper presents a practical application of a new, simplified method of Lyapunov exponents estimation. The method has been applied to optimization of a real, nonlinear inverted pendulum system. Authors presented how the algorithm of the Largest Lyapunov Exponent (LLE) estimation can be applied to evaluate control systems performance. The new LLE-based control performance index has been proposed. Equations of the inverted pendulum system of the fourth order have been found. The nonlinear friction of the regulation object has been identified by means of the nonlinear least squares method. Three different friction models have been tested: linear, cubic and Coulomb model. The Differential Evolution (DE) algorithm has been used to search for the best set of parameters of the general linear regulator. This work proves that proposed method is efficient and results in faster perturbation rejection, especially when disturbances are significant.

Nonlinear flight control design using backstepping methodology

NASA Astrophysics Data System (ADS)

Tran, Thanh Trung

The subject of nonlinear flight control design using backstepping control methodology is investigated in the dissertation research presented here. Control design methods based on nonlinear models of the dynamic system provide higher utility and versatility because the design model more closely matches the physical system behavior. Obtaining requisite model fidelity is only half of the overall design process, however. Design of the nonlinear control loops can lessen the effects of nonlinearity, or even exploit nonlinearity, to achieve higher levels of closed-loop stability, performance, and robustness. The goal of the research is to improve control quality for a general class of strict-feedback dynamic systems and provide flight control architectures to augment the aircraft motion. The research is divided into two parts: theoretical control development for the strict-feedback form of nonlinear dynamic systems and application of the proposed theory for nonlinear flight dynamics. In the first part, the research is built on two components: transforming the nonlinear dynamic model to a canonical strict-feedback form and then applying backstepping control theory to the canonical model. The research considers a process to determine when this transformation is possible, and when it is possible, a systematic process to transfer the model is also considered when practical. When this is not the case, certain modeling assumptions are explored to facilitate the transformation. After achieving the canonical form, a systematic design procedure for formulating a backstepping control law is explored in the research. Starting with the simplest subsystem and ending with the full system, pseudo control concepts based on Lyapunov control functions are used to control each successive subsystem. Typically each pseudo control must be solved from a nonlinear algebraic equation. At the end of this process, the physical control input must be re-expressed in terms of the physical states by eliminating the pseudo control transformations. In the second part, the research focuses on nonlinear control design for flight dynamics of aircraft motion. Some assumptions on aerodynamics of the aircraft are addressed to transform full nonlinear flight dynamics into the canonical strict-feedback form. The assumptions are also analyzed, validated, and compared to show the advantages and disadvantages of the design models. With the achieved models, investigation focuses on formulating the backstepping control laws and provides an advanced control algorithm for nonlinear flight dynamics of the aircraft. Experimental and simulation studies are successfully implemented to validate the proposed control method. Advancement of nonlinear backstepping control theory and its application to nonlinear flight control are achieved in the dissertation research.

Drag reduction in channel flow using nonlinear control

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1993-01-01

Two nonlinear control schemes have been applied to the problem of drag reduction in channel flow. Both schemes have been tested using numerical simulations at a mass flux Reynolds numbers of 4408, utilizing 2D nonlinear neutral modes for goal dynamics. The OGY-method, which requires feedback, reduces drag to 60-80 percent of the turbulent value at the same Reynolds number, and employs forcing only within a thin region near the wall. The H-method, or model-based control, fails to achieve any drag reduction when starting from a fully turbulent initial condition, but shows potential for suppressing or retarding laminar-to-turbulent transition by imposing instead a transition to a low drag, nonlinear traveling wave solution to the Navier-Stokes equation. The drag in this state corresponds to that achieved by the OGY-method. Model-based control requires no feedback, but in experiments to date has required the forcing be imposed within a thicker layer than the OGY-method. Control energy expenditures in both methods are small, representing less than 0.1 percent of the uncontrolled flow's energy.

A computer-aided approach to nonlinear control systhesis

NASA Technical Reports Server (NTRS)

Wie, Bong; Anthony, Tobin

1988-01-01

The major objective of this project is to develop a computer-aided approach to nonlinear stability analysis and nonlinear control system design. This goal is to be obtained by refining the describing function method as a synthesis tool for nonlinear control design. The interim report outlines the approach by this study to meet these goals including an introduction to the INteractive Controls Analysis (INCA) program which was instrumental in meeting these study objectives. A single-input describing function (SIDF) design methodology was developed in this study; coupled with the software constructed in this study, the results of this project provide a comprehensive tool for design and integration of nonlinear control systems.

Robust nonlinear control of vectored thrust aircraft

NASA Technical Reports Server (NTRS)

Doyle, John C.; Murray, Richard; Morris, John

1993-01-01

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.

A nonlinear Kalman filtering approach to embedded control of turbocharged diesel engines

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan

2014-10-01

The development of efficient embedded control for turbocharged Diesel engines, requires the programming of elaborated nonlinear control and filtering methods. To this end, in this paper nonlinear control for turbocharged Diesel engines is developed with the use of Differential flatness theory and the Derivative-free nonlinear Kalman Filter. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances the Derivative-free nonlinear Kalman Filter is used and redesigned as a disturbance observer. The filter consists of the Kalman Filter recursion on the linearized equivalent of the Diesel engine model and of an inverse transformation based on differential flatness theory which enables to obtain estimates for the state variables of the initial nonlinear model. Once the disturbances variables are identified it is possible to compensate them by including an additional control term in the feedback loop. The efficiency of the proposed control method is tested through simulation experiments.

Robust nonlinear variable selective control for networked systems

NASA Astrophysics Data System (ADS)

Rahmani, Behrooz

2016-10-01

This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.

Model-Based Adaptive Event-Triggered Control of Strict-Feedback Nonlinear Systems.

PubMed

Li, Yuan-Xin; Yang, Guang-Hong

2018-04-01

This paper is concerned with the adaptive event-triggered control problem of nonlinear continuous-time systems in strict-feedback form. By using the event-sampled neural network (NN) to approximate the unknown nonlinear function, an adaptive model and an associated event-triggered controller are designed by exploiting the backstepping method. In the proposed method, the feedback signals and the NN weights are aperiodically updated only when the event-triggered condition is violated. A positive lower bound on the minimum intersample time is guaranteed to avoid accumulation point. The closed-loop stability of the resulting nonlinear impulsive dynamical system is rigorously proved via Lyapunov analysis under an adaptive event sampling condition. In comparing with the traditional adaptive backstepping design with a fixed sample period, the event-triggered method samples the state and updates the NN weights only when it is necessary. Therefore, the number of transmissions can be significantly reduced. Finally, two simulation examples are presented to show the effectiveness of the proposed control method.

Robust Gain-Scheduled Fault Tolerant Control for a Transport Aircraft

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob; Gregory, Irene

2007-01-01

This paper presents an application of robust gain-scheduled control concepts using a linear parameter-varying (LPV) control synthesis method to design fault tolerant controllers for a civil transport aircraft. To apply the robust LPV control synthesis method, the nonlinear dynamics must be represented by an LPV model, which is developed using the function substitution method over the entire flight envelope. The developed LPV model associated with the aerodynamic coefficient uncertainties represents nonlinear dynamics including those outside the equilibrium manifold. Passive and active fault tolerant controllers (FTC) are designed for the longitudinal dynamics of the Boeing 747-100/200 aircraft in the presence of elevator failure. Both FTC laws are evaluated in the full nonlinear aircraft simulation in the presence of the elevator fault and the results are compared to show pros and cons of each control law.

Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.

PubMed

Li, Yafeng; Hua, Changchun; Wu, Shuangshuang; Guan, Xinping

2017-01-31

In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.

Prediction of jump phenomena in rotationally-coupled maneuvers of aircraft, including nonlinear aerodynamic effects

NASA Technical Reports Server (NTRS)

Young, J. W.; Schy, A. A.; Johnson, K. G.

1977-01-01

An analytical method has been developed for predicting critical control inputs for which nonlinear rotational coupling may cause sudden jumps in aircraft response. The analysis includes the effect of aerodynamics which are nonlinear in angle of attack. The method involves the simultaneous solution of two polynomials in roll rate, whose coefficients are functions of angle of attack and the control inputs. Results obtained using this procedure are compared with calculated time histories to verify the validity of the method for predicting jump-like instabilities.

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

NASA Astrophysics Data System (ADS)

Kanjilal, Oindrila; Manohar, C. S.

2017-07-01

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.

Based on interval type-2 fuzzy-neural network direct adaptive sliding mode control for SISO nonlinear systems

NASA Astrophysics Data System (ADS)

Lin, Tsung-Chih

2010-12-01

In this paper, a novel direct adaptive interval type-2 fuzzy-neural tracking control equipped with sliding mode and Lyapunov synthesis approach is proposed to handle the training data corrupted by noise or rule uncertainties for nonlinear SISO nonlinear systems involving external disturbances. By employing adaptive fuzzy-neural control theory, the update laws will be derived for approximating the uncertain nonlinear dynamical system. In the meantime, the sliding mode control method and the Lyapunov stability criterion are incorporated into the adaptive fuzzy-neural control scheme such that the derived controller is robust with respect to unmodeled dynamics, external disturbance and approximation errors. In comparison with conventional methods, the advocated approach not only guarantees closed-loop stability but also the output tracking error of the overall system will converge to zero asymptotically without prior knowledge on the upper bound of the lumped uncertainty. Furthermore, chattering effect of the control input will be substantially reduced by the proposed technique. To illustrate the performance of the proposed method, finally simulation example will be given.

Adaptive Actor-Critic Design-Based Integral Sliding-Mode Control for Partially Unknown Nonlinear Systems With Input Disturbances.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2016-01-01

This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.

Data-Driven Zero-Sum Neuro-Optimal Control for a Class of Continuous-Time Unknown Nonlinear Systems With Disturbance Using ADP.

PubMed

Wei, Qinglai; Song, Ruizhuo; Yan, Pengfei

2016-02-01

This paper is concerned with a new data-driven zero-sum neuro-optimal control problem for continuous-time unknown nonlinear systems with disturbance. According to the input-output data of the nonlinear system, an effective recurrent neural network is introduced to reconstruct the dynamics of the nonlinear system. Considering the system disturbance as a control input, a two-player zero-sum optimal control problem is established. Adaptive dynamic programming (ADP) is developed to obtain the optimal control under the worst case of the disturbance. Three single-layer neural networks, including one critic and two action networks, are employed to approximate the performance index function, the optimal control law, and the disturbance, respectively, for facilitating the implementation of the ADP method. Convergence properties of the ADP method are developed to show that the system state will converge to a finite neighborhood of the equilibrium. The weight matrices of the critic and the two action networks are also convergent to finite neighborhoods of their optimal ones. Finally, the simulation results will show the effectiveness of the developed data-driven ADP methods.

Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Killingsworth, W. R., Jr.

1972-01-01

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Nonlinear feedback method of robot control - A preliminary experimental study

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Ganguly, S.; Li, Z.; Bejczy, A. K.

1990-01-01

The nonlinear feedback method of robot control has been experimentally implemented on two PUMA 560 robot arms. The feasibility of the proposed controller, which was shown viable through simulation results earlier, is stressed. The servomechanism operates in task space, and the nonlinear feedback takes care of the necessary transformations to compute the necessary joint currents. A discussion is presented of the implementation with details of the experiments performed. The performance of the controller is encouraging but was limited to 100-Hz sampling frequency and to derived velocity information at the time of the experimentation. The setup of the lab, the software aspects, results, and the control hardware architecture that has recently been implemented are discussed.

Robust adaptive controller design for a class of uncertain nonlinear systems using online T-S fuzzy-neural modeling approach.

PubMed

Chien, Yi-Hsing; Wang, Wei-Yen; Leu, Yih-Guang; Lee, Tsu-Tian

2011-04-01

This paper proposes a novel method of online modeling and control via the Takagi-Sugeno (T-S) fuzzy-neural model for a class of uncertain nonlinear systems with some kinds of outputs. Although studies about adaptive T-S fuzzy-neural controllers have been made on some nonaffine nonlinear systems, little is known about the more complicated uncertain nonlinear systems. Because the nonlinear functions of the systems are uncertain, traditional T-S fuzzy control methods can model and control them only with great difficulty, if at all. Instead of modeling these uncertain functions directly, we propose that a T-S fuzzy-neural model approximates a so-called virtual linearized system (VLS) of the system, which includes modeling errors and external disturbances. We also propose an online identification algorithm for the VLS and put significant emphasis on robust tracking controller design using an adaptive scheme for the uncertain systems. Moreover, the stability of the closed-loop systems is proven by using strictly positive real Lyapunov theory. The proposed overall scheme guarantees that the outputs of the closed-loop systems asymptotically track the desired output trajectories. To illustrate the effectiveness and applicability of the proposed method, simulation results are given in this paper.

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

PubMed Central

Li, YuHui; Jin, FeiTeng

2017-01-01

The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller. PMID:29410680

Optimal second order sliding mode control for nonlinear uncertain systems.

PubMed

Das, Madhulika; Mahanta, Chitralekha

2014-07-01

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

On controlling networks of limit-cycle oscillators

NASA Astrophysics Data System (ADS)

Skardal, Per Sebastian; Arenas, Alex

2016-09-01

The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here, we study the control of network-coupled limit cycle oscillators, extending the previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of controls. The first type directs oscillators towards larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Nonlinear adaptive control system design with asymptotically stable parameter estimation error

NASA Astrophysics Data System (ADS)

Mishkov, Rumen; Darmonski, Stanislav

2018-01-01

The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Practical Methodology for the Inclusion of Nonlinear Slosh Damping in the Stability Analysis of Liquid-Propelled Space Vehicles

NASA Technical Reports Server (NTRS)

Ottander, John A.; Hall, Robert A.; Powers, J. F.

2018-01-01

A method is presented that allows for the prediction of the magnitude of limit cycles due to adverse control-slosh interaction in liquid propelled space vehicles using non-linear slosh damping. Such a method is an alternative to the industry practice of assuming linear damping and relying on: mechanical slosh baffles to achieve desired stability margins; accepting minimal slosh stability margins; or time domain non-linear analysis to accept time periods of poor stability. Sinusoidal input describing functional analysis is used to develop a relationship between the non-linear slosh damping and an equivalent linear damping at a given slosh amplitude. In addition, a more accurate analytical prediction of the danger zone for slosh mass locations in a vehicle under proportional and derivative attitude control is presented. This method is used in the control-slosh stability analysis of the NASA Space Launch System.

Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

NASA Astrophysics Data System (ADS)

Nazemizadeh, M.; Rahimi, H. N.; Amini Khoiy, K.

2012-03-01

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.

Nonlinear Decoupling Control With ANFIS-Based Unmodeled Dynamics Compensation for a Class of Complex Industrial Processes.

PubMed

Zhang, Yajun; Chai, Tianyou; Wang, Hong; Wang, Dianhui; Chen, Xinkai

2018-06-01

Complex industrial processes are multivariable and generally exhibit strong coupling among their control loops with heavy nonlinear nature. These make it very difficult to obtain an accurate model. As a result, the conventional and data-driven control methods are difficult to apply. Using a twin-tank level control system as an example, a novel multivariable decoupling control algorithm with adaptive neural-fuzzy inference system (ANFIS)-based unmodeled dynamics (UD) compensation is proposed in this paper for a class of complex industrial processes. At first, a nonlinear multivariable decoupling controller with UD compensation is introduced. Different from the existing methods, the decomposition estimation algorithm using ANFIS is employed to estimate the UD, and the desired estimating and decoupling control effects are achieved. Second, the proposed method does not require the complicated switching mechanism which has been commonly used in the literature. This significantly simplifies the obtained decoupling algorithm and its realization. Third, based on some new lemmas and theorems, the conditions on the stability and convergence of the closed-loop system are analyzed to show the uniform boundedness of all the variables. This is then followed by the summary on experimental tests on a heavily coupled nonlinear twin-tank system that demonstrates the effectiveness and the practicability of the proposed method.

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kanjilal, Oindrila, E-mail: oindrila@civil.iisc.ernet.in; Manohar, C.S., E-mail: manohar@civil.iisc.ernet.in

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the secondmore » explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.« less

Study of a Simulation Tool to Determine Achievable Control Dynamics and Control Power Requirements with Perfect Tracking

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.

1998-01-01

This paper contains a study of two methods for use in a generic nonlinear simulation tool that could be used to determine achievable control dynamics and control power requirements while performing perfect tracking maneuvers over the entire flight envelope. The two methods are NDI (nonlinear dynamic inversion) and the SOFFT(Stochastic Optimal Feedforward and Feedback Technology) feedforward control structure. Equivalent discrete and continuous SOFFT feedforward controllers have been developed. These equivalent forms clearly show that the closed-loop plant model loop is a plant inversion and is the same as the NDI formulation. The main difference is that the NDI formulation has a closed-loop controller structure whereas SOFFT uses an open-loop command model. Continuous, discrete, and hybrid controller structures have been developed and integrated into the formulation. Linear simulation results show that seven different configurations all give essentially the same response, with the NDI hybrid being slightly different. The SOFFT controller gave better tracking performance compared to the NDI controller when a nonlinear saturation element was added. Future plans include evaluation using a nonlinear simulation.

Gap-metric-based robustness analysis of nonlinear systems with full and partial feedback linearisation

NASA Astrophysics Data System (ADS)

Al-Gburi, A.; Freeman, C. T.; French, M. C.

2018-06-01

This paper uses gap metric analysis to derive robustness and performance margins for feedback linearising controllers. Distinct from previous robustness analysis, it incorporates the case of output unstructured uncertainties, and is shown to yield general stability conditions which can be applied to both stable and unstable plants. It then expands on existing feedback linearising control schemes by introducing a more general robust feedback linearising control design which classifies the system nonlinearity into stable and unstable components and cancels only the unstable plant nonlinearities. This is done in order to preserve the stabilising action of the inherently stabilising nonlinearities. Robustness and performance margins are derived for this control scheme, and are expressed in terms of bounds on the plant nonlinearities and the accuracy of the cancellation of the unstable plant nonlinearity by the controller. Case studies then confirm reduced conservatism compared with standard methods.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Nonlinear dynamics of mini-satellite respinup by weak internal controllable torques

NASA Astrophysics Data System (ADS)

Somov, Yevgeny

2014-12-01

Contemporary space engineering advanced new problem before theoretical mechanics and motion control theory: a spacecraft directed respinup by the weak restricted control internal forces. The paper presents some results on this problem, which is very actual for energy supply of information mini-satellites (for communication, geodesy, radio- and opto-electronic observation of the Earth et al.) with electro-reaction plasma thrusters and gyro moment cluster based on the reaction wheels or the control moment gyros. The solution achieved is based on the methods for synthesis of nonlinear robust control and on rigorous analytical proof for the required spacecraft rotation stability by Lyapunov function method. These results were verified by a computer simulation of strongly nonlinear oscillatory processes at respinuping of a flexible spacecraft.

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Multi-application controls: Robust nonlinear multivariable aerospace controls applications

NASA Technical Reports Server (NTRS)

Enns, Dale F.; Bugajski, Daniel J.; Carter, John; Antoniewicz, Bob

1994-01-01

This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented as a method for analyzing robust performance and the mu-synthesis method will be presented as a method for synthesizing a robust control system. The paper concludes with the author's expectations regarding future applications of robust nonlinear multivariable controls.

The equivalent angle-of-attack method for estimating the nonlinear aerodynamic characteristics of missile wings and control surfaces

NASA Technical Reports Server (NTRS)

Hemsch, M. J.; Nielsen, J. N.

1982-01-01

A method has been developed for estimating the nonlinear aerodynamic characteristics of missile wing and control surfaces. The method is based on the following assumption: if a fin on a body has the same normal-force coefficient as a wing alone composed of two of the same fins joined together at their root chords, then the other force and moment coefficients of the fin and the wing alone are the same including the nonlinearities. The method can be used for deflected fins at arbitrary bank angles and at high angles of attack. In the paper, a full derivation of the method is given, its accuracy demonstrated and its use in extending missile data bases is shown.

Direct Optimal Control of Duffing Dynamics

NASA Technical Reports Server (NTRS)

Oz, Hayrani; Ramsey, John K.

2002-01-01

The "direct control method" is a novel concept that is an attractive alternative and competitor to the differential-equation-based methods. The direct method is equally well applicable to nonlinear, linear, time-varying, and time-invariant systems. For all such systems, the method yields explicit closed-form control laws based on minimization of a quadratic control performance measure. We present an application of the direct method to the dynamics and optimal control of the Duffing system where the control performance measure is not restricted to a quadratic form and hence may include a quartic energy term. The results we present in this report also constitute further generalizations of our earlier work in "direct optimal control methodology." The approach is demonstrated for the optimal control of the Duffing equation with a softening nonlinear stiffness.

A nonlinear strategy for sensor based vehicle path control

NASA Technical Reports Server (NTRS)

Mayr, R.

1994-01-01

A method of transverse control which makes use of nonlinear formulations is presented. The strategy is utilized to stabilize a vehicle. The vehicle is autonomously guided and takes its control inputs from an optical sensing system. Additionally, the velocity of the vehicle is dictated by a longitudinal controller, which is also discussed.

Multi-linear model set design based on the nonlinearity measure and H-gap metric.

PubMed

Shaghaghi, Davood; Fatehi, Alireza; Khaki-Sedigh, Ali

2017-05-01

This paper proposes a model bank selection method for a large class of nonlinear systems with wide operating ranges. In particular, nonlinearity measure and H-gap metric are used to provide an effective algorithm to design a model bank for the system. Then, the proposed model bank is accompanied with model predictive controllers to design a high performance advanced process controller. The advantage of this method is the reduction of excessive switch between models and also decrement of the computational complexity in the controller bank that can lead to performance improvement of the control system. The effectiveness of the method is verified by simulations as well as experimental studies on a pH neutralization laboratory apparatus which confirms the efficiency of the proposed algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A self-adaption compensation control for hysteresis nonlinearity in piezo-actuated stages based on Pi-sigma fuzzy neural network

NASA Astrophysics Data System (ADS)

Xu, Rui; Zhou, Miaolei

2018-04-01

Piezo-actuated stages are widely applied in the high-precision positioning field nowadays. However, the inherent hysteresis nonlinearity in piezo-actuated stages greatly deteriorates the positioning accuracy of piezo-actuated stages. This paper first utilizes a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model based on the Pi-sigma fuzzy neural network (PSFNN) to construct an online rate-dependent hysteresis model for describing the hysteresis nonlinearity in piezo-actuated stages. In order to improve the convergence rate of PSFNN and modeling precision, we adopt the gradient descent algorithm featuring three different learning factors to update the model parameters. The convergence of the NARMAX model based on the PSFNN is analyzed effectively. To ensure that the parameters can converge to the true values, the persistent excitation condition is considered. Then, a self-adaption compensation controller is designed for eliminating the hysteresis nonlinearity in piezo-actuated stages. A merit of the proposed controller is that it can directly eliminate the complex hysteresis nonlinearity in piezo-actuated stages without any inverse dynamic models. To demonstrate the effectiveness of the proposed model and control methods, a set of comparative experiments are performed on piezo-actuated stages. Experimental results show that the proposed modeling and control methods have excellent performance.

Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints.

PubMed

Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai

2015-07-01

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.

Dual RBFNNs-Based Model-Free Adaptive Control With Aspen HYSYS Simulation.

PubMed

Zhu, Yuanming; Hou, Zhongsheng; Qian, Feng; Du, Wenli

2017-03-01

In this brief, we propose a new data-driven model-free adaptive control (MFAC) method with dual radial basis function neural networks (RBFNNs) for a class of discrete-time nonlinear systems. The main novelty lies in that it provides a systematic design method for controller structure by the direct usage of I/O data, rather than using the first-principle model or offline identified plant model. The controller structure is determined by equivalent-dynamic-linearization representation of the ideal nonlinear controller, and the controller parameters are tuned by the pseudogradient information extracted from the I/O data of the plant, which can deal with the unknown nonlinear system. The stability of the closed-loop control system and the stability of the training process for RBFNNs are guaranteed by rigorous theoretical analysis. Meanwhile, the effectiveness and the applicability of the proposed method are further demonstrated by the numerical example and Aspen HYSYS simulation of distillation column in crude styrene produce process.

Control of nonlinear systems represented in quasilinear form. Ph.D. Thesis, 1994 Final Report

NASA Technical Reports Server (NTRS)

Coetsee, Josef A.

1993-01-01

Methods to synthesize controllers for nonlinear systems are developed by exploiting the fact that under mild differentiability conditions, systems of the form: x-dot = f(x) + G(x)u can be represented in quasilinear form, viz: x-dot = A(x)x + B(x)u. Two classes of control methods are investigated. The first is zero-look-ahead control, where the control input depends only on the current values of A(x) and B(x). For this case the control input is computed by continuously solving a matrix Riccati equation as the system progresses along a trajectory. The second is controllers with look-ahead, where the control input depends on the future behavior of A(x) and B(x). These controllers use the similarity between quasilinear systems and linear time varying systems to find approximate solutions to optimal control type problems. The methods that are developed are not guaranteed to be globally stable. However in simulation studies they were found to be useful alternatives for synthesizing control laws for a general class of nonlinear systems.

Sliding mode control for a two-joint coupling nonlinear system based on extended state observer.

PubMed

Zhao, Ling; Cheng, Haiyan; Wang, Tao

2018-02-01

A two-joint coupling nonlinear system driven by pneumatic artificial muscles is introduced in this paper. A sliding mode controller with extended state observer is proposed to cope with nonlinearities and disturbances for the two-joint coupling nonlinear system. In addition, convergence of the extended state observer is presented and stability analysis of the closed-loop system is also demonstrated with the sliding mode controller. Lastly, some experiments are carried out to show the reality effectiveness of the proposed method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Neural networks for feedback feedforward nonlinear control systems.

PubMed

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Retrieval of all effective susceptibilities in nonlinear metamaterials

NASA Astrophysics Data System (ADS)

Larouche, Stéphane; Radisic, Vesna

2018-04-01

Electromagnetic metamaterials offer a great avenue to engineer and amplify the nonlinear response of materials. Their electric, magnetic, and magnetoelectric linear and nonlinear response are related to their structure, providing unprecedented liberty to control those properties. Both the linear and the nonlinear properties of metamaterials are typically anisotropic. While the methods to retrieve the effective linear properties are well established, existing nonlinear retrieval methods have serious limitations. In this work, we generalize a nonlinear transfer matrix approach to account for all nonlinear susceptibility terms and show how to use this approach to retrieve all effective nonlinear susceptibilities of metamaterial elements. The approach is demonstrated using sum frequency generation, but can be applied to other second-order or higher-order processes.

Nonlinear dynamics and control of a vibrating rectangular plate

NASA Technical Reports Server (NTRS)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems.

PubMed

Choi, Yun Ho; Yoo, Sung Jin

2016-12-01

A decentralized adaptive backstepping control design using minimal function approximators is proposed for nonlinear large-scale systems with unknown unmatched time-varying delayed interactions and unknown backlash-like hysteresis nonlinearities. Compared with existing decentralized backstepping methods, the contribution of this paper is to design a simple local control law for each subsystem, consisting of an actual control with one adaptive function approximator, without requiring the use of multiple function approximators and regardless of the order of each subsystem. The virtual controllers for each subsystem are used as intermediate signals for designing a local actual control at the last step. For each subsystem, a lumped unknown function including the unknown nonlinear terms and the hysteresis nonlinearities is derived at the last step and is estimated by one function approximator. Thus, the proposed approach only uses one function approximator to implement each local controller, while existing decentralized backstepping control methods require the number of function approximators equal to the order of each subsystem and a calculation of virtual controllers to implement each local actual controller. The stability of the total controlled closed-loop system is analyzed using the Lyapunov stability theorem.

H∞ output tracking control of uncertain and disturbed nonlinear systems based on neural network model

NASA Astrophysics Data System (ADS)

Li, Chengcheng; Li, Yuefeng; Wang, Guanglin

2017-07-01

The work presented in this paper seeks to address the tracking problem for uncertain continuous nonlinear systems with external disturbances. The objective is to obtain a model that uses a reference-based output feedback tracking control law. The control scheme is based on neural networks and a linear difference inclusion (LDI) model, and a PDC structure and H∞ performance criterion are used to attenuate external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key principles of the proposed approach are as follows: neural networks are first used to approximate nonlinearities, to enable a nonlinear system to then be represented as a linearised LDI model. An LMI (linear matrix inequality) formula is obtained for uncertain and disturbed linear systems. This formula enables a solution to be obtained through an interior point optimisation method for some nonlinear output tracking control problems. Finally, simulations and comparisons are provided on two practical examples to illustrate the validity and effectiveness of the proposed method.

Power maximization of variable-speed variable-pitch wind turbines using passive adaptive neural fault tolerant control

NASA Astrophysics Data System (ADS)

Habibi, Hamed; Rahimi Nohooji, Hamed; Howard, Ian

2017-09-01

Power maximization has always been a practical consideration in wind turbines. The question of how to address optimal power capture, especially when the system dynamics are nonlinear and the actuators are subject to unknown faults, is significant. This paper studies the control methodology for variable-speed variable-pitch wind turbines including the effects of uncertain nonlinear dynamics, system fault uncertainties, and unknown external disturbances. The nonlinear model of the wind turbine is presented, and the problem of maximizing extracted energy is formulated by designing the optimal desired states. With the known system, a model-based nonlinear controller is designed; then, to handle uncertainties, the unknown nonlinearities of the wind turbine are estimated by utilizing radial basis function neural networks. The adaptive neural fault tolerant control is designed passively to be robust on model uncertainties, disturbances including wind speed and model noises, and completely unknown actuator faults including generator torque and pitch actuator torque. The Lyapunov direct method is employed to prove that the closed-loop system is uniformly bounded. Simulation studies are performed to verify the effectiveness of the proposed method.

Nonlinear dynamics of mini-satellite respinup by weak internal controllable torques

DOE Office of Scientific and Technical Information (OSTI.GOV)

Somov, Yevgeny, E-mail: e-somov@mail.ru

Contemporary space engineering advanced new problem before theoretical mechanics and motion control theory: a spacecraft directed respinup by the weak restricted control internal forces. The paper presents some results on this problem, which is very actual for energy supply of information mini-satellites (for communication, geodesy, radio- and opto-electronic observation of the Earth et al.) with electro-reaction plasma thrusters and gyro moment cluster based on the reaction wheels or the control moment gyros. The solution achieved is based on the methods for synthesis of nonlinear robust control and on rigorous analytical proof for the required spacecraft rotation stability by Lyapunov functionmore » method. These results were verified by a computer simulation of strongly nonlinear oscillatory processes at respinuping of a flexible spacecraft.« less

An analytical fuzzy-based approach to ?-gain optimal control of input-affine nonlinear systems using Newton-type algorithm

NASA Astrophysics Data System (ADS)

Milic, Vladimir; Kasac, Josip; Novakovic, Branko

2015-10-01

This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

Static Methods in the Design of Nonlinear Automatic Control Systems,

DTIC Science & Technology

1984-06-27

227 Chapter VI. Ways of Decrease of the Number of Statistical Nodes During the Research of Nonlinear Systems...at present occupies the central place. This region of research was called the statistical dynamics of nonlinear H automatic control systems...receives further development in the numerous research of Soviet and C foreign scientists. Special role in the development of the statistical dynamics of

A Hybrid Nonlinear Control Scheme for Active Magnetic Bearings

NASA Technical Reports Server (NTRS)

Xia, F.; Albritton, N. G.; Hung, J. Y.; Nelms, R. M.

1996-01-01

A nonlinear control scheme for active magnetic bearings is presented in this work. Magnet winding currents are chosen as control inputs for the electromechanical dynamics, which are linearized using feedback linearization. Then, the desired magnet currents are enforced by sliding mode control design of the electromagnetic dynamics. The overall control scheme is described by a multiple loop block diagram; the approach also falls in the class of nonlinear controls that are collectively known as the 'integrator backstepping' method. Control system hardware and new switching power electronics for implementing the controller are described. Various experiments and simulation results are presented to demonstrate the concepts' potentials.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery such as inlets, ramjets, and scramjets. The discussion is separated into four sections: (1) computational fluid dynamics model for the entire nonlinear system or high order nonlinear models; (2) high order linearized model derived from fundamental physics; (3) low order linear models obtained from other high order models; and (4) low order nonlinear models. Included are special considerations on any relevant control system designs. The methods discussed are for the quasi-one dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, moving normal shocks, hammershocks, subsonic combustion via heat addition, temperature dependent gases, detonation, and thermal choking.

A new method for analysis of limit cycle behavior of the NASA/JPL 70-meter antenna axis servos

NASA Technical Reports Server (NTRS)

Hill, R. E.

1989-01-01

A piecewise linear method of analyzing the effects of discontinuous nonlinearities on control system performance is described. The limit cycle oscillatory behavior of the system resulting from the nonlinearities is described in terms of a sequence of linear system transient responses. The equations are derived which relate the initial and the terminal conditions of successive transients and the boundary conditions imposed by the non-linearities. The method leads to a convenient computation algorithm for prediction of limit cycle characteristics resulting from discontinuous nonlinearities such as friction, deadzones, and hysteresis.

Nonclassical Flight Control for Unhealthy Aircraft

NASA Technical Reports Server (NTRS)

Lu, Ping

1997-01-01

This research set out to investigate flight control of aircraft which has sustained damage in regular flight control effectors, due to jammed control surfaces or complete loss of hydraulic power. It is recognized that in such an extremely difficult situation unconventional measures may need to be taken to regain control and stability of the aircraft. Propulsion controlled aircraft (PCA) concept, initiated at the NASA Dryden Flight Research Center. represents a ground-breaking effort in this direction. In this approach, the engine is used as the only flight control effector in the rare event of complete loss of normal flight control system. Studies and flight testing conducted at NASA Dryden have confirmed the feasibility of the PCA concept. During the course of this research (March 98, 1997 to November 30, 1997), a comparative study has been done using the full nonlinear model of an F-18 aircraft. Linear controllers and nonlinear controllers based on a nonlinear predictive control method have been designed for normal flight control system and propulsion controlled aircraft. For the healthy aircraft with normal flight control, the study shows that an appropriately designed linear controller can perform as well as a nonlinear controller. On the other hand. when the normal flight control is lost and the engine is the only available means of flight control, a nonlinear PCA controller can significantly increase the size of the recoverable region in which the stability of the unstable aircraft can be attained by using only thrust modulation. The findings and controller design methods have been summarized in an invited paper entitled.

Robust fast controller design via nonlinear fractional differential equations.

PubMed

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

High angle of attack control law development for a free-flight wind tunnel model using direct eigenstructure assignment

NASA Technical Reports Server (NTRS)

Wendel, Thomas R.; Boland, Joseph R.; Hahne, David E.

1991-01-01

Flight-control laws are developed for a wind-tunnel aircraft model flying at a high angle of attack by using a synthesis technique called direct eigenstructure assignment. The method employs flight guidelines and control-power constraints to develop the control laws, and gain schedules and nonlinear feedback compensation provide a framework for considering the nonlinear nature of the attack angle. Linear and nonlinear evaluations show that the control laws are effective, a conclusion that is further confirmed by a scale model used for free-flight testing.

Data-Driven Nonlinear Subspace Modeling for Prediction and Control of Molten Iron Quality Indices in Blast Furnace Ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Song, Heda; Wang, Hong

Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multi-phase and multi-field coupling and large time delay occur during its operation. In BF operation, the molten iron temperature (MIT) as well as Si, P and S contents of molten iron are the most essential molten iron quality (MIQ) indices, whose measurement, modeling and control have always been important issues in metallurgic engineering and automation field. This paper develops a novel data-driven nonlinear state space modeling for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques. First, to improvemore » modeling efficiency, a data-driven hybrid method combining canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modeling inputs from multitudinous factors would affect the MIQ indices. Then, a Hammerstein model for the prediction of MIQ indices is established using the LS-SVM based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method to fit the complex nonlinear kernel function. Compared to the original Hammerstein model, this simplified model can not only significantly reduce the computational complexity, but also has almost the same reliability and accuracy for a stable prediction of MIQ indices. Last, in order to verify the practicability of the developed model, it is applied in designing a genetic algorithm based nonlinear predictive controller for multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approach.« less

Control strategies for systems with limited actuators

NASA Technical Reports Server (NTRS)

Marcopoli, Vincent R.; Phillips, Stephen M.

1994-01-01

This work investigates the effects of actuator saturation in multi-input, multi-output (MIMO) control systems. The adverse system behavior introduced by the saturation nonlinearity is viewed here as resulting from two mechanisms: controller windup - a problem caused by the discrepancy between the limited actuator commands and the corresponding control signals, and directionality - the problem of how to use nonlimited actuators when a limited condition exists. The tracking mode and Hanus methods are two common strategies for dealing with the windup problem. It is seen that while these methods alleviate windup, performance problems remain due to plant directionality. Though high gain conventional antiwindup as well as more general linear methods have the potential to address both windup and directionality, no systematic design method for these schemes has emerged; most approaches used in practice are application driven. An alternative method of addressing the directionality problem is presented which involves the introduction of a control direction preserving nonlinearity to the Hanus antiwindup system. A nonlinearity is subsequently proposed which reduces the conservation inherent in the former direction-preserving approach, improving performance. The concept of multivariable sensitivity is seen to play a key role in the success of the new method.

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

PubMed

Mobayen, Saleh

2018-06-01

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Fuzzy control for nonlinear structure with semi-active friction damper

NASA Astrophysics Data System (ADS)

Zhao, Da-Hai; Li, Hong-Nan

2007-04-01

The implementation of semi-active friction damper for vibration mitigation of seismic structure generally requires an efficient control strategy. In this paper, the fuzzy logic based on Takagi-Sugeno model is proposed for controlling a semi-active friction damper that is installed on a nonlinear building subjected to strong earthquakes. The continuous Bouc-Wen hysteretic model for the stiffness is used to describe nonlinear characteristic of the building. The optimal sliding force with friction damper is determined by nonlinear time history analysis under normal earthquakes. The Takagi-Sugeno fuzzy logic model is employed to adjust the clamping force acted on the friction damper according to the semi-active control strategy. Numerical simulation results demonstrate that the proposed method is very efficient in reducing the peak inter-story drift and acceleration of the nonlinear building structure under earthquake excitations.

Multilevel adaptive control of nonlinear interconnected systems.

PubMed

Motallebzadeh, Farzaneh; Ozgoli, Sadjaad; Momeni, Hamid Reza

2015-01-01

This paper presents an adaptive backstepping-based multilevel approach for the first time to control nonlinear interconnected systems with unknown parameters. The system consists of a nonlinear controller at the first level to neutralize the interaction terms, and some adaptive controllers at the second level, in which the gains are optimally tuned using genetic algorithm. The presented scheme can be used in systems with strong couplings where completely ignoring the interactions leads to problems in performance or stability. In order to test the suitability of the method, two case studies are provided: the uncertain double and triple coupled inverted pendulums connected by springs with unknown parameters. The simulation results show that the method is capable of controlling the system effectively, in both regulation and tracking tasks. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Ultimate boundedness stability and controllability of hereditary systems

NASA Technical Reports Server (NTRS)

Chukwu, E. N.

1979-01-01

By generalizing the Liapunov-Yoshizawa techniques, necessary and sufficient conditions are given for uniform boundedness and uniform ultimate boundedness of a rather general class of nonlinear differential equations of neutral type. Among the applications treated by the methods are the Lienard equation of neutral type and hereditary systems of Lurie type. The absolute stability of this later equation is also investigated. A certain existence result of a solution of a neutral functional differential inclusion with two point boundary values is applied to study the exact function space controllability of a nonlinear neutral functional differential control system. A geometric growth condition is used to characterize both the function space and Euclidean controllability of another nonlinear delay system which has a compact and convex control set. This yields conditions under which perturbed nonlinear delay controllable systems are controllable.

Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation

NASA Astrophysics Data System (ADS)

Peter, Simon; Leine, Remco I.

2017-11-01

Phase resonance testing is one method for the experimental extraction of nonlinear normal modes. This paper proposes a novel method for nonlinear phase resonance testing. Firstly, the issue of appropriate excitation is approached on the basis of excitation power considerations. Therefore, power quantities known from nonlinear systems theory in electrical engineering are transferred to nonlinear structural dynamics applications. A new power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments. Secondly, the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller. This method provides a very user-friendly and fast way for obtaining the backbone curve. Furthermore, the method allows to exploit specific advantages of phase control such as the robustness for lightly damped systems and the stabilization of unstable branches of the frequency response. The reduced tuning time for the excitation makes the commonly used free-decay measurements for the extraction of backbone curves unnecessary. Instead, steady-state measurements for every point of the curve are obtained. In conjunction with the new mode indicator function, the correlation of every measured point with the associated nonlinear normal mode of the underlying conservative system can be evaluated. Moreover, it is shown that the analysis of the excitation power helps to locate sources of inaccuracies in the force appropriation process. The method is illustrated by a numerical example and its functionality in experiments is demonstrated on a benchmark beam structure.

Imitative modeling automatic system Control of steam pressure in the main steam collector with the influence on the main Servomotor steam turbine

NASA Astrophysics Data System (ADS)

Andriushin, A. V.; Zverkov, V. P.; Kuzishchin, V. F.; Ryzhkov, O. S.; Sabanin, V. R.

2017-11-01

The research and setting results of steam pressure in the main steam collector “Do itself” automatic control system (ACS) with high-speed feedback on steam pressure in the turbine regulating stage are presented. The ACS setup is performed on the simulation model of the controlled object developed for this purpose with load-dependent static and dynamic characteristics and a non-linear control algorithm with pulse control of the turbine main servomotor. A method for tuning nonlinear ACS with a numerical algorithm for multiparametric optimization and a procedure for separate dynamic adjustment of control devices in a two-loop ACS are proposed and implemented. It is shown that the nonlinear ACS adjusted with the proposed method with the regulators constant parameters ensures reliable and high-quality operation without the occurrence of oscillations in the transient processes the operating range of the turbine loads.

The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition

NASA Astrophysics Data System (ADS)

Chen, Shuhong; Tan, Zhong

2007-11-01

In this paper, we consider the nonlinear elliptic systems under controllable growth condition. We use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution.

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob

2007-01-01

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

Modeling and comparative study of linear and nonlinear controllers for rotary inverted pendulum

NASA Astrophysics Data System (ADS)

Lima, Byron; Cajo, Ricardo; Huilcapi, Víctor; Agila, Wilton

2017-01-01

The rotary inverted pendulum (RIP) is a problem difficult to control, several studies have been conducted where different control techniques have been applied. Literature reports that, although problem is nonlinear, classical PID controllers presents appropriate performances when applied to the system. In this paper, a comparative study of the performances of linear and nonlinear PID structures is carried out. The control algorithms are evaluated in the RIP system, using indices of performance and power consumption, which allow the categorization of control strategies according to their performance. This article also presents the modeling system, which has been estimated some of the parameters involved in the RIP system, using computer-aided design tools (CAD) and experimental methods or techniques proposed by several authors attended. The results indicate a better performance of the nonlinear controller with an increase in the robustness and faster response than the linear controller.

Effective Desynchronization by Nonlinear Delayed Feedback

NASA Astrophysics Data System (ADS)

Popovych, Oleksandr V.; Hauptmann, Christian; Tass, Peter A.

2005-04-01

We show that nonlinear delayed feedback opens up novel means for the control of synchronization. In particular, we propose a demand-controlled method for powerful desynchronization, which does not require any time-consuming calibration. Our technique distinguishes itself by its robustness against variations of system parameters, even in strongly coupled ensembles of oscillators. We suggest our method for mild and effective deep brain stimulation in neurological diseases characterized by pathological cerebral synchronization.

Neural dynamic programming and its application to control systems

NASA Astrophysics Data System (ADS)

Seong, Chang-Yun

There are few general practical feedback control methods for nonlinear MIMO (multi-input-multi-output) systems, although such methods exist for their linear counterparts. Neural Dynamic Programming (NDP) is proposed as a practical design method of optimal feedback controllers for nonlinear MIMO systems. NDP is an offspring of both neural networks and optimal control theory. In optimal control theory, the optimal solution to any nonlinear MIMO control problem may be obtained from the Hamilton-Jacobi-Bellman equation (HJB) or the Euler-Lagrange equations (EL). The two sets of equations provide the same solution in different forms: EL leads to a sequence of optimal control vectors, called Feedforward Optimal Control (FOC); HJB yields a nonlinear optimal feedback controller, called Dynamic Programming (DP). DP produces an optimal solution that can reject disturbances and uncertainties as a result of feedback. Unfortunately, computation and storage requirements associated with DP solutions can be problematic, especially for high-order nonlinear systems. This dissertation presents an approximate technique for solving the DP problem based on neural network techniques that provides many of the performance benefits (e.g., optimality and feedback) of DP and benefits from the numerical properties of neural networks. We formulate neural networks to approximate optimal feedback solutions whose existence DP justifies. We show the conditions under which NDP closely approximates the optimal solution. Finally, we introduce the learning operator characterizing the learning process of the neural network in searching the optimal solution. The analysis of the learning operator provides not only a fundamental understanding of the learning process in neural networks but also useful guidelines for selecting the number of weights of the neural network. As a result, NDP finds---with a reasonable amount of computation and storage---the optimal feedback solutions to nonlinear MIMO control problems that would be very difficult to solve with DP. NDP was demonstrated on several applications such as the lateral autopilot logic for a Boeing 747, the minimum fuel control of a double-integrator plant with bounded control, the backward steering of a two-trailer truck, and the set-point control of a two-link robot arm.

Nonlinear control for a class of hydraulic servo system.

PubMed

Yu, Hong; Feng, Zheng-jin; Wang, Xu-yong

2004-11-01

The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control.

PubMed

Hou, Huazhou; Zhang, Qingling

2016-11-01

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Optimization of Stability Constrained Geometrically Nonlinear Shallow Trusses Using an Arc Length Sparse Method with a Strain Energy Density Approach

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.; Nguyen, Duc T.

2008-01-01

A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.

Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach.

PubMed

Yang, Jun; Zolotas, Argyrios; Chen, Wen-Hua; Michail, Konstantinos; Li, Shihua

2011-07-01

Robust control of a class of uncertain systems that have disturbances and uncertainties not satisfying "matching" condition is investigated in this paper via a disturbance observer based control (DOBC) approach. In the context of this paper, "matched" disturbances/uncertainties stand for the disturbances/uncertainties entering the system through the same channels as control inputs. By properly designing a disturbance compensation gain, a novel composite controller is proposed to counteract the "mismatched" lumped disturbances from the output channels. The proposed method significantly extends the applicability of the DOBC methods. Rigorous stability analysis of the closed-loop system with the proposed method is established under mild assumptions. The proposed method is applied to a nonlinear MAGnetic LEViation (MAGLEV) suspension system. Simulation shows that compared to the widely used integral control method, the proposed method provides significantly improved disturbance rejection and robustness against load variation. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Synthesizing Virtual Oscillators to Control Islanded Inverters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Brian B.; Sinha, Mohit; Ainsworth, Nathan G.

Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged modelsmore » reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.« less

Neural networks for function approximation in nonlinear control

NASA Technical Reports Server (NTRS)

Linse, Dennis J.; Stengel, Robert F.

1990-01-01

Two neural network architectures are compared with a classical spline interpolation technique for the approximation of functions useful in a nonlinear control system. A standard back-propagation feedforward neural network and a cerebellar model articulation controller (CMAC) neural network are presented, and their results are compared with a B-spline interpolation procedure that is updated using recursive least-squares parameter identification. Each method is able to accurately represent a one-dimensional test function. Tradeoffs between size requirements, speed of operation, and speed of learning indicate that neural networks may be practical for identification and adaptation in a nonlinear control environment.

Modeling a multivariable reactor and on-line model predictive control.

PubMed

Yu, D W; Yu, D L

2005-10-01

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.

Discrete time learning control in nonlinear systems

NASA Technical Reports Server (NTRS)

Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh

1992-01-01

In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.

Investigation of the Flutter Suppression by Fuzzy Logic Control for Hypersonic Wing

NASA Astrophysics Data System (ADS)

Li, Dongxu; Luo, Qing; Xu, Rui

This paper presents a fundamental study of flutter characteristics and control performance of an aeroelastic system based on a two-dimensional double wedge wing in the hypersonic regime. Dynamic equations were established based on the modified third order nonlinear piston theory and some nonlinear structural effects are also included. A set of important parameters are observed. And then aeroelastic control law is designed to suppress the amplitude of the LCOs for the system in the sub/supercritical speed range by applying fuzzy logic control on the input of the deflection of the flap. The overall effects of the parameters on the aeroelastic system were outlined. Nonlinear aeroelastic responses in the open- and closed-loop system are obtained through numerical methods. The simulations show fuzzy logic control methods are effective in suppressing flutter and provide a smart approach for this complicated system.

Nonlinear Performance Seeking Control using Fuzzy Model Reference Learning Control and the Method of Steepest Descent

NASA Technical Reports Server (NTRS)

Kopasakis, George

1997-01-01

Performance Seeking Control (PSC) attempts to find and control the process at the operating condition that will generate maximum performance. In this paper a nonlinear multivariable PSC methodology will be developed, utilizing the Fuzzy Model Reference Learning Control (FMRLC) and the method of Steepest Descent or Gradient (SDG). This PSC control methodology employs the SDG method to find the operating condition that will generate maximum performance. This operating condition is in turn passed to the FMRLC controller as a set point for the control of the process. The conventional SDG algorithm is modified in this paper in order for convergence to occur monotonically. For the FMRLC control, the conventional fuzzy model reference learning control methodology is utilized, with guidelines generated here for effective tuning of the FMRLC controller.

Application of the concept of dynamic trim control and nonlinear system inverses to automatic control of a vertical attitude takeoff and landing aircraft

NASA Technical Reports Server (NTRS)

Smith, G. A.; Meyer, G.

1981-01-01

A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.

Nonlinear Model Reduction in Power Systems by Balancing of Empirical Controllability and Observability Covariances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qi, Junjian; Wang, Jianhui; Liu, Hui

Abstract: In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods, the external system does not need to be linearized but is directly dealt with as a nonlinear system. A transformation is found to balance the controllability and observability covariances in order to determine which states have the greatest contribution to the input-output behavior. The original system model is then reduced by Galerkin projection based on this transformation. The proposed method is tested and validated on a systemmore » comprised of a 16-machine 68-bus system and an IEEE 50-machine 145-bus system. The results show that by using the proposed model reduction the calculation efficiency can be greatly improved; at the same time, the obtained state trajectories are close to those for directly simulating the whole system or partitioning the system while not performing reduction. Compared with the balanced truncation method based on a linearized model, the proposed nonlinear model reduction method can guarantee higher accuracy and similar calculation efficiency. It is shown that the proposed method is not sensitive to the choice of the matrices for calculating the empirical covariances.« less

A robust hybrid fuzzy-simulated annealing-intelligent water drops approach for tuning a distribution static compensator nonlinear controller in a distribution system

NASA Astrophysics Data System (ADS)

Bagheri Tolabi, Hajar; Hosseini, Rahil; Shakarami, Mahmoud Reza

2016-06-01

This article presents a novel hybrid optimization approach for a nonlinear controller of a distribution static compensator (DSTATCOM). The DSTATCOM is connected to a distribution system with the distributed generation units. The nonlinear control is based on partial feedback linearization. Two proportional-integral-derivative (PID) controllers regulate the voltage and track the output in this control system. In the conventional scheme, the trial-and-error method is used to determine the PID controller coefficients. This article uses a combination of a fuzzy system, simulated annealing (SA) and intelligent water drops (IWD) algorithms to optimize the parameters of the controllers. The obtained results reveal that the response of the optimized controlled system is effectively improved by finding a high-quality solution. The results confirm that using the tuning method based on the fuzzy-SA-IWD can significantly decrease the settling and rising times, the maximum overshoot and the steady-state error of the voltage step response of the DSTATCOM. The proposed hybrid tuning method for the partial feedback linearizing (PFL) controller achieved better regulation of the direct current voltage for the capacitor within the DSTATCOM. Furthermore, in the event of a fault the proposed controller tuned by the fuzzy-SA-IWD method showed better performance than the conventional controller or the PFL controller without optimization by the fuzzy-SA-IWD method with regard to both fault duration and clearing times.

Application of Nonlinear Systems Inverses to Automatic Flight Control Design: System Concepts and Flight Evaluations

NASA Technical Reports Server (NTRS)

Meyer, G.; Cicolani, L.

1981-01-01

A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.

Computational alternatives to obtain time optimal jet engine control. M.S. Thesis

NASA Technical Reports Server (NTRS)

Basso, R. J.; Leake, R. J.

1976-01-01

Two computational methods to determine an open loop time optimal control sequence for a simple single spool turbojet engine are described by a set of nonlinear differential equations. Both methods are modifications of widely accepted algorithms which can solve fixed time unconstrained optimal control problems with a free right end. Constrained problems to be considered have fixed right ends and free time. Dynamic programming is defined on a standard problem and it yields a successive approximation solution to the time optimal problem of interest. A feedback control law is obtained and it is then used to determine the corresponding open loop control sequence. The Fletcher-Reeves conjugate gradient method has been selected for adaptation to solve a nonlinear optimal control problem with state variable and control constraints.

Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Boskovic, Jovan D.

2008-01-01

This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.

Decoupling control of steering and driving system for in-wheel-motor-drive electric vehicle

NASA Astrophysics Data System (ADS)

Zhang, Han; Zhao, Wanzhong

2018-02-01

To improve the maneuverability and stability of in-wheel-motor-drive electric vehicle, a control strategy based on nonlinear decoupling control method is proposed in this paper, realizing the coordinated control of the steering and driving system. At first, the nonlinear models of the in-wheel-motor-drive electric vehicle and its sub-system are constructed. Then the inverse system decoupling theory is applied to decompose the nonlinear system into several independent subsystems, which makes it possible to realize the coordinated control of each subsystem. Next, the μ-Synthesis theory is applied to eliminate the influence of model uncertainty, improving the stability, robustness and tracking performance of in-wheel-motor-drive electric vehicle. Simulation and experiment results and numerical analyses, based on the electric vehicle actuated by in-wheel-motors, prove that the proposed control method is effective to accomplish the decoupling control of the steering and driving system in both simulation and real practice.

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings.

PubMed

Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

2013-02-01

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

Nonlinear feedback model attitude control using CCD in magnetic suspension system

NASA Technical Reports Server (NTRS)

Lin, CHIN-E.; Hou, Ann-San

1994-01-01

A model attitude control system for a CCD camera magnetic suspension system is studied in this paper. In a recent work, a position and attitude sensing method was proposed. From this result, model position and attitude of a magnetic suspension system can be detected by generating digital outputs. Based on this achievement, a control system design using nonlinear feedback techniques for magnetic suspended model attitude control is proposed.

Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

NASA Astrophysics Data System (ADS)

Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.

2017-03-01

Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frinks, Neal T.

2016-01-01

Several improvements to the mixed-elementUSM3Ddiscretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay

NASA Astrophysics Data System (ADS)

Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai

2016-08-01

In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.

Differential quadrature method of nonlinear bending of functionally graded beam

NASA Astrophysics Data System (ADS)

Gangnian, Xu; Liansheng, Ma; Wang, Youzhi; Quan, Yuan; Weijie, You

2018-02-01

Using the third-order shear deflection beam theory (TBT), nonlinear bending of functionally graded (FG) beams composed with various amounts of ceramic and metal is analyzed utilizing the differential quadrature method (DQM). The properties of beam material are supposed to accord with the power law index along to thickness. First, according to the principle of stationary potential energy, the partial differential control formulae of the FG beams subjected to a distributed lateral force are derived. To obtain numerical results of the nonlinear bending, non-dimensional boundary conditions and control formulae are dispersed by applying the DQM. To verify the present solution, several examples are analyzed for nonlinear bending of homogeneous beams with various edges. A minute parametric research is in progress about the effect of the law index, transverse shear deformation, distributed lateral force and boundary conditions.

Evaluation of crack status in a meter-size concrete structure using the ultrasonic nonlinear coda wave interferometry.

PubMed

Legland, Jean-Baptiste; Zhang, Yuxiang; Abraham, Odile; Durand, Olivier; Tournat, Vincent

2017-10-01

The field of civil engineering is in need of new methods of non-destructive testing, especially in order to prevent and monitor the serious deterioration of concrete structures. In this work, experimental results are reported on fault detection and characterization in a meter-scale concrete structure using an ultrasonic nonlinear coda wave interferometry (NCWI) method. This method entails the nonlinear mixing of strong pump waves with multiple scattered probe (coda) waves, along with analysis of the net effect using coda wave interferometry. A controlled damage protocol is implemented on a post-tensioned, meter-scale concrete structure in order to generate cracking within a specific area being monitored by NCWI. The nonlinear acoustic response due to the high amplitude of acoustic modulation yields information on the elastic nonlinearities of concrete, as evaluated by two specific nonlinear observables. The increase in nonlinearity level corresponds to the creation of a crack with a network of microcracks localized at its base. In addition, once the crack closes as a result of post-tensioning, the residual nonlinearities confirm the presence of the closed crack. Last, the benefits and applicability of this NCWI method to the characterization and monitoring of large structures are discussed.

Joint nonlinearity effects in the design of a flexible truss structure control system

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1986-01-01

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

Galerkin Method for Nonlinear Dynamics

NASA Astrophysics Data System (ADS)

Noack, Bernd R.; Schlegel, Michael; Morzynski, Marek; Tadmor, Gilead

A Galerkin method is presented for control-oriented reduced-order models (ROM). This method generalizes linear approaches elaborated by M. Morzyński et al. for the nonlinear Navier-Stokes equation. These ROM are used as plants for control design in the chapters by G. Tadmor et al., S. Siegel, and R. King in this volume. Focus is placed on empirical ROM which compress flow data in the proper orthogonal decomposition (POD). The chapter shall provide a complete description for construction of straight-forward ROM as well as the physical understanding and teste

Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

PubMed

Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

2017-03-01

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

Evaluating Rebar Corrosion Using Nonlinear Ultrasound

NASA Astrophysics Data System (ADS)

Woodward, Clinton; Amin, Md. Nurul

2008-02-01

The early detection of rebar corrosion in reinforced concrete is difficult using current methods. This pilot study investigated the viability of using nonlinear ultrasound to detect the effects of rebar corrosion in its early stages. The study utilized three accelerated corrosion specimens and one control specimen. Results showed that when corrosion developed in the area isonified by a Rayleigh wave, nonlinear parameters increased. As corrosion progressed, these nonlinear parameters also increased.

A novel auto-tuning PID control mechanism for nonlinear systems.

PubMed

Cetin, Meric; Iplikci, Serdar

2015-09-01

In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear analysis of switched semi-active controlled systems

NASA Astrophysics Data System (ADS)

Eslaminasab, Nima; Vahid A., Orang; Golnaraghi, Farid

2011-02-01

Semi-active systems improve suspension performance of the vehicles more effectively than conventional passive systems by simultaneously improving ride comfort and road handling. Also, because of size, weight, price and performance advantages, they have gained more interest over the active as well as passive systems. Probably the most neglected aspect of the semi-active on-off control systems and strategies is the effects of the added nonlinearities of those systems, which are introduced and analysed in this paper. To do so, numerical techniques, analytical method of averaging and experimental analysis are deployed. In this paper, a new method to analyse, calculate and compare the performances of the semi-active controlled systems is proposed; further, a new controller based on the observations of actual test data is proposed to eliminate the adverse effects of added nonlinearities. The significance of the proposed new system is the simplicity of the algorithm and ease of implementation. In fact, this new semi-active control strategy could be easily adopted and used with most of the existing semi-active control systems.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant.

Koopman operator theory: Past, present, and future

NASA Astrophysics Data System (ADS)

Brunton, Steven; Kaiser, Eurika; Kutz, Nathan

2017-11-01

Koopman operator theory has emerged as a dominant method to represent nonlinear dynamics in terms of an infinite-dimensional linear operator. The Koopman operator acts on the space of all possible measurement functions of the system state, advancing these measurements with the flow of the dynamics. A linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. Dynamic mode decomposition has become the leading data-driven method to approximate the Koopman operator, although there are still open questions and challenges around how to obtain accurate approximations for strongly nonlinear systems. This talk will provide an introductory overview of modern Koopman operator theory, reviewing the basics and describing recent theoretical and algorithmic developments. Particular emphasis will be placed on the use of data-driven Koopman theory to characterize and control high-dimensional fluid dynamic systems. This talk will also address key advances in the rapidly growing fields of machine learning and data science that are likely to drive future developments.

Commande de vol non lineaire d'un drone a voilure fixe par la methode du backstepping

NASA Astrophysics Data System (ADS)

Finoki, Edouard

This thesis describes the design of a non-linear controller for a UAV using the backstepping method. It is a fixed-wing UAV, the NexSTAR ARF from HobbicoRTM. The aim is to find the expressions of the aileron, the elevator, and the rudder deflection in order to command the flight path angle, the heading angle and the sideslip angle. Controlling the flight path angle allows a steady, climb or descent flight, controlling the heading cap allows to choose the heading and annul the sideslip angle allows an efficient flight. A good technical control has to ensure the stability of the system and provide optimal performances. Backstepping interlaces the choice of a Lyapunov function with the design of feedback control. This control technique works with the true non-linear model without any approximation. The procedure is to transform intermediate state variables into virtual inputs which will control other state variables. Advantages of this technique are its recursivity, its minimum control effort and its cascaded structure that allows dividing a high order system into several simpler lower order systems. To design this non-linear controller, a non-linear model of the UAV was used. Equations of motion are very accurate, aerodynamic coefficients result from interpolations between several essential variables in flight. The controller has been implemented in Matlab/Simulink and FlightGear.

Quantitative evaluation method for nonlinear characteristics of piezoelectric transducers under high stress with complex nonlinear elastic constant

NASA Astrophysics Data System (ADS)

Miyake, Susumu; Kasashima, Takashi; Yamazaki, Masato; Okimura, Yasuyuki; Nagata, Hajime; Hosaka, Hiroshi; Morita, Takeshi

2018-07-01

The high power properties of piezoelectric transducers were evaluated considering a complex nonlinear elastic constant. The piezoelectric LCR equivalent circuit with nonlinear circuit parameters was utilized to measure them. The deformed admittance curve of piezoelectric transducers was measured under a high stress and the complex nonlinear elastic constant was calculated by curve fitting. Transducers with various piezoelectric materials, Pb(Zr,Ti)O3, (K,Na)NbO3, and Ba(Zr,Ti)O3–(Ba,Ca)TiO3, were investigated by the proposed method. The measured complex nonlinear elastic constant strongly depends on the linear elastic and piezoelectric constants. This relationship indicates that piezoelectric high power properties can be controlled by modifying the linear elastic and piezoelectric constants.

Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections.

PubMed

Yang, Xiong; He, Haibo

2018-05-26

In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Nonlinear stability research on the hydraulic system of double-side rolling shear.

PubMed

Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

2015-10-01

This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

Nonlinear stability research on the hydraulic system of double-side rolling shear

NASA Astrophysics Data System (ADS)

Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

2015-10-01

This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

Robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with multiplicative noises.

PubMed

Chang, Wen-Jer; Huang, Bo-Jyun

2014-11-01

The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi-Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive Event-Triggered Control Based on Heuristic Dynamic Programming for Nonlinear Discrete-Time Systems.

PubMed

Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo

2017-07-01

This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.

Stability analysis of piecewise non-linear systems and its application to chaotic synchronisation with intermittent control

NASA Astrophysics Data System (ADS)

Wang, Qingzhi; Tan, Guanzheng; He, Yong; Wu, Min

2017-10-01

This paper considers a stability analysis issue of piecewise non-linear systems and applies it to intermittent synchronisation of chaotic systems. First, based on piecewise Lyapunov function methods, more general and less conservative stability criteria of piecewise non-linear systems in periodic and aperiodic cases are presented, respectively. Next, intermittent synchronisation conditions of chaotic systems are derived which extend existing results. Finally, Chua's circuit is taken as an example to verify the validity of our methods.

Fault-tolerant nonlinear adaptive flight control using sliding mode online learning.

PubMed

Krüger, Thomas; Schnetter, Philipp; Placzek, Robin; Vörsmann, Peter

2012-08-01

An expanded nonlinear model inversion flight control strategy using sliding mode online learning for neural networks is presented. The proposed control strategy is implemented for a small unmanned aircraft system (UAS). This class of aircraft is very susceptible towards nonlinearities like atmospheric turbulence, model uncertainties and of course system failures. Therefore, these systems mark a sensible testbed to evaluate fault-tolerant, adaptive flight control strategies. Within this work the concept of feedback linearization is combined with feed forward neural networks to compensate for inversion errors and other nonlinear effects. Backpropagation-based adaption laws of the network weights are used for online training. Within these adaption laws the standard gradient descent backpropagation algorithm is augmented with the concept of sliding mode control (SMC). Implemented as a learning algorithm, this nonlinear control strategy treats the neural network as a controlled system and allows a stable, dynamic calculation of the learning rates. While considering the system's stability, this robust online learning method therefore offers a higher speed of convergence, especially in the presence of external disturbances. The SMC-based flight controller is tested and compared with the standard gradient descent backpropagation algorithm in the presence of system failures. Copyright © 2012 Elsevier Ltd. All rights reserved.

Algorithms for sum-of-squares-based stability analysis and control design of uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Ataei-Esfahani, Armin

In this dissertation, we present algorithmic procedures for sum-of-squares based stability analysis and control design for uncertain nonlinear systems. In particular, we consider the case of robust aircraft control design for a hypersonic aircraft model subject to parametric uncertainties in its aerodynamic coefficients. In recent years, Sum-of-Squares (SOS) method has attracted increasing interest as a new approach for stability analysis and controller design of nonlinear dynamic systems. Through the application of SOS method, one can describe a stability analysis or control design problem as a convex optimization problem, which can efficiently be solved using Semidefinite Programming (SDP) solvers. For nominal systems, the SOS method can provide a reliable and fast approach for stability analysis and control design for low-order systems defined over the space of relatively low-degree polynomials. However, The SOS method is not well-suited for control problems relating to uncertain systems, specially those with relatively high number of uncertainties or those with non-affine uncertainty structure. In order to avoid issues relating to the increased complexity of the SOS problems for uncertain system, we present an algorithm that can be used to transform an SOS problem with uncertainties into a LMI problem with uncertainties. A new Probabilistic Ellipsoid Algorithm (PEA) is given to solve the robust LMI problem, which can guarantee the feasibility of a given solution candidate with an a-priori fixed probability of violation and with a fixed confidence level. We also introduce two approaches to approximate the robust region of attraction (RROA) for uncertain nonlinear systems with non-affine dependence on uncertainties. The first approach is based on a combination of PEA and SOS method and searches for a common Lyapunov function, while the second approach is based on the generalized Polynomial Chaos (gPC) expansion theorem combined with the SOS method and searches for parameter-dependent Lyapunov functions. The control design problem is investigated through a case study of a hypersonic aircraft model with parametric uncertainties. Through time-scale decomposition and a series of function approximations, the complexity of the aircraft model is reduced to fall within the capability of SDP solvers. The control design problem is then formulated as a convex problem using the dual of the Lyapunov theorem. A nonlinear robust controller is searched using the combined PEA/SOS method. The response of the uncertain aircraft model is evaluated for two sets of pilot commands. As the simulation results show, the aircraft remains stable under up to 50% uncertainty in aerodynamic coefficients and can follow the pilot commands.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Adaptive neural control for a class of nonlinear time-varying delay systems with unknown hysteresis.

PubMed

Liu, Zhi; Lai, Guanyu; Zhang, Yun; Chen, Xin; Chen, Chun Lung Philip

2014-12-01

This paper investigates the fusion of unknown direction hysteresis model with adaptive neural control techniques in face of time-delayed continuous time nonlinear systems without strict-feedback form. Compared with previous works on the hysteresis phenomenon, the direction of the modified Bouc-Wen hysteresis model investigated in the literature is unknown. To reduce the computation burden in adaptation mechanism, an optimized adaptation method is successfully applied to the control design. Based on the Lyapunov-Krasovskii method, two neural-network-based adaptive control algorithms are constructed to guarantee that all the system states and adaptive parameters remain bounded, and the tracking error converges to an adjustable neighborhood of the origin. In final, some numerical examples are provided to validate the effectiveness of the proposed control methods.

Dynamics and control for Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Partll

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques were applied to derive the dynamics of a Differential Wheeled Mobile Robot (DWMR) in the companion paper. The present paper formulates a control system design for trajectory tracking of this class of robots. The method develops a feedback linearization technique for the nonlinear system using dynamic extension algorithm. The effectiveness of the nonlinear controller is illustrated with simulation example.

Adaptive Control for Uncertain Nonlinear Multi-Input Multi-Output Systems

NASA Technical Reports Server (NTRS)

Cao, Chengyu (Inventor); Hovakimyan, Naira (Inventor); Xargay, Enric (Inventor)

2014-01-01

Systems and methods of adaptive control for uncertain nonlinear multi-input multi-output systems in the presence of significant unmatched uncertainty with assured performance are provided. The need for gain-scheduling is eliminated through the use of bandwidth-limited (low-pass) filtering in the control channel, which appropriately attenuates the high frequencies typically appearing in fast adaptation situations and preserves the robustness margins in the presence of fast adaptation.

A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control.

PubMed

Wang, Tong; Gao, Huijun; Qiu, Jianbin

2016-02-01

This paper investigates the multirate networked industrial process control problem in double-layer architecture. First, the output tracking problem for sampled-data nonlinear plant at device layer with sampling period T(d) is investigated using adaptive neural network (NN) control, and it is shown that the outputs of subsystems at device layer can track the decomposed setpoints. Then, the outputs and inputs of the device layer subsystems are sampled with sampling period T(u) at operation layer to form the index prediction, which is used to predict the overall performance index at lower frequency. Radial basis function NN is utilized as the prediction function due to its approximation ability. Then, considering the dynamics of the overall closed-loop system, nonlinear model predictive control method is proposed to guarantee the system stability and compensate the network-induced delays and packet dropouts. Finally, a continuous stirred tank reactor system is given in the simulation part to demonstrate the effectiveness of the proposed method.

Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinha, Mohit; Dorfler, Florian; Johnson, Brian B.

This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear oscillators presents a compelling time-domain alternative to ubiquitous droop control methods which presume the existence of a quasistationary sinusoidal steady state and operate on phasor quantities. We present two main results in this paper. First, by leveraging the method of periodic averaging, we demonstrate that droop laws are intrinsically embedded within a slower time scale in the nonlinear dynamics of Van der Pol oscillators. Second,more » we establish the global convergence of amplitude and phase dynamics in a resistive network interconnecting inverters controlled as Van der Pol oscillators. Furthermore, under a set of nonrestrictive decoupling approximations, we derive sufficient conditions for local exponential stability of desirable equilibria of the linearized amplitude and phase dynamics.« less

Application of the MNA design method to a nonlinear turbofan engine. [multivariable Nyquist array method

NASA Technical Reports Server (NTRS)

Leininger, G. G.

1981-01-01

Using nonlinear digital simulation as a representative model of the dynamic operation of the QCSEE turbofan engine, a feedback control system is designed by variable frequency design techniques. Transfer functions are generated for each of five power level settings covering the range of operation from approach power to full throttle (62.5% to 100% full power). These transfer functions are then used by an interactive control system design synthesis program to provide a closed loop feedback control using the multivariable Nyquist array and extensions to multivariable Bode diagrams and Nichols charts.

The composition of heterogeneous control laws

NASA Technical Reports Server (NTRS)

Kuipers, Benjamin; Astrom, Karl

1991-01-01

The fuzzy control literature and industrial practice provide certain nonlinear methods for combining heterogeneous control laws, but these methods have been very difficult to analyze theoretically. An alternate formulation and extension of this approach is presented that has several practical and theoretical benefits. An example of heterogeneous control is given and two alternate analysis methods are presented.

NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model

NASA Technical Reports Server (NTRS)

1979-01-01

A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.

Nonlinear Tracking Control of a Conductive Supercoiled Polymer Actuator.

PubMed

Luong, Tuan Anh; Cho, Kyeong Ho; Song, Min Geun; Koo, Ja Choon; Choi, Hyouk Ryeol; Moon, Hyungpil

2018-04-01

Artificial muscle actuators made from commercial nylon fishing lines have been recently introduced and shown as a new type of actuator with high performance. However, the actuators also exhibit significant nonlinearities, which make them difficult to control, especially in precise trajectory-tracking applications. In this article, we present a nonlinear mathematical model of a conductive supercoiled polymer (SCP) actuator driven by Joule heating for model-based feedback controls. Our efforts include modeling of the hysteresis behavior of the actuator. Based on nonlinear modeling, we design a sliding mode controller for SCP actuator-driven manipulators. The system with proposed control law is proven to be asymptotically stable using the Lyapunov theory. The control performance of the proposed method is evaluated experimentally and compared with that of a proportional-integral-derivative (PID) controller through one-degree-of-freedom SCP actuator-driven manipulators. Experimental results show that the proposed controller's performance is superior to that of a PID controller, such as the tracking errors are nearly 10 times smaller compared with those of a PID controller, and it is more robust to external disturbances such as sensor noise and actuator modeling error.

Nonlinear robust control of hypersonic aircrafts with interactions between flight dynamics and propulsion systems.

PubMed

Li, Zhaoying; Zhou, Wenjie; Liu, Hao

2016-09-01

This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Servo-hydraulic actuator in controllable canonical form: Identification and experimental validation

NASA Astrophysics Data System (ADS)

Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

2018-02-01

Hydraulic actuators have been widely used to experimentally examine structural behavior at multiple scales. Real-time hybrid simulation (RTHS) is one innovative testing method that largely relies on such servo-hydraulic actuators. In RTHS, interface conditions must be enforced in real time, and controllers are often used to achieve tracking of the desired displacements. Thus, neglecting the dynamics of hydraulic transfer system may result either in system instability or sub-optimal performance. Herein, we propose a nonlinear dynamical model for a servo-hydraulic actuator (a.k.a. hydraulic transfer system) coupled with a nonlinear physical specimen. The nonlinear dynamical model is transformed into controllable canonical form for further tracking control design purposes. Through a number of experiments, the controllable canonical model is validated.

On neural networks in identification and control of dynamic systems

NASA Technical Reports Server (NTRS)

Phan, Minh; Juang, Jer-Nan; Hyland, David C.

1993-01-01

This paper presents a discussion of the applicability of neural networks in the identification and control of dynamic systems. Emphasis is placed on the understanding of how the neural networks handle linear systems and how the new approach is related to conventional system identification and control methods. Extensions of the approach to nonlinear systems are then made. The paper explains the fundamental concepts of neural networks in their simplest terms. Among the topics discussed are feed forward and recurrent networks in relation to the standard state-space and observer models, linear and nonlinear auto-regressive models, linear, predictors, one-step ahead control, and model reference adaptive control for linear and nonlinear systems. Numerical examples are presented to illustrate the application of these important concepts.

Adaptive output-feedback control for switched stochastic uncertain nonlinear systems with time-varying delay.

PubMed

Song, Zhibao; Zhai, Junyong

2018-04-01

This paper addresses the problem of adaptive output-feedback control for a class of switched stochastic time-delay nonlinear systems with uncertain output function, where both the control coefficients and time-varying delay are unknown. The drift and diffusion terms are subject to unknown homogeneous growth condition. By virtue of adding a power integrator technique, an adaptive output-feedback controller is designed to render that the closed-loop system is bounded in probability, and the state of switched stochastic nonlinear system can be globally regulated to the origin almost surely. A numerical example is provided to demonstrate the validity of the proposed control method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Chaotic dynamical aperture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S.Y.; Tepikian, S.

1985-01-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator designs have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take a tremendous amount of computing time. In this review the method of determining chaotic orbit and applying the method to nonlinear problems in accelerator physics is discussed. We then discuss the scaling properties and effect of random sextupoles.« less

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

NASA Technical Reports Server (NTRS)

Agapov, A. V.; Kolosov, B. I.

1979-01-01

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Nonlinear Unsteady Aerodynamic Modeling Using Wind Tunnel and Computational Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.

2016-01-01

Extensions to conventional aircraft aerodynamic models are required to adequately predict responses when nonlinear unsteady flight regimes are encountered, especially at high incidence angles and under maneuvering conditions. For a number of reasons, such as loss of control, both military and civilian aircraft may extend beyond normal and benign aerodynamic flight conditions. In addition, military applications may require controlled flight beyond the normal envelope, and civilian flight may require adequate recovery or prevention methods from these adverse conditions. These requirements have led to the development of more general aerodynamic modeling methods and provided impetus for researchers to improve both techniques and the degree of collaboration between analytical and experimental research efforts. In addition to more general mathematical model structures, dynamic test methods have been designed to provide sufficient information to allow model identification. This paper summarizes research to develop a modeling methodology appropriate for modeling aircraft aerodynamics that include nonlinear unsteady behaviors using both experimental and computational test methods. This work was done at Langley Research Center, primarily under the NASA Aviation Safety Program, to address aircraft loss of control, prevention, and recovery aerodynamics.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

Adaptive Importance Sampling for Control and Inference

NASA Astrophysics Data System (ADS)

Kappen, H. J.; Ruiz, H. C.

2016-03-01

Path integral (PI) control problems are a restricted class of non-linear control problems that can be solved formally as a Feynman-Kac PI and can be estimated using Monte Carlo sampling. In this contribution we review PI control theory in the finite horizon case. We subsequently focus on the problem how to compute and represent control solutions. We review the most commonly used methods in robotics and control. Within the PI theory, the question of how to compute becomes the question of importance sampling. Efficient importance samplers are state feedback controllers and the use of these requires an efficient representation. Learning and representing effective state-feedback controllers for non-linear stochastic control problems is a very challenging, and largely unsolved, problem. We show how to learn and represent such controllers using ideas from the cross entropy method. We derive a gradient descent method that allows to learn feed-back controllers using an arbitrary parametrisation. We refer to this method as the path integral cross entropy method or PICE. We illustrate this method for some simple examples. The PI control methods can be used to estimate the posterior distribution in latent state models. In neuroscience these problems arise when estimating connectivity from neural recording data using EM. We demonstrate the PI control method as an accurate alternative to particle filtering.

On Mixed Data and Event Driven Design for Adaptive-Critic-Based Nonlinear $H_{\\infty}$ Control.

PubMed

Wang, Ding; Mu, Chaoxu; Liu, Derong; Ma, Hongwen

2018-04-01

In this paper, based on the adaptive critic learning technique, the control for a class of unknown nonlinear dynamic systems is investigated by adopting a mixed data and event driven design approach. The nonlinear control problem is formulated as a two-player zero-sum differential game and the adaptive critic method is employed to cope with the data-based optimization. The novelty lies in that the data driven learning identifier is combined with the event driven design formulation, in order to develop the adaptive critic controller, thereby accomplishing the nonlinear control. The event driven optimal control law and the time driven worst case disturbance law are approximated by constructing and tuning a critic neural network. Applying the event driven feedback control, the closed-loop system is built with stability analysis. Simulation studies are conducted to verify the theoretical results and illustrate the control performance. It is significant to observe that the present research provides a new avenue of integrating data-based control and event-triggering mechanism into establishing advanced adaptive critic systems.

Reconfigurable Flight Control Using Nonlinear Dynamic Inversion with a Special Accelerometer Implementation

NASA Technical Reports Server (NTRS)

Bacon, Barton J.; Ostroff, Aaron J.

2000-01-01

This paper presents an approach to on-line control design for aircraft that have suffered either actuator failure, missing effector surfaces, surface damage, or any combination. The approach is based on a modified version of nonlinear dynamic inversion. The approach does not require a model of the baseline vehicle (effectors at zero deflection), but does require feedback of accelerations and effector positions. Implementation issues are addressed and the method is demonstrated on an advanced tailless aircraft. An experimental simulation analysis tool is used to directly evaluate the nonlinear system's stability robustness.

Neuro-adaptive backstepping control of SISO non-affine systems with unknown gain sign.

PubMed

Ramezani, Zahra; Arefi, Mohammad Mehdi; Zargarzadeh, Hassan; Jahed-Motlagh, Mohammad Reza

2016-11-01

This paper presents two neuro-adaptive controllers for a class of uncertain single-input, single-output (SISO) nonlinear non-affine systems with unknown gain sign. The first approach is state feedback controller, so that a neuro-adaptive state-feedback controller is constructed based on the backstepping technique. The second approach is an observer-based controller and K-filters are designed to estimate the system states. The proposed method relaxes a priori knowledge of control gain sign and therefore by utilizing the Nussbaum-type functions this problem is addressed. In these methods, neural networks are employed to approximate the unknown nonlinear functions. The proposed adaptive control schemes guarantee that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). Finally, the theoretical results are numerically verified through simulation examples. Simulation results show the effectiveness of the proposed methods. Copyright © 2016 ISA. All rights reserved.

Nonlinear dynamics as an engine of computation.

PubMed

Kia, Behnam; Lindner, John F; Ditto, William L

2017-03-06

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Nonlinear dynamics as an engine of computation

PubMed Central

Lindner, John F.; Ditto, William L.

2017-01-01

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics—cybernetical physics—opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115619

Stability of multiloop LQ regulators with nonlinearities. I - Regions of attraction. II - Regions of ultimate boundedness

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1986-01-01

An investigation is conducted for the closed loop stability of linear time-invariant systems controlled by linear quadratic (LQ) regulators, in cases where nonlinearities exist in the control channels lying outside the stability sector in regions away from the origin. The estimate of the region of attraction thus obtained furnishes methods for the selection of performance function weights for more robust LQ designs. Attention is then given to the closed loop stability of linear time-invariant systems controlled by the LQ regulators when the nonlinearities in the loops escape the stability sector in a bounded region containing the origin.

Observed-Based Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems With Dead-Zone.

PubMed

Tong, Shaocheng; Sui, Shuai; Li, Yongming

2015-12-01

In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach.

Adaptive output feedback control of uncertain nonlinear systems using single-hidden-layer neural networks.

PubMed

Hovakimyan, N; Nardi, F; Calise, A; Kim, Nakwan

2002-01-01

We consider adaptive output feedback control of uncertain nonlinear systems, in which both the dynamics and the dimension of the regulated system may be unknown. However, the relative degree of the regulated output is assumed to be known. Given a smooth reference trajectory, the problem is to design a controller that forces the system measurement to track it with bounded errors. The classical approach requires a state observer. Finding a good observer for an uncertain nonlinear system is not an obvious task. We argue that it is sufficient to build an observer for the output tracking error. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. The theoretical results are illustrated in the design of a controller for a fourth-order nonlinear system of relative degree two and a high-bandwidth attitude command system for a model R-50 helicopter.

Time optimal control of a jet engine using a quasi-Hermite interpolation model. M.S. Thesis

NASA Technical Reports Server (NTRS)

Comiskey, J. G.

1979-01-01

This work made preliminary efforts to generate nonlinear numerical models of a two-spooled turbofan jet engine, and subject these models to a known method of generating global, nonlinear, time optimal control laws. The models were derived numerically, directly from empirical data, as a first step in developing an automatic modelling procedure.

A nonlinear controlling function of geological features on magmatic–hydrothermal mineralization

PubMed Central

Zuo, Renguang

2016-01-01

This paper reports a nonlinear controlling function of geological features on magmatic–hydrothermal mineralization, and proposes an alternative method to measure the spatial relationships between geological features and mineral deposits using multifractal singularity theory. It was observed that the greater the proximity to geological controlling features, the greater the number of mineral deposits developed, indicating a nonlinear spatial relationship between these features and mineral deposits. This phenomenon can be quantified using the relationship between the numbers of mineral deposits N(ε) of a D-dimensional set and the scale of ε. The density of mineral deposits can be expressed as ρ(ε) = Cε−(De−a), where ε is the buffer width of geological controlling features, De is Euclidean dimension of space (=2 in this case), a is singularity index, and C is a constant. The expression can be rewritten as ρ = Cεa−2. When a < 2, there is a significant spatial correlation between specific geological features and mineral deposits; lower a values indicate a more significant spatial correlation. This nonlinear relationship and the advantages of this method were illustrated using a case study from Fujian Province in China and a case study from Baguio district in Philippines. PMID:27255794

A nonlinear controlling function of geological features on magmatic-hydrothermal mineralization.

PubMed

Zuo, Renguang

2016-06-03

This paper reports a nonlinear controlling function of geological features on magmatic-hydrothermal mineralization, and proposes an alternative method to measure the spatial relationships between geological features and mineral deposits using multifractal singularity theory. It was observed that the greater the proximity to geological controlling features, the greater the number of mineral deposits developed, indicating a nonlinear spatial relationship between these features and mineral deposits. This phenomenon can be quantified using the relationship between the numbers of mineral deposits N(ε) of a D-dimensional set and the scale of ε. The density of mineral deposits can be expressed as ρ(ε) = Cε(-(De-a)), where ε is the buffer width of geological controlling features, De is Euclidean dimension of space (=2 in this case), a is singularity index, and C is a constant. The expression can be rewritten as ρ = Cε(a-2). When a < 2, there is a significant spatial correlation between specific geological features and mineral deposits; lower a values indicate a more significant spatial correlation. This nonlinear relationship and the advantages of this method were illustrated using a case study from Fujian Province in China and a case study from Baguio district in Philippines.

Automatic weight determination in nonlinear model predictive control of wind turbines using swarm optimization technique

NASA Astrophysics Data System (ADS)

Tofighi, Elham; Mahdizadeh, Amin

2016-09-01

This paper addresses the problem of automatic tuning of weighting coefficients for the nonlinear model predictive control (NMPC) of wind turbines. The choice of weighting coefficients in NMPC is critical due to their explicit impact on efficiency of the wind turbine control. Classically, these weights are selected based on intuitive understanding of the system dynamics and control objectives. The empirical methods, however, may not yield optimal solutions especially when the number of parameters to be tuned and the nonlinearity of the system increase. In this paper, the problem of determining weighting coefficients for the cost function of the NMPC controller is formulated as a two-level optimization process in which the upper- level PSO-based optimization computes the weighting coefficients for the lower-level NMPC controller which generates control signals for the wind turbine. The proposed method is implemented to tune the weighting coefficients of a NMPC controller which drives the NREL 5-MW wind turbine. The results are compared with similar simulations for a manually tuned NMPC controller. Comparison verify the improved performance of the controller for weights computed with the PSO-based technique.

Further studies using matched filter theory and stochastic simulation for gust loads prediction

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd Iii

1993-01-01

This paper describes two analysis methods -- one deterministic, the other stochastic -- for computing maximized and time-correlated gust loads for aircraft with nonlinear control systems. The first method is based on matched filter theory; the second is based on stochastic simulation. The paper summarizes the methods, discusses the selection of gust intensity for each method and presents numerical results. A strong similarity between the results from the two methods is seen to exist for both linear and nonlinear configurations.

Discrete-time online learning control for a class of unknown nonaffine nonlinear systems using reinforcement learning.

PubMed

Yang, Xiong; Liu, Derong; Wang, Ding; Wei, Qinglai

2014-07-01

In this paper, a reinforcement-learning-based direct adaptive control is developed to deliver a desired tracking performance for a class of discrete-time (DT) nonlinear systems with unknown bounded disturbances. We investigate multi-input-multi-output unknown nonaffine nonlinear DT systems and employ two neural networks (NNs). By using Implicit Function Theorem, an action NN is used to generate the control signal and it is also designed to cancel the nonlinearity of unknown DT systems, for purpose of utilizing feedback linearization methods. On the other hand, a critic NN is applied to estimate the cost function, which satisfies the recursive equations derived from heuristic dynamic programming. The weights of both the action NN and the critic NN are directly updated online instead of offline training. By utilizing Lyapunov's direct method, the closed-loop tracking errors and the NN estimated weights are demonstrated to be uniformly ultimately bounded. Two numerical examples are provided to show the effectiveness of the present approach. Copyright © 2014 Elsevier Ltd. All rights reserved.

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

PubMed

Vandewalle, Joos; De Moor, Bart L.R.; Suykens, Johan A.K.

1997-06-01

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.

Switched-Observer-Based Adaptive Neural Control of MIMO Switched Nonlinear Systems With Unknown Control Gains.

PubMed

Long, Lijun; Zhao, Jun

2017-07-01

In this paper, the problem of adaptive neural output-feedback control is addressed for a class of multi-input multioutput (MIMO) switched uncertain nonlinear systems with unknown control gains. Neural networks (NNs) are used to approximate unknown nonlinear functions. In order to avoid the conservativeness caused by adoption of a common observer for all subsystems, an MIMO NN switched observer is designed to estimate unmeasurable states. A new switched observer-based adaptive neural control technique for the problem studied is then provided by exploiting the classical average dwell time (ADT) method and the backstepping method and the Nussbaum gain technique. It effectively handles the obstacle about the coexistence of multiple Nussbaum-type function terms, and improves the classical ADT method, since the exponential decline property of Lyapunov functions for individual subsystems is no longer satisfied. It is shown that the technique proposed is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop system under a class of switching signals with ADT, and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the approach proposed is illustrated by its application to a two inverted pendulum system.

A novel single thruster control strategy for spacecraft attitude stabilization

NASA Astrophysics Data System (ADS)

Godard; Kumar, Krishna Dev; Zou, An-Min

2013-05-01

Feasibility of achieving three axis attitude stabilization using a single thruster is explored in this paper. Torques are generated using a thruster orientation mechanism with which the thrust vector can be tilted on a two axis gimbal. A robust nonlinear control scheme is developed based on the nonlinear kinematic and dynamic equations of motion of a rigid body spacecraft in the presence of gravity gradient torque and external disturbances. The spacecraft, controlled using the proposed concept, constitutes an underactuated system (a system with fewer independent control inputs than degrees of freedom) with nonlinear dynamics. Moreover, using thruster gimbal angles as control inputs make the system non-affine (control terms appear nonlinearly in the state equation). This necessitates the control algorithms to be developed based on nonlinear control theory since linear control methods are not directly applicable. The stability conditions for the spacecraft attitude motion for robustness against uncertainties and disturbances are derived to establish the regions of asymptotic 3-axis attitude stabilization. Several numerical simulations are presented to demonstrate the efficacy of the proposed controller and validate the theoretical results. The control algorithm is shown to compensate for time-varying external disturbances including solar radiation pressure, aerodynamic forces, and magnetic disturbances; and uncertainties in the spacecraft inertia parameters. The numerical results also establish the robustness of the proposed control scheme to negate disturbances caused by orbit eccentricity.

Neural robust stabilization via event-triggering mechanism and adaptive learning technique.

PubMed

Wang, Ding; Liu, Derong

2018-06-01

The robust control synthesis of continuous-time nonlinear systems with uncertain term is investigated via event-triggering mechanism and adaptive critic learning technique. We mainly focus on combining the event-triggering mechanism with adaptive critic designs, so as to solve the nonlinear robust control problem. This can not only make better use of computation and communication resources, but also conduct controller design from the view of intelligent optimization. Through theoretical analysis, the nonlinear robust stabilization can be achieved by obtaining an event-triggered optimal control law of the nominal system with a newly defined cost function and a certain triggering condition. The adaptive critic technique is employed to facilitate the event-triggered control design, where a neural network is introduced as an approximator of the learning phase. The performance of the event-triggered robust control scheme is validated via simulation studies and comparisons. The present method extends the application domain of both event-triggered control and adaptive critic control to nonlinear systems possessing dynamical uncertainties. Copyright © 2018 Elsevier Ltd. All rights reserved.

Attitude control/momentum management and payload pointing in advanced space vehicles

NASA Technical Reports Server (NTRS)

Parlos, Alexander G.; Jayasuriya, Suhada

1990-01-01

The design and evaluation of an attitude control/momentum management system for highly asymmetric spacecraft configurations are presented. The preliminary development and application of a nonlinear control system design methodology for tracking control of uncertain systems, such as spacecraft payload pointing systems are also presented. Control issues relevant to both linear and nonlinear rigid-body spacecraft dynamics are addressed, whereas any structural flexibilities are not taken into consideration. Results from the first task indicate that certain commonly used simplifications in the equations of motions result in unstable attitude control systems, when used for highly asymmetric spacecraft configurations. An approach is suggested circumventing this problem. Additionally, even though preliminary results from the second task are encouraging, the proposed nonlinear control system design method requires further investigation prior to its application and use as an effective payload pointing system design technique.

Partial and total actuator faults accommodation for input-affine nonlinear process plants.

PubMed

Mihankhah, Amin; Salmasi, Farzad R; Salahshoor, Karim

2013-05-01

In this paper, a new fault-tolerant control system is proposed for input-affine nonlinear plants based on Model Reference Adaptive System (MRAS) structure. The proposed method has the capability to accommodate both partial and total actuator failures along with bounded external disturbances. In this methodology, the conventional MRAS control law is modified by augmenting two compensating terms. One of these terms is added to eliminate the nonlinear dynamic, while the other is reinforced to compensate the distractive effects of the total actuator faults and external disturbances. In addition, no Fault Detection and Diagnosis (FDD) unit is needed in the proposed method. Moreover, the control structure has good robustness capability against the parameter variation. The performance of this scheme is evaluated using a CSTR system and the results were satisfactory. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

PubMed

Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

2018-06-01

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

Real time optimal guidance of low-thrust spacecraft: an application of nonlinear model predictive control.

PubMed

Arrieta-Camacho, Juan José; Biegler, Lorenz T

2005-12-01

Real time optimal guidance is considered for a class of low thrust spacecraft. In particular, nonlinear model predictive control (NMPC) is utilized for computing the optimal control actions required to transfer a spacecraft from a low Earth orbit to a mission orbit. The NMPC methodology presented is able to cope with unmodeled disturbances. The dynamics of the transfer are modeled using a set of modified equinoctial elements because they do not exhibit singularities for zero inclination and zero eccentricity. The idea behind NMPC is the repeated solution of optimal control problems; at each time step, a new control action is computed. The optimal control problem is solved using a direct method-fully discretizing the equations of motion. The large scale nonlinear program resulting from the discretization procedure is solved using IPOPT--a primal-dual interior point algorithm. Stability and robustness characteristics of the NMPC algorithm are reviewed. A numerical example is presented that encourages further development of the proposed methodology: the transfer from low-Earth orbit to a molniya orbit.

High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

NASA Astrophysics Data System (ADS)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

Data-driven methods towards learning the highly nonlinear inverse kinematics of tendon-driven surgical manipulators.

PubMed

Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang

2017-09-01

Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.

On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.

2004-01-01

The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD.

Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.

PubMed

Zhang, Yanjun; Tao, Gang; Chen, Mou

2016-09-01

This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.

Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations

DOE PAGES

Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; ...

2013-01-01

We inmore » troduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N , the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.« less

Off-Policy Integral Reinforcement Learning Method to Solve Nonlinear Continuous-Time Multiplayer Nonzero-Sum Games.

PubMed

Song, Ruizhuo; Lewis, Frank L; Wei, Qinglai

2017-03-01

This paper establishes an off-policy integral reinforcement learning (IRL) method to solve nonlinear continuous-time (CT) nonzero-sum (NZS) games with unknown system dynamics. The IRL algorithm is presented to obtain the iterative control and off-policy learning is used to allow the dynamics to be completely unknown. Off-policy IRL is designed to do policy evaluation and policy improvement in the policy iteration algorithm. Critic and action networks are used to obtain the performance index and control for each player. The gradient descent algorithm makes the update of critic and action weights simultaneously. The convergence analysis of the weights is given. The asymptotic stability of the closed-loop system and the existence of Nash equilibrium are proved. The simulation study demonstrates the effectiveness of the developed method for nonlinear CT NZS games with unknown system dynamics.

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

NASA Technical Reports Server (NTRS)

Jacquotte, Olivier P.; Oden, J. Tinsley

1994-01-01

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Modelling and control of a nonlinear magnetostrictive actuator system

NASA Astrophysics Data System (ADS)

Ramli, M. H. M.; Majeed, A. P. P. Abdul; Anuar, M. A. M.; Mohamed, Z.

2018-04-01

This paper explores the implementation of a feedforward control method to a nonlinear control system, in particular, Magnetostrictive Actuators (MA) that has excellent properties of energy conversion between the mechanical and magnetic form through magnetostriction effects which could be used in actuating and sensing application. MA is known to exhibit hysteresis behaviour and it is rate dependent (the level of hysteresis depends closely on the rate of input excitation frequency). This is, nonetheless, an undesirable behaviour and has to be eliminated in realising high precision application. The MA is modelled by a phenomenological modelling approach via Prandtl-Ishlinskii (P-I) operator to characterise the hysteresis nonlinearities. A feedforward control strategy is designed and implemented to linearize and eliminate the hysteresis by model inversion. The results show that the P-I operator has the capability to model the hysteretic nonlinearity of MA with an acceptable accuracy. Furthermore, the proposed control scheme has demonstrated to be effective in providing superior trajectory tracking.

SPHERES tethered formation flight testbed: application to NASA's SPECS mission

NASA Astrophysics Data System (ADS)

Chung, Soon-Jo; Kong, Edmund M.; Miller, David W.

2005-08-01

This paper elaborates on theory and experiment of the formation flight control for the future space-borne tethered interferometers. The nonlinear equations of multi-vehicle tethered spacecraft system are derived by Lagrange equations and decoupling method. The preliminary analysis predicts unstable dynamics depending on the direction of the tether motor. The controllability analysis indicates that both array resizing and spin-up are fully controllable only by the reaction wheels and the tether motor, thereby eliminating the need for thrusters. Linear and nonlinear decentralized control techniques have been implemented into the tethered SPHERES testbed, and tested at the NASA MSFC's flat floor facility using two and three SPHERES configurations. The nonlinear control using feedback linearization technique performed successfully in both two SPHERES in-line configuration and three triangular configuration while varying the tether length. The relative metrology system, using the ultra sound metrology system and the inertial sensors as well as the decentralized nonlinear estimator, is developed to provide necessary state information.

Study on Control Scheme for the Inverters in Low Voltage Microgrid with Nonlinear Loads

NASA Astrophysics Data System (ADS)

Xu, Jiqiang; Lu, Wenzhou; Wu, Lei

2017-05-01

There are a lot of nonlinear loads in real low voltage microgrid system. It will cause serious output voltage and grid current harmonic distortions problems in island and grid-connected modes, respectively. To solve this problem, this paper proposes a droop control scheme with quasi-proportion and resonant (quasi-PR) controller based on αβ stationary reference frame to make microgrid smoothly switch between grid-connected and island modes without changing control method. Moreover, in island mode, not only stable output voltage and frequency, but also reduced output voltage harmonics with added nonlinear loads can be achieved; In grid-connected mode, not only constant power, but also reduced grid current harmonics can be achieved. Simulation results verify the effectiveness of the proposed control scheme.

Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input.

PubMed

Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali

2017-09-01

In this paper, an identifier-critic structure is introduced to find an online near-optimal controller for continuous-time nonaffine nonlinear systems having saturated control signal. By employing two Neural Networks (NNs), the solution of Hamilton-Jacobi-Bellman (HJB) equation associated with the cost function is derived without requiring a priori knowledge about system dynamics. Weights of the identifier and critic NNs are tuned online and simultaneously such that unknown terms are approximated accurately and the control signal is kept between the saturation bounds. The convergence of NNs' weights, identification error, and system states is guaranteed using Lyapunov's direct method. Finally, simulation results are performed on two nonlinear systems to confirm the effectiveness of the proposed control strategy. Copyright © 2017 Elsevier Ltd. All rights reserved.

Robustness of controllability and observability of linear time-varying systems with application to the emergency control of power systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sastry, S. S.; Desoer, C. A.

1980-01-01

Fixed point methods from nonlinear anaysis are used to establish conditions under which the uniform complete controllability of linear time-varying systems is preserved under non-linear perturbations in the state dynamics and the zero-input uniform complete observability of linear time-varying systems is preserved under non-linear perturbation in the state dynamics and output read out map. Algorithms for computing the specific input to steer the perturbed systems from a given initial state to a given final state are also presented. As an application, a very specific emergency control of an interconnected power system is formulated as a steering problem and it ismore » shown that this emergency control is indeed possible in finite time.« less

Knowledge acquisition for a simple expert controller

NASA Technical Reports Server (NTRS)

Bieker, B.

1987-01-01

A method is presented for process control which has the properties of being incremental, cyclic and top-down. It is described on the basis of the development of an expert controller for a simple, but nonlinear control route. A quality comparison between expert controller and process operator shows the ability of the method for knowledge acquisition.

Adaptive variable structure hierarchical fuzzy control for a class of high-order nonlinear dynamic systems.

PubMed

Mansouri, Mohammad; Teshnehlab, Mohammad; Aliyari Shoorehdeli, Mahdi

2015-05-01

In this paper, a novel adaptive hierarchical fuzzy control system based on the variable structure control is developed for a class of SISO canonical nonlinear systems in the presence of bounded disturbances. It is assumed that nonlinear functions of the systems be completely unknown. Switching surfaces are incorporated into the hierarchical fuzzy control scheme to ensure the system stability. A fuzzy soft switching system decides the operation area of the hierarchical fuzzy control and variable structure control systems. All the nonlinearly appeared parameters of conclusion parts of fuzzy blocks located in different layers of the hierarchical fuzzy control system are adjusted through adaptation laws deduced from the defined Lyapunov function. The proposed hierarchical fuzzy control system reduces the number of rules and consequently the number of tunable parameters with respect to the ordinary fuzzy control system. Global boundedness of the overall adaptive system and the desired precision are achieved using the proposed adaptive control system. In this study, an adaptive hierarchical fuzzy system is used for two objectives; it can be as a function approximator or a control system based on an intelligent-classic approach. Three theorems are proven to investigate the stability of the nonlinear dynamic systems. The important point about the proposed theorems is that they can be applied not only to hierarchical fuzzy controllers with different structures of hierarchical fuzzy controller, but also to ordinary fuzzy controllers. Therefore, the proposed algorithm is more general. To show the effectiveness of the proposed method four systems (two mechanical, one mathematical and one chaotic) are considered in simulations. Simulation results demonstrate the validity, efficiency and feasibility of the proposed approach to control of nonlinear dynamic systems. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Continuous uniformly finite time exact disturbance observer based control for fixed-time stabilization of nonlinear systems with mismatched disturbances

PubMed Central

Liu, Chongxin; Liu, Hang

2017-01-01

This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme. PMID:28406966

Nonlinear Adaptive PID Control for Greenhouse Environment Based on RBF Network

PubMed Central

Zeng, Songwei; Hu, Haigen; Xu, Lihong; Li, Guanghui

2012-01-01

This paper presents a hybrid control strategy, combining Radial Basis Function (RBF) network with conventional proportional, integral, and derivative (PID) controllers, for the greenhouse climate control. A model of nonlinear conservation laws of enthalpy and matter between numerous system variables affecting the greenhouse climate is formulated. RBF network is used to tune and identify all PID gain parameters online and adaptively. The presented Neuro-PID control scheme is validated through simulations of set-point tracking and disturbance rejection. We compare the proposed adaptive online tuning method with the offline tuning scheme that employs Genetic Algorithm (GA) to search the optimal gain parameters. The results show that the proposed strategy has good adaptability, strong robustness and real-time performance while achieving satisfactory control performance for the complex and nonlinear greenhouse climate control system, and it may provide a valuable reference to formulate environmental control strategies for actual application in greenhouse production. PMID:22778587

An energy-saving nonlinear position control strategy for electro-hydraulic servo systems.

PubMed

Baghestan, Keivan; Rezaei, Seyed Mehdi; Talebi, Heidar Ali; Zareinejad, Mohammad

2015-11-01

The electro-hydraulic servo system (EHSS) demonstrates numerous advantages in size and performance compared to other actuation methods. Oftentimes, its utilization in industrial and machinery settings is limited by its inferior efficiency. In this paper, a nonlinear backstepping control algorithm with an energy-saving approach is proposed for position control in the EHSS. To achieve improved efficiency, two control valves including a proportional directional valve (PDV) and a proportional relief valve (PRV) are used to achieve the control objectives. To design the control algorithm, the state space model equations of the system are transformed to their normal form and the control law through the PDV is designed using a backstepping approach for position tracking. Then, another nonlinear set of laws is derived to achieve energy-saving through the PRV input. This control design method, based on the normal form representation, imposes internal dynamics on the closed-loop system. The stability of the internal dynamics is analyzed in special cases of operation. Experimental results verify that both tracking and energy-saving objectives are satisfied for the closed-loop system. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence

NASA Technical Reports Server (NTRS)

Sidwell, K.

1976-01-01

An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.

A direct application of the non-linear inverse transformation flight control system design on a STOVL aircraft

NASA Technical Reports Server (NTRS)

Chung, W. W.; Mcneill, W. E.; Stortz, M. W.

1993-01-01

The nonlinear inverse transformation flight control system design method is applied to the Lockheed Ft. Worth Company's E-7D short takeoff and vertical land (STOVL) supersonic fighter/attack aircraft design with a modified General Electric F110 engine which has augmented propulsive lift capability. The system is fully augmented to provide flight path control and velocity control, and rate command attitude hold for angular axes during the transition and hover operations. In cruise mode, the flight control system is configured to provide direct thrust command, rate command attitude hold for pitch and roll axes, and sideslip command with turn coordination. A control selector based on the nonlinear inverse transformation method is designed specifically to be compatible with the propulsion system's physical configuration which has a two dimensional convergent-divergent aft nozzle, a vectorable ventral nozzle, and a thrust augmented ejector. The nonlinear inverse transformation is used to determine the propulsive forces and nozzle deflections, which in combination with the aerodynamic forces and moments (including propulsive induced contributions), and gravitational force, are required to achieve the longitudinal and vertical acceleration commands. The longitudinal control axes are fully decoupled within the propulsion system's performance envelope. A piloted motion-base flight simulation was conducted on the Vertical Motion Simulator (VMS) at NASA Ames Research Center to examine the handling qualities of this design. Based on results of the simulation, refinements to the control system have been made and will also be covered in the report.

The chaotic dynamical aperture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S.Y.; Tepikian, S.

1985-10-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles.« less

Distributed Adaptive Containment Control for a Class of Nonlinear Multiagent Systems With Input Quantization.

PubMed

Wang, Chenliang; Wen, Changyun; Hu, Qinglei; Wang, Wei; Zhang, Xiuyu

2018-06-01

This paper is devoted to distributed adaptive containment control for a class of nonlinear multiagent systems with input quantization. By employing a matrix factorization and a novel matrix normalization technique, some assumptions involving control gain matrices in existing results are relaxed. By fusing the techniques of sliding mode control and backstepping control, a two-step design method is proposed to construct controllers and, with the aid of neural networks, all system nonlinearities are allowed to be unknown. Moreover, a linear time-varying model and a similarity transformation are introduced to circumvent the obstacle brought by quantization, and the controllers need no information about the quantizer parameters. The proposed scheme is able to ensure the boundedness of all closed-loop signals and steer the containment errors into an arbitrarily small residual set. The simulation results illustrate the effectiveness of the scheme.

Overview of computational control research at UT Austin

NASA Technical Reports Server (NTRS)

Bong, Wie

1989-01-01

An overview of current research activities at UT Austin is presented to discuss certain technical issues in the following areas: (1) Computer-Aided Nonlinear Control Design: In this project, the describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. INCA program has been enhanced to allow the numerical calculation of describing functions as well as the nonlinear limit cycle analysis capability in the frequency domain; (2) Robust Linear Quadratic Gaussian (LQG) Compensator Synthesis: Robust control design techniques and software tools are developed for flexible space structures with parameter uncertainty. In particular, an interactive, robust multivariable control design capability is being developed for INCA program; and (3) LQR-Based Autonomous Control System for the Space Station: In this project, real time implementation of LQR-based autonomous control system is investigated for the space station with time-varying inertias and with significant multibody dynamic interactions.

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators. [Linear Quadratic

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

Distributed robust adaptive control of high order nonlinear multi agent systems.

PubMed

Hashemi, Mahnaz; Shahgholian, Ghazanfar

2018-03-01

In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

NASA Astrophysics Data System (ADS)

Sun, Limin; Chen, Lin

2017-10-01

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

Use of the dynamic stiffness method to interpret experimental data from a nonlinear system

NASA Astrophysics Data System (ADS)

Tang, Bin; Brennan, M. J.; Gatti, G.

2018-05-01

The interpretation of experimental data from nonlinear structures is challenging, primarily because of dependency on types and levels of excitation, and coupling issues with test equipment. In this paper, the use of the dynamic stiffness method, which is commonly used in the analysis of linear systems, is used to interpret the data from a vibration test of a controllable compressed beam structure coupled to a test shaker. For a single mode of the system, this method facilitates the separation of mass, stiffness and damping effects, including nonlinear stiffness effects. It also allows the separation of the dynamics of the shaker from the structure under test. The approach needs to be used with care, and is only suitable if the nonlinear system has a response that is predominantly at the excitation frequency. For the structure under test, the raw experimental data revealed little about the underlying causes of the dynamic behaviour. However, the dynamic stiffness approach allowed the effects due to the nonlinear stiffness to be easily determined.

Nonlinear model-order reduction for compressible flow solvers using the Discrete Empirical Interpolation Method

NASA Astrophysics Data System (ADS)

Fosas de Pando, Miguel; Schmid, Peter J.; Sipp, Denis

2016-11-01

Nonlinear model reduction for large-scale flows is an essential component in many fluid applications such as flow control, optimization, parameter space exploration and statistical analysis. In this article, we generalize the POD-DEIM method, introduced by Chaturantabut & Sorensen [1], to address nonlocal nonlinearities in the equations without loss of performance or efficiency. The nonlinear terms are represented by nested DEIM-approximations using multiple expansion bases based on the Proper Orthogonal Decomposition. These extensions are imperative, for example, for applications of the POD-DEIM method to large-scale compressible flows. The efficient implementation of the presented model-reduction technique follows our earlier work [2] on linearized and adjoint analyses and takes advantage of the modular structure of our compressible flow solver. The efficacy of the nonlinear model-reduction technique is demonstrated to the flow around an airfoil and its acoustic footprint. We could obtain an accurate and robust low-dimensional model that captures the main features of the full flow.

Fuzzy Finite-Time Command Filtered Control of Nonlinear Systems With Input Saturation.

PubMed

Yu, Jinpeng; Zhao, Lin; Yu, Haisheng; Lin, Chong; Dong, Wenjie

2017-08-22

This paper considers the fuzzy finite-time tracking control problem for a class of nonlinear systems with input saturation. A novel fuzzy finite-time command filtered backstepping approach is proposed by introducing the fuzzy finite-time command filter, designing the new virtual control signals and the modified error compensation signals. The proposed approach not only holds the advantages of the conventional command-filtered backstepping control, but also guarantees the finite-time convergence. A practical example is included to show the effectiveness of the proposed method.

Off-policy reinforcement learning for H∞ control design.

PubMed

Luo, Biao; Wu, Huai-Ning; Huang, Tingwen

2015-01-01

The H∞ control design problem is considered for nonlinear systems with unknown internal system model. It is known that the nonlinear H∞ control problem can be transformed into solving the so-called Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that is generally impossible to be solved analytically. Even worse, model-based approaches cannot be used for approximately solving HJI equation, when the accurate system model is unavailable or costly to obtain in practice. To overcome these difficulties, an off-policy reinforcement leaning (RL) method is introduced to learn the solution of HJI equation from real system data instead of mathematical system model, and its convergence is proved. In the off-policy RL method, the system data can be generated with arbitrary policies rather than the evaluating policy, which is extremely important and promising for practical systems. For implementation purpose, a neural network (NN)-based actor-critic structure is employed and a least-square NN weight update algorithm is derived based on the method of weighted residuals. Finally, the developed NN-based off-policy RL method is tested on a linear F16 aircraft plant, and further applied to a rotational/translational actuator system.

Adaptive Constrained Optimal Control Design for Data-Based Nonlinear Discrete-Time Systems With Critic-Only Structure.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning

2018-06-01

Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.

A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

NASA Technical Reports Server (NTRS)

Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

1979-01-01

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

Distributed Adaptive Neural Network Output Tracking of Leader-Following High-Order Stochastic Nonlinear Multiagent Systems With Unknown Dead-Zone Input.

PubMed

Hua, Changchun; Zhang, Liuliu; Guan, Xinping

2017-01-01

This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.

Composite Intelligent Learning Control of Strict-Feedback Systems With Disturbance.

PubMed

Xu, Bin; Sun, Fuchun

2018-02-01

This paper addresses the dynamic surface control of uncertain nonlinear systems on the basis of composite intelligent learning and disturbance observer in presence of unknown system nonlinearity and time-varying disturbance. The serial-parallel estimation model with intelligent approximation and disturbance estimation is built to obtain the prediction error and in this way the composite law for weights updating is constructed. The nonlinear disturbance observer is developed using intelligent approximation information while the disturbance estimation is guaranteed to converge to a bounded compact set. The highlight is that different from previous work directly toward asymptotic stability, the transparency of the intelligent approximation and disturbance estimation is included in the control scheme. The uniformly ultimate boundedness stability is analyzed via Lyapunov method. Through simulation verification, the composite intelligent learning with disturbance observer can efficiently estimate the effect caused by system nonlinearity and disturbance while the proposed approach obtains better performance with higher accuracy.

Force and Moment Approach for Achievable Dynamics Using Nonlinear Dynamic Inversion

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Bacon, Barton J.

1999-01-01

This paper describes a general form of nonlinear dynamic inversion control for use in a generic nonlinear simulation to evaluate candidate augmented aircraft dynamics. The implementation is specifically tailored to the task of quickly assessing an aircraft's control power requirements and defining the achievable dynamic set. The achievable set is evaluated while undergoing complex mission maneuvers, and perfect tracking will be accomplished when the desired dynamics are achievable. Variables are extracted directly from the simulation model each iteration, so robustness is not an issue. Included in this paper is a description of the implementation of the forces and moments from simulation variables, the calculation of control effectiveness coefficients, methods for implementing different types of aerodynamic and thrust vectoring controls, adjustments for control effector failures, and the allocation approach used. A few examples illustrate the perfect tracking results obtained.

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.

Distributed adaptive neural network control for a class of heterogeneous nonlinear multi-agent systems subject to actuation failures

NASA Astrophysics Data System (ADS)

Cui, Bing; Zhao, Chunhui; Ma, Tiedong; Feng, Chi

2017-02-01

In this paper, the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems on directed graph is addressed. Each follower is modelled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics, disturbances and actuator failures. Cooperative fault tolerant neural network tracking controllers with online adaptive learning features are proposed to guarantee that all agents synchronise to the trajectory of one leader with bounded adjustable synchronisation errors. With the help of linear quadratic regulator-based optimal design, a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology, one virtual matrix and some design parameters. Of particular interest is that if the control gain is selected appropriately, the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not. Furthermore, the fault detection and isolation are not needed to implement. Finally, a simulation is given to verify the effectiveness of the proposed method.

Finite-time adaptive sliding mode force control for electro-hydraulic load simulator based on improved GMS friction model

NASA Astrophysics Data System (ADS)

Kang, Shuo; Yan, Hao; Dong, Lijing; Li, Changchun

2018-03-01

This paper addresses the force tracking problem of electro-hydraulic load simulator under the influence of nonlinear friction and uncertain disturbance. A nonlinear system model combined with the improved generalized Maxwell-slip (GMS) friction model is firstly derived to describe the characteristics of load simulator system more accurately. Then, by using particle swarm optimization (PSO) algorithm ​combined with the system hysteresis characteristic analysis, the GMS friction parameters are identified. To compensate for nonlinear friction and uncertain disturbance, a finite-time adaptive sliding mode control method is proposed based on the accurate system model. This controller has the ability to ensure that the system state moves along the nonlinear sliding surface to steady state in a short time as well as good dynamic properties under the influence of parametric uncertainties and disturbance, which further improves the force loading accuracy and rapidity. At the end of this work, simulation and experimental results are employed to demonstrate the effectiveness of the proposed sliding mode control strategy.

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

Model predictive control of non-linear systems over networks with data quantization and packet loss.

PubMed

Yu, Jimin; Nan, Liangsheng; Tang, Xiaoming; Wang, Ping

2015-11-01

This paper studies the approach of model predictive control (MPC) for the non-linear systems under networked environment where both data quantization and packet loss may occur. The non-linear controlled plant in the networked control system (NCS) is represented by a Tagaki-Sugeno (T-S) model. The sensed data and control signal are quantized in both links and described as sector bound uncertainties by applying sector bound approach. Then, the quantized data are transmitted in the communication networks and may suffer from the effect of packet losses, which are modeled as Bernoulli process. A fuzzy predictive controller which guarantees the stability of the closed-loop system is obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming

NASA Astrophysics Data System (ADS)

Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai

2013-09-01

In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Adaptive Neural Control of Uncertain MIMO Nonlinear Systems With State and Input Constraints.

PubMed

Chen, Ziting; Li, Zhijun; Chen, C L Philip

2017-06-01

An adaptive neural control strategy for multiple input multiple output nonlinear systems with various constraints is presented in this paper. To deal with the nonsymmetric input nonlinearity and the constrained states, the proposed adaptive neural control is combined with the backstepping method, radial basis function neural network, barrier Lyapunov function (BLF), and disturbance observer. By ensuring the boundedness of the BLF of the closed-loop system, it is demonstrated that the output tracking is achieved with all states remaining in the constraint sets and the general assumption on nonsingularity of unknown control coefficient matrices has been eliminated. The constructed adaptive neural control has been rigorously proved that it can guarantee the semiglobally uniformly ultimate boundedness of all signals in the closed-loop system. Finally, the simulation studies on a 2-DOF robotic manipulator system indicate that the designed adaptive control is effective.

Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay.

PubMed

Khazaee, Mostafa; Markazi, Amir H D; Omidi, Ehsan

2015-11-01

In this paper, a new Adaptive Fuzzy Predictive Sliding Mode Control (AFP-SMC) is presented for nonlinear systems with uncertain dynamics and unknown input delay. The control unit consists of a fuzzy inference system to approximate the ideal linearization control, together with a switching strategy to compensate for the estimation errors. Also, an adaptive fuzzy predictor is used to estimate the future values of the system states to compensate for the time delay. The adaptation laws are used to tune the controller and predictor parameters, which guarantee the stability based on a Lyapunov-Krasovskii functional. To evaluate the method effectiveness, the simulation and experiment on an overhead crane system are presented. According to the obtained results, AFP-SMC can effectively control the uncertain nonlinear systems, subject to input delays of known bound. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

PubMed

Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

2011-01-01

In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

Performance bounds for nonlinear systems with a nonlinear ℒ2-gain property

NASA Astrophysics Data System (ADS)

Zhang, Huan; Dower, Peter M.

2012-09-01

Nonlinear ℒ2-gain is a finite gain concept that generalises the notion of conventional (linear) finite ℒ2-gain to admit the application of ℒ2-gain analysis tools of a broader class of nonlinear systems. The computation of tight comparison function bounds for this nonlinear ℒ2-gain property is important in applications such as small gain design. This article presents an approximation framework for these comparison function bounds through the formulation and solution of an optimal control problem. Key to the solution of this problem is the lifting of an ℒ2-norm input constraint, which is facilitated via the introduction of an energy saturation operator. This admits the solution of the optimal control problem of interest via dynamic programming and associated numerical methods, leading to the computation of the proposed bounds. Two examples are presented to demonstrate this approach.

Data-based virtual unmodeled dynamics driven multivariable nonlinear adaptive switching control.

PubMed

Chai, Tianyou; Zhang, Yajun; Wang, Hong; Su, Chun-Yi; Sun, Jing

2011-12-01

For a complex industrial system, its multivariable and nonlinear nature generally make it very difficult, if not impossible, to obtain an accurate model, especially when the model structure is unknown. The control of this class of complex systems is difficult to handle by the traditional controller designs around their operating points. This paper, however, explores the concepts of controller-driven model and virtual unmodeled dynamics to propose a new design framework. The design consists of two controllers with distinct functions. First, using input and output data, a self-tuning controller is constructed based on a linear controller-driven model. Then the output signals of the controller-driven model are compared with the true outputs of the system to produce so-called virtual unmodeled dynamics. Based on the compensator of the virtual unmodeled dynamics, the second controller based on a nonlinear controller-driven model is proposed. Those two controllers are integrated by an adaptive switching control algorithm to take advantage of their complementary features: one offers stabilization function and another provides improved performance. The conditions on the stability and convergence of the closed-loop system are analyzed. Both simulation and experimental tests on a heavily coupled nonlinear twin-tank system are carried out to confirm the effectiveness of the proposed method.

Neural Networks for Flight Control

NASA Technical Reports Server (NTRS)

Jorgensen, Charles C.

1996-01-01

Neural networks are being developed at NASA Ames Research Center to permit real-time adaptive control of time varying nonlinear systems, enhance the fault-tolerance of mission hardware, and permit online system reconfiguration. In general, the problem of controlling time varying nonlinear systems with unknown structures has not been solved. Adaptive neural control techniques show considerable promise and are being applied to technical challenges including automated docking of spacecraft, dynamic balancing of the space station centrifuge, online reconfiguration of damaged aircraft, and reducing cost of new air and spacecraft designs. Our experiences have shown that neural network algorithms solved certain problems that conventional control methods have been unable to effectively address. These include damage mitigation in nonlinear reconfiguration flight control, early performance estimation of new aircraft designs, compensation for damaged planetary mission hardware by using redundant manipulator capability, and space sensor platform stabilization. This presentation explored these developments in the context of neural network control theory. The discussion began with an overview of why neural control has proven attractive for NASA application domains. The more important issues in control system development were then discussed with references to significant technical advances in the literature. Examples of how these methods have been applied were given, followed by projections of emerging application needs and directions.

Alternatives for Jet Engine Control

NASA Technical Reports Server (NTRS)

Leake, R. J.; Sain, M. K.

1976-01-01

Approaches are developed as alternatives to current design methods which rely heavily on linear quadratic and Riccati equation methods. The main alternatives are discussed in two broad categories, local multivariable frequency domain methods and global nonlinear optimal methods.

The development of the deterministic nonlinear PDEs in particle physics to stochastic case

NASA Astrophysics Data System (ADS)

Abdelrahman, Mahmoud A. E.; Sohaly, M. A.

2018-06-01

In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.

Further results on global state feedback stabilization of nonlinear high-order feedforward systems.

PubMed

Xie, Xue-Jun; Zhang, Xing-Hui

2014-03-01

In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics.

PubMed

Taheri, Mehdi; Sheikholeslam, Farid; Najafi, Majddedin; Zekri, Maryam

2017-07-01

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.

PubMed

Mei, Jie; Ren, Wei; Li, Bing; Ma, Guangfu

2015-09-01

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Management of Occupational Exposure to Engineered Nanoparticles Through a Chance-Constrained Nonlinear Programming Approach

PubMed Central

Chen, Zhi; Yuan, Yuan; Zhang, Shu-Shen; Chen, Yu; Yang, Feng-Lin

2013-01-01

Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial production and minimize the risks of workplace exposure to MNMs. The CCNLP method integrates nonlinear programming (NLP) and chance-constrained programming (CCP), and handles uncertainties associated with both the nanomaterial production and workplace exposure control. The CCNLP method was examined through a single-walled carbon nanotube (SWNT) manufacturing process. The study results provide optimal production strategies and alternatives. It reveal that a high control measure guarantees that environmental health and safety (EHS) standards regulations are met, while a lower control level leads to increased risk of violating EHS regulations. The CCNLP optimization approach is a decision support tool for the optimization of the increasing MNMS manufacturing with workplace safety constraints under uncertainties. PMID:23531490

Management of occupational exposure to engineered nanoparticles through a chance-constrained nonlinear programming approach.

PubMed

Chen, Zhi; Yuan, Yuan; Zhang, Shu-Shen; Chen, Yu; Yang, Feng-Lin

2013-03-26

Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial production and minimize the risks of workplace exposure to MNMs. The CCNLP method integrates nonlinear programming (NLP) and chance-constrained programming (CCP), and handles uncertainties associated with both the nanomaterial production and workplace exposure control. The CCNLP method was examined through a single-walled carbon nanotube (SWNT) manufacturing process. The study results provide optimal production strategies and alternatives. It reveal that a high control measure guarantees that environmental health and safety (EHS) standards regulations are met, while a lower control level leads to increased risk of violating EHS regulations. The CCNLP optimization approach is a decision support tool for the optimization of the increasing MNMS manufacturing with workplace safety constraints under uncertainties.

Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control.

PubMed

Palese, Stephen; Cheung, Eric; Goodno, Gregory; Shih, Chun-Ching; Di Teodoro, Fabio; McComb, Timothy; Weber, Mark

2012-03-26

Two high pulse contrast (> 95 dB) polarization maintaining all-fiber amplifier chains were coherently combined to generate 0.42 mJ, 1 ns 25 kHz pulses with 79% efficiency despite 38 radians of intra-pulse phase distortion. A recursive intra-pulse phase compensation method was utilized to correct for the large nonlinear chirp providing a path for improved coherent waveform control of nanosecond pulse trains.

Controlling modal interactions in lasers for frequency selection and power enhancement

NASA Astrophysics Data System (ADS)

Ge, Li

2015-03-01

The laser is an out-of-equilibrium non-linear wave system where the interplay of the cavity geometry and non-linear wave interactions determines the self-organized oscillation frequencies and the associated spatial field patterns. Using the correspondence between nonlinear and linear systems, we propose a simple and systematic method to achieve selective excitation of lasing modes that would have been dwarfed by more dominant ones. The key idea is incorporating the control of modal interaction into the spatial pump profile. Our proposal is most valuable in the regime of spatially and spectrally overlapping modes, which can lead to a significant enhancement of laser power as well.

Nonlinear system guidance in the presence of transmission zero dynamics

NASA Technical Reports Server (NTRS)

Meyer, G.; Hunt, L. R.; Su, R.

1995-01-01

An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.

Control-based continuation: Bifurcation and stability analysis for physical experiments

NASA Astrophysics Data System (ADS)

Barton, David A. W.

2017-02-01

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.

Gain scheduled linear quadratic control for quadcopter

NASA Astrophysics Data System (ADS)

Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.

2017-12-01

This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.

Nonlinear gearshifts control of dual-clutch transmissions during inertia phase.

PubMed

Hu, Yunfeng; Tian, Lu; Gao, Bingzhao; Chen, Hong

2014-07-01

In this paper, a model-based nonlinear gearshift controller is designed by the backstepping method to improve the shift quality of vehicles with a dual-clutch transmission (DCT). Considering easy-implementation, the controller is rearranged into a concise structure which contains a feedforward control and a feedback control. Then, robustness of the closed-loop error system is discussed in the framework of the input to state stability (ISS) theory, where model uncertainties are considered as the additive disturbance inputs. Furthermore, due to the application of the backstepping method, the closed-loop error system is ordered as a linear system. Using the linear system theory, a guideline for selecting the controller parameters is deduced which could reduce the workload of parameters tuning. Finally, simulation results and Hardware in the Loop (HiL) simulation are presented to validate the effectiveness of the designed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Fuzzy Adaptive Control Design and Discretization for a Class of Nonlinear Uncertain Systems.

PubMed

Zhao, Xudong; Shi, Peng; Zheng, Xiaolong

2016-06-01

In this paper, tracking control problems are investigated for a class of uncertain nonlinear systems in lower triangular form. First, a state-feedback controller is designed by using adaptive backstepping technique and the universal approximation ability of fuzzy logic systems. During the design procedure, a developed method with less computation is proposed by constructing one maximum adaptive parameter. Furthermore, adaptive controllers with nonsymmetric dead-zone are also designed for the systems. Then, a sampled-data control scheme is presented to discretize the obtained continuous-time controller by using the forward Euler method. It is shown that both proposed continuous and discrete controllers can ensure that the system output tracks the target signal with a small bounded error and the other closed-loop signals remain bounded. Two simulation examples are presented to verify the effectiveness and applicability of the proposed new design techniques.

MTPA control of mechanical sensorless IPMSM based on adaptive nonlinear control.

PubMed

Najjar-Khodabakhsh, Abbas; Soltani, Jafar

2016-03-01

In this paper, an adaptive nonlinear control scheme has been proposed for implementing maximum torque per ampere (MTPA) control strategy corresponding to interior permanent magnet synchronous motor (IPMSM) drive. This control scheme is developed in the rotor d-q axis reference frame using adaptive input-output state feedback linearization (AIOFL) method. The drive system control stability is supported by Lyapunov theory. The motor inductances are online estimated by an estimation law obtained by AIOFL. The estimation errors of these parameters are proved to be asymptotically converged to zero. Based on minimizing the motor current amplitude, the MTPA control strategy is performed by using the nonlinear optimization technique while considering the online reference torque. The motor reference torque is generated by a conventional rotor speed PI controller. By performing MTPA control strategy, the generated online motor d-q reference currents were used in AIOFL controller to obtain the SV-PWM reference voltages and the online estimation of the motor d-q inductances. In addition, the stator resistance is online estimated using a conventional PI controller. Moreover, the rotor position is detected using the online estimation of the stator flux and online estimation of the motor q-axis inductance. Simulation and experimental results obtained prove the effectiveness and the capability of the proposed control method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

On a program manifold's stability of one contour automatic control systems

NASA Astrophysics Data System (ADS)

Zumatov, S. S.

2017-12-01

Methodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold's absolute stability of one contour automatic control systems are obtained. The Hurwitz's angle of absolute stability was determined. The sufficient conditions of program manifold's absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov's second method.

Model-based estimation and control for off-axis parabolic mirror alignment

NASA Astrophysics Data System (ADS)

Fang, Joyce; Savransky, Dmitry

2018-02-01

This paper propose an model-based estimation and control method for an off-axis parabolic mirror (OAP) alignment. Current studies in automated optical alignment systems typically require additional wavefront sensors. We propose a self-aligning method using only focal plane images captured by the existing camera. Image processing methods and Karhunen-Loève (K-L) decomposition are used to extract measurements for the observer in closed-loop control system. Our system has linear dynamic in state transition, and a nonlinear mapping from the state to the measurement. An iterative extended Kalman filter (IEKF) is shown to accurately predict the unknown states, and nonlinear observability is discussed. Linear-quadratic regulator (LQR) is applied to correct the misalignments. The method is validated experimentally on the optical bench with a commercial OAP. We conduct 100 tests in the experiment to demonstrate the consistency in between runs.

Adaptive fuzzy control of a class of nonaffine nonlinear system with input saturation based on passivity theorem.

PubMed

Molavi, Ali; Jalali, Aliakbar; Ghasemi Naraghi, Mahdi

2017-07-01

In this paper, based on the passivity theorem, an adaptive fuzzy controller is designed for a class of unknown nonaffine nonlinear systems with arbitrary relative degree and saturation input nonlinearity to track the desired trajectory. The system equations are in normal form and its unforced dynamic may be unstable. As relative degree one is a structural obstacle in system passivation approach, in this paper, backstepping method is used to circumvent this obstacle and passivate the system step by step. Because of the existence of uncertainty and disturbance in the system, exact passivation and reference tracking cannot be tackled, so the approximate passivation or passivation with respect to a set is obtained to hold the tracking error in a neighborhood around zero. Furthermore, in order to overcome the non-smoothness of the saturation input nonlinearity, a parametric smooth nonlinear function with arbitrary approximation error is used to approximate the input saturation. Finally, the simulation results for the theoretical and practical examples are given to validate the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Open-closed-loop iterative learning control for a class of nonlinear systems with random data dropouts

NASA Astrophysics Data System (ADS)

Cheng, X. Y.; Wang, H. B.; Jia, Y. L.; Dong, YH

2018-05-01

In this paper, an open-closed-loop iterative learning control (ILC) algorithm is constructed for a class of nonlinear systems subjecting to random data dropouts. The ILC algorithm is implemented by a networked control system (NCS), where only the off-line data is transmitted by network while the real-time data is delivered in the point-to-point way. Thus, there are two controllers rather than one in the control system, which makes better use of the saved and current information and thereby improves the performance achieved by open-loop control alone. During the transfer of off-line data between the nonlinear plant and the remote controller data dropout occurs randomly and the data dropout rate is modeled as a binary Bernoulli random variable. Both measurement and control data dropouts are taken into consideration simultaneously. The convergence criterion is derived based on rigorous analysis. Finally, the simulation results verify the effectiveness of the proposed method.

Tethered satellite system control using electromagnetic forces and reaction wheels

NASA Astrophysics Data System (ADS)

Alandi Hallaj, Mohammad Amin; Assadian, Nima

2015-12-01

In this paper a novel non-rotating space tethered configuration is introduced which its relative positions controlled using electromagnetic forces. The attitude dynamics is controlled by three reaction wheels in the body axes. The nonlinear coupled orbital dynamics of a dumbbell tethered satellite formation flight are derived through a constrained Lagrangian approach. These equations are presented in the leader satellite orbital frame. The tether is assumed to be mass-less and straight, and the J2 perturbation is included to the analysis. The forces and the moments of the electromagnetic coils are modeled based on the far-filed model of the magnetic dipoles. A guidance scheme for generating the desired positions as a function of time in Cartesian form is presented. The satellite tethered formation with variable length is controlled utilizing a linear controller. This approach is applied to a specified scenario and it is shown that the nonlinear guidance method and the linear controller can control the nonlinear system of the tethered formation and the results are compared with optimal control approach.

A VLF-based technique in applications to digital control of nonlinear hybrid multirate systems

NASA Astrophysics Data System (ADS)

Vassilyev, Stanislav; Ulyanov, Sergey; Maksimkin, Nikolay

2017-01-01

In this paper, a technique for rigorous analysis and design of nonlinear multirate digital control systems on the basis of the reduction method and sublinear vector Lyapunov functions is proposed. The control system model under consideration incorporates continuous-time dynamics of the plant and discrete-time dynamics of the controller and takes into account uncertainties of the plant, bounded disturbances, nonlinear characteristics of sensors and actuators. We consider a class of multirate systems where the control update rate is slower than the measurement sampling rates and periodic non-uniform sampling is admitted. The proposed technique does not use the preliminary discretization of the system, and, hence, allows one to eliminate the errors associated with the discretization and improve the accuracy of analysis. The technique is applied to synthesis of digital controller for a flexible spacecraft in the fine stabilization mode and decentralized controller for a formation of autonomous underwater vehicles. Simulation results are provided to validate the good performance of the designed controllers.

Proposal of ultra-compact NAND/NOR/XNOR all-optical logic gates based on a nonlinear 3x1 multimode interference

NASA Astrophysics Data System (ADS)

Tajaldini, Mehdi; Mat Jafri, M. Z.

2014-05-01

We present a highly miniaturized multimode interference (MMI) coupler based on nonlinear modal propagation analysis (NMPA) method as a novel design method and potential application for optical NAND, NOR and XNOR logic gates for Boolean logic signal processing devices. Crystalline polydiacetylene is used to allow the appearances of nonlinear effects in low input intensities and ultra- short length to control the MMI coupler as an active device to access light switching due to its high nonlinear susceptibility. We consider a 10x33 μm2 MMI structure with three inputs and one output. Notably, the access facets are single-mode waveguides with sub-micron width. The center input contributes to control the induced light propagation in MMI by intensity variation whereas others could be launched by particular intensity when they are ON and 0 in OFF. Output intensity is analyzed in various sets of inputs to show the capability of Boolean logic gates, the contrast between ON and OFF is calculated on mentioned gates to present the efficiency. Good operation in low intensity and highly miniaturized MMI coupler is observed. Furthermore, nonlinear effects could be realized through the modal interferences. The issue of high insertion loss is addressed with a 3×3 upgraded coupler. Furthermore, the main significant aspect of this paper is simulating an MMI coupler that is launched by three nonlinear inputs, simultaneously, whereas last presents have never studied more than one input in nonlinear regimes.

New nonlinear control algorithms for multiple robot arms

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Bejczy, A. K.; Yun, X.

1988-01-01

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems.

PubMed

Herzallah, Randa

2013-06-01

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.

Semiconductor Nonlinear Waveguide Devices and Integrated-Mirror Etalons

NASA Astrophysics Data System (ADS)

Chuang, Chih-Li.

This dissertation investigates different III-V semiconductor devices for applications in nonlinear photonics. These include passive and active nonlinear directional couplers, current-controlled optical phase shifter, and integrated -mirror etalons. A novel method to find the propagation constants of an optical waveguide is introduced. The same method is applied, with minor modifications, to find the coupling length of a directional coupler. The method presented provides a tool for the design of optical waveguide devices. The design, fabrication, and performance of a nonlinear directional coupler are presented. This device uses light intensity to control the direction of light coming out. This is achieved through photo-generated-carriers mechanism in the picosecond regime and through the optical Stark effect in the femtosecond regime. A two-transverse -dimensions beam-propagation computation is used to model the switching behavior in the nonlinear directional coupler. It is found that, by considering the pulse degradation effect, the computation agrees well with experiments. The possibility of operating a nonlinear directional coupler with gain is investigated. It is concluded that by injecting current into the nonlinear directional coupler does not provide the advantages hoped for and the modelling using 2-D beam -propagation methods verifies that. Using current injection to change the refractive index of a waveguide, an optical phase shifter is constructed. This device has the merit of delivering large phase shift with almost no intensity modulation. A phase shift as large as 3pi is produced in a waveguide 400 μm in length. Finally, a new structure, grown by the molecular beam epitaxy machine, is described. The structure consists of two quarter-wave stacks and a spacer layer to form an integrated-mirror etalon. The theory, design principles, spectral analyses are discussed with design examples to clarify the ideas. Emphasis is given to the vertical-cavity surface-emitting laser constructed from this structure. Here we demonstrated the cw operation of the VCSEL at room temperature.

Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems

NASA Astrophysics Data System (ADS)

Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei

2016-07-01

This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.

Fine Output Voltage Control Method considering Time-Delay of Digital Inverter System for X-ray Computed Tomography

NASA Astrophysics Data System (ADS)

Shibata, Junji; Kaneko, Kazuhide; Ohishi, Kiyoshi; Ando, Itaru; Ogawa, Mina; Takano, Hiroshi

This paper proposes a new output voltage control for an inverter system, which has time-delay and nonlinear load. In the next generation X-ray computed tomography of a medical device (X-ray CT) that uses the contactless power transfer method, the feedback signal often contains time-delay due to AD/DA conversion and error detection/correction time. When the PID controller of the inverter system is received the adverse effects of the time-delay, the controller often has an overshoot and a oscillated response. In order to overcome this problem, this paper proposes a compensation method based on the Smith predictor for an inverter system having a time-delay and the nonlinear loads which are the diode bridge rectifier and X-ray tube. The proposed compensation method consists of the hybrid Smith predictor system based on an equivalent analog circuit and DSP. The experimental results confirm the validity of the proposed system.

Controllable chaos in hybrid electro-optomechanical systems

PubMed Central

Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

2016-01-01

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication. PMID:26948505

Controllable chaos in hybrid electro-optomechanical systems.

PubMed

Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

2016-03-07

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication.

Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

PubMed

Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

2015-11-01

The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

Preliminary demonstration of a robust controller design method

NASA Technical Reports Server (NTRS)

Anderson, L. R.

1980-01-01

Alternative computational procedures for obtaining a feedback control law which yields a control signal based on measurable quantitites are evaluated. The three methods evaluated are: (1) the standard linear quadratic regulator design model; (2) minimization of the norm of the feedback matrix, k via nonlinear programming subject to the constraint that the closed loop eigenvalues be in a specified domain in the complex plane; and (3) maximize the angles between the closed loop eigenvectors in combination with minimizing the norm of K also via the constrained nonlinear programming. The third or robust design method was chosen to yield a closed loop system whose eigenvalues are insensitive to small changes in the A and B matrices. The relationship between orthogonality of closed loop eigenvectors and the sensitivity of closed loop eigenvalues is described. Computer programs are described.

A new adaptive control strategy for a class of nonlinear system using RBF neuro-sliding-mode technique: application to SEIG wind turbine control system

NASA Astrophysics Data System (ADS)

Kenné, Godpromesse; Fotso, Armel Simo; Lamnabhi-Lagarrigue, Françoise

2017-04-01

In this paper, a new hybrid method which combines radial basis function (RBF) neural network with a sliding-mode technique to take advantage of their common features is used to control a class of nonlinear systems. A real-time dynamic nonlinear learning law of the weight vector is synthesized and the closed-loop stability has been demonstrated using Lyapunov theory. The solution presented in this work does not need the knowledge of the perturbation bounds, neither the knowledge of the full state of the nonlinear system. In addition, the bounds of the nonlinear functions are assumed to be unknown and the proposed RBF structure uses reduced number of hidden units. This hybrid control strategy is applied to extract the maximum available energy from a stand-alone self-excited variable low-wind speed energy conversion system and design the dc-voltage and rotor flux controllers as well as the load-side frequency and voltage regulators assuming that the measured outputs are the rotor speed, stator currents, load-side currents and voltages despite large variation of the rotor resistance and uncertainties on the inductances. Finally, simulation results compared with those obtained using the well-known second-order sliding-mode controller are given to show the effectiveness and feasibility of the proposed approach.

Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.

PubMed

Nagarale, Ravindrakumar M; Patre, B M

2014-05-01

This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive Output-Feedback Neural Control of Switched Uncertain Nonlinear Systems With Average Dwell Time.

PubMed

Long, Lijun; Zhao, Jun

2015-07-01

This paper investigates the problem of adaptive neural tracking control via output-feedback for a class of switched uncertain nonlinear systems without the measurements of the system states. The unknown control signals are approximated directly by neural networks. A novel adaptive neural control technique for the problem studied is set up by exploiting the average dwell time method and backstepping. A switched filter and different update laws are designed to reduce the conservativeness caused by adoption of a common observer and a common update law for all subsystems. The proposed controllers of subsystems guarantee that all closed-loop signals remain bounded under a class of switching signals with average dwell time, while the output tracking error converges to a small neighborhood of the origin. As an application of the proposed design method, adaptive output feedback neural tracking controllers for a mass-spring-damper system are constructed.

Synchronization controller design of two coupling permanent magnet synchronous motors system with nonlinear constraints.

PubMed

Deng, Zhenhua; Shang, Jing; Nian, Xiaohong

2015-11-01

In this paper, two coupling permanent magnet synchronous motors system with nonlinear constraints is studied. First of all, the mathematical model of the system is established according to the engineering practices, in which the dynamic model of motor and the nonlinear coupling effect between two motors are considered. In order to keep the two motors synchronization, a synchronization controller based on load observer is designed via cross-coupling idea and interval matrix. Moreover, speed, position and current signals of two motor all are taken as self-feedback signal as well as cross-feedback signal in the proposed controller, which is conducive to improving the dynamical performance and the synchronization performance of the system. The proposed control strategy is verified by simulation via Matlab/Simulink program. The simulation results show that the proposed control method has a better control performance, especially synchronization performance, than that of the conventional PI controller. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Thrusting maneuver control of a small spacecraft via only gimbaled-thruster scheme

NASA Astrophysics Data System (ADS)

Kabganian, Mansour; Kouhi, Hamed; Shahravi, Morteza; Fani Saberi, Farhad

2018-05-01

The thrust vector control (TVC) scheme is a powerful method in spacecraft attitude control. Since the control of a small spacecraft is being studied here, a solid rocket motor (SRM) should be used instead of a liquid propellant motor. Among the TVC methods, gimbaled-TVC as an efficient method is employed in this paper. The spacecraft structure is composed of a body and a gimbaled-SRM where common attitude control systems such as reaction control system (RCS) and spin-stabilization are not presented. A nonlinear two-body model is considered for the characterization of the gimbaled-thruster spacecraft where, the only control input is provided by a gimbal actuator. The attitude of the spacecraft is affected by a large exogenous disturbance torque which is generated by a thrust vector misalignment from the center of mass (C.M). A linear control law is designed to stabilize the spacecraft attitude while rejecting the mentioned disturbance torque. A semi-analytical formulation of the region of attraction (RoA) is developed to ensure the local stability and fast convergence of the nonlinear closed-loop system. Simulation results of the 3D maneuvers are included to show the applicability of this method for use in a small spacecraft.

Controllable nonlinear refraction characteristics in hydrogenated nanocrystalline silicon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, D. Q.; Ye, Q. H.; Shen, W. Z., E-mail: wzshen@sjtu.edu.cn

2014-02-07

Nonlinear refraction (NLR) of hydrogenated nanocrystalline silicon (nc-Si:H) has been investigated through the close aperture Z-scan method. We demonstrate a significant NLR and a unique feature of controllable NLR characteristics between saturable and Kerr NLR with the incident photon energy. We numerically evaluate the proportion of these two mechanisms in different wavelengths by a modified NLR equation. The band tail of nc-Si:H appears to play a crucial role in such NLR responses.

Nonlinear absorption enhancement of AuNPs based polymer nanocomposites

NASA Astrophysics Data System (ADS)

Zulina, Natalia A.; Baranov, Mikhail A.; Kniazev, Kirill I.; Kaliabin, Viacheslav O.; Denisyuk, Igor Yu.; Achor, Susan U.; Sitnikova, Vera E.

2018-07-01

Au nanoparticles (AuNPs) based polymer nanocomposites with high nonlinear absorption coefficient were synthesized by UV-photocuring. AuNPs were synthesized by laser ablation method in liquid monomer isodecyl acrylate (IDA). In this research, two colloids with 70 nm and 20 nm nanoparticles average sizes were studied. Size control was performed with SEM and STEM. Prepared nanomaterials exhibit strong third-order nonlinear optical responses under CW laser irradiation at 532 nm, which was estimated by using z-scan technique performed with open aperture. It was found experimentally that nonlinear absorption β is almost twice higher for nanocomposites with smaller AuNPs.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1979-01-01

The research is classified in two categories: (1) the use of modern multivariable frequency domain methods for control of engine models in the neighborhood of a set-point, and (2) the use of nonlinear modelling and optimization techniques for control of engine models over a more extensive part of the flight envelope. Progress in the first category included the extension of CARDIAD (Complex Acceptability Region for Diagonal Dominance) methods developed with the help of the grant to the case of engine models with four inputs and four outputs. A suitable bounding procedure for the dominance function was determined. Progress in the second category had its principal focus on automatic nonlinear model generation. Simulations of models produced satisfactory results where compared with the NASA DYNGEN digital engine deck.

Adaptive control of servo system based on LuGre model

NASA Astrophysics Data System (ADS)

Jin, Wang; Niancong, Liu; Jianlong, Chen; Weitao, Geng

2018-03-01

This paper established a mechanical model of feed system based on LuGre model. In order to solve the influence of nonlinear factors on the system running stability, a nonlinear single observer is designed to estimate the parameter z in the LuGre model and an adaptive friction compensation controller is designed. Simulink simulation results show that the control method can effectively suppress the adverse effects of friction and external disturbances. The simulation show that the adaptive parameter kz is between 0.11-0.13, and the value of gamma1 is between 1.9-2.1. Position tracking error reaches level 10-3 and is stabilized near 0 values within 0.3 seconds, the compensation method has better tracking accuracy and robustness.

Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.

PubMed

Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang

2016-10-31

Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.

A Robust Control of Two-Wheeled Mobile Manipulator with Underactuated Joint by Nonlinear Backstepping Method

NASA Astrophysics Data System (ADS)

Acar, Cihan; Murakami, Toshiyuki

In this paper, a robust control of two-wheeled mobile manipulator with underactuated joint is considered. Two-wheeled mobile manipulators are dynamically balanced two-wheeled driven systems that do not have any caster or extra wheels to stabilize their body. Two-wheeled mobile manipulators mainly have an important feature that makes them more flexible and agile than the statically stable mobile manipulators. However, two-wheeled mobile manipulator is an underactuated system due to its two-wheeled structure. Therefore, it is required to stabilize the underactuated passive body and, at the same time, control the position of the center of gravity (CoG) of the manipulator in this system. To realize this, nonlinear backstepping based control method with virtual double inverted pendulum model is proposed in this paper. Backstepping is used with sliding mode to increase the robustness of the system against modeling errors and other perturbations. Then robust acceleration control is also achieved by utilizing disturbance observer. Performance of the proposed method is evaluated by several experiments.

Input and output constraints-based stabilisation of switched nonlinear systems with unstable subsystems and its application

NASA Astrophysics Data System (ADS)

Chen, Chao; Liu, Qian; Zhao, Jun

2018-01-01

This paper studies the problem of stabilisation of switched nonlinear systems with output and input constraints. We propose a recursive approach to solve this issue. None of the subsystems are assumed to be stablisable while the switched system is stabilised by dual design of controllers for subsystems and a switching law. When only dealing with bounded input, we provide nested switching controllers using an extended backstepping procedure. If both input and output constraints are taken into consideration, a Barrier Lyapunov Function is employed during operation to construct multiple Lyapunov functions for switched nonlinear system in the backstepping procedure. As a practical example, the control design of an equilibrium manifold expansion model of aero-engine is given to demonstrate the effectiveness of the proposed design method.

Kalman filter control of a model of spatiotemporal cortical dynamics

PubMed Central

Schiff, Steven J; Sauer, Tim

2007-01-01

Recent advances in Kalman filtering to estimate system state and parameters in nonlinear systems have offered the potential to apply such approaches to spatiotemporal nonlinear systems. We here adapt the nonlinear method of unscented Kalman filtering to observe the state and estimate parameters in a computational spatiotemporal excitable system that serves as a model for cerebral cortex. We demonstrate the ability to track spiral wave dynamics, and to use an observer system to calculate control signals delivered through applied electrical fields. We demonstrate how this strategy can control the frequency of such a system, or quench the wave patterns, while minimizing the energy required for such results. These findings are readily testable in experimental applications, and have the potential to be applied to the treatment of human disease. PMID:18310806

Fuzzy logic-based flight control system design

NASA Astrophysics Data System (ADS)

Nho, Kyungmoon

The application of fuzzy logic to aircraft motion control is studied in this dissertation. The self-tuning fuzzy techniques are developed by changing input scaling factors to obtain a robust fuzzy controller over a wide range of operating conditions and nonlinearities for a nonlinear aircraft model. It is demonstrated that the properly adjusted input scaling factors can meet the required performance and robustness in a fuzzy controller. For a simple demonstration of the easy design and control capability of a fuzzy controller, a proportional-derivative (PD) fuzzy control system is compared to the conventional controller for a simple dynamical system. This thesis also describes the design principles and stability analysis of fuzzy control systems by considering the key features of a fuzzy control system including the fuzzification, rule-base and defuzzification. The wing-rock motion of slender delta wings, a linear aircraft model and the six degree of freedom nonlinear aircraft dynamics are considered to illustrate several self-tuning methods employing change in input scaling factors. Finally, this dissertation is concluded with numerical simulation of glide-slope capture in windshear demonstrating the robustness of the fuzzy logic based flight control system.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diaz, J. I.; Henry, J.; Ramos, A. M.

We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

PubMed

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Feedforward-Feedback Hybrid Control for Magnetic Shape Memory Alloy Actuators Based on the Krasnosel'skii-Pokrovskii Model

PubMed Central

Zhou, Miaolei; Zhang, Qi; Wang, Jingyuan

2014-01-01

As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system. PMID:24828010

Feedforward-feedback hybrid control for magnetic shape memory alloy actuators based on the Krasnosel'skii-Pokrovskii model.

PubMed

Zhou, Miaolei; Zhang, Qi; Wang, Jingyuan

2014-01-01

As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system.

Via generalized function projective synchronization in nonlinear Schrödinger equation for secure communication

NASA Astrophysics Data System (ADS)

Zhao, L. W.; Du, J. G.; Yin, J. L.

2018-05-01

This paper proposes a novel secured communication scheme in a chaotic system by applying generalized function projective synchronization of the nonlinear Schrödinger equation. This phenomenal approach guarantees a secured and convenient communication. Our study applied the Melnikov theorem with an active control strategy to suppress chaos in the system. The transmitted information signal is modulated into the parameter of the nonlinear Schrödinger equation in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical nonlinear Schrödinger equation with the unknown parameter asymptotically synchronized. The numerical simulation results of our study confirmed the validity, effectiveness and the feasibility of the proposed novel synchronization method and error estimate for a secure communication. The Chaos masking signals of the information communication scheme, further guaranteed a safer and secured information communicated via this approach.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

NASA Astrophysics Data System (ADS)

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

ISS method for coordination control of nonlinear dynamical agents under directed topology.

PubMed

Wang, Xiangke; Qin, Jiahu; Yu, Changbin

2014-10-01

The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.

The U.S. Geological Survey Modular Ground-Water Model - PCGN: A Preconditioned Conjugate Gradient Solver with Improved Nonlinear Control

USGS Publications Warehouse

Naff, Richard L.; Banta, Edward R.

2008-01-01

The preconditioned conjugate gradient with improved nonlinear control (PCGN) package provides addi-tional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. Picard iteration is used to solve nonlinear ground-water flow equations by iteratively solving a linear approximation of the nonlinear equations. The linear solution is provided by means of the preconditioned conjugate gradient algorithm where preconditioning is provided by the modi-fied incomplete Cholesky algorithm. The incomplete Cholesky scheme incorporates two levels of fill, 0 and 1, in which the pivots can be modified so that the row sums of the preconditioning matrix and the original matrix are approximately equal. A relaxation factor is used to implement the modified pivots, which determines the degree of modification allowed. The effects of fill level and degree of pivot modification are briefly explored by means of a synthetic, heterogeneous finite-difference matrix; results are reported in the final section of this report. The preconditioned conjugate gradient method is coupled with Picard iteration so as to efficiently solve the nonlinear equations associated with many ground-water flow problems. The description of this coupling of the linear solver with Picard iteration is a primary concern of this document.

A design methodology for nonlinear systems containing parameter uncertainty: Application to nonlinear controller design

NASA Technical Reports Server (NTRS)

Young, G.

1982-01-01

A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.

Nonlinear identification using a B-spline neural network and chaotic immune approaches

NASA Astrophysics Data System (ADS)

dos Santos Coelho, Leandro; Pessôa, Marcelo Wicthoff

2009-11-01

One of the important applications of B-spline neural network (BSNN) is to approximate nonlinear functions defined on a compact subset of a Euclidean space in a highly parallel manner. Recently, BSNN, a type of basis function neural network, has received increasing attention and has been applied in the field of nonlinear identification. BSNNs have the potential to "learn" the process model from input-output data or "learn" fault knowledge from past experience. BSNN can be used as function approximators to construct the analytical model for residual generation too. However, BSNN is trained by gradient-based methods that may fall into local minima during the learning procedure. When using feed-forward BSNNs, the quality of approximation depends on the control points (knots) placement of spline functions. This paper describes the application of a modified artificial immune network inspired optimization method - the opt-aiNet - combined with sequences generate by Hénon map to provide a stochastic search to adjust the control points of a BSNN. The numerical results presented here indicate that artificial immune network optimization methods are useful for building good BSNN model for the nonlinear identification of two case studies: (i) the benchmark of Box and Jenkins gas furnace, and (ii) an experimental ball-and-tube system.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems.

PubMed

Wu, Chengwei; Liu, Jianxing; Xiong, Yongyang; Wu, Ligang

2017-06-28

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of ''explosion of complexity''. Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

Design of nonlinear PID controller and nonlinear model predictive controller for a continuous stirred tank reactor.

PubMed

Prakash, J; Srinivasan, K

2009-07-01

In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.

Virtual Passive Controller for Robot Systems Using Joint Torque Sensors

NASA Technical Reports Server (NTRS)

Aldridge, Hal A.; Juang, Jer-Nan

1997-01-01

This paper presents a control method based on virtual passive dynamic control that will stabilize a robot manipulator using joint torque sensors and a simple joint model. The method does not require joint position or velocity feedback for stabilization. The proposed control method is stable in the sense of Lyaponov. The control method was implemented on several joints of a laboratory robot. The controller showed good stability robustness to system parameter error and to the exclusion of nonlinear dynamic effects on the joints. The controller enhanced position tracking performance and, in the absence of position control, dissipated joint energy.

Event-Triggered Adaptive Dynamic Programming for Continuous-Time Systems With Control Constraints.

PubMed

Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo

2016-08-31

In this paper, an event-triggered near optimal control structure is developed for nonlinear continuous-time systems with control constraints. Due to the saturating actuators, a nonquadratic cost function is introduced and the Hamilton-Jacobi-Bellman (HJB) equation for constrained nonlinear continuous-time systems is formulated. In order to solve the HJB equation, an actor-critic framework is presented. The critic network is used to approximate the cost function and the action network is used to estimate the optimal control law. In addition, in the proposed method, the control signal is transmitted in an aperiodic manner to reduce the computational and the transmission cost. Both the networks are only updated at the trigger instants decided by the event-triggered condition. Detailed Lyapunov analysis is provided to guarantee that the closed-loop event-triggered system is ultimately bounded. Three case studies are used to demonstrate the effectiveness of the proposed method.

Fuzzy Adaptive Output Feedback Control of Uncertain Nonlinear Systems With Prescribed Performance.

PubMed

Zhang, Jin-Xi; Yang, Guang-Hong

2018-05-01

This paper investigates the tracking control problem for a family of strict-feedback systems in the presence of unknown nonlinearities and immeasurable system states. A low-complexity adaptive fuzzy output feedback control scheme is proposed, based on a backstepping method. In the control design, a fuzzy adaptive state observer is first employed to estimate the unmeasured states. Then, a novel error transformation approach together with a new modification mechanism is introduced to guarantee the finite-time convergence of the output error to a predefined region and ensure the closed-loop stability. Compared with the existing methods, the main advantages of our approach are that: 1) without using extra command filters or auxiliary dynamic surface control techniques, the problem of explosion of complexity can still be addressed and 2) the design procedures are independent of the initial conditions. Finally, two practical examples are performed to further illustrate the above theoretic findings.

Fuzzy chaos control for vehicle lateral dynamics based on active suspension system

NASA Astrophysics Data System (ADS)

Huang, Chen; Chen, Long; Jiang, Haobin; Yuan, Chaochun; Xia, Tian

2014-07-01

The existing research of the active suspension system (ASS) mainly focuses on the different evaluation indexes and control strategies. Among the different components, the nonlinear characteristics of practical systems and control are usually not considered for vehicle lateral dynamics. But the vehicle model has some shortages on tyre model with side-slip angle, road adhesion coefficient, vertical load and velocity. In this paper, the nonlinear dynamic model of lateral system is considered and also the adaptive neural network of tire is introduced. By nonlinear analysis methods, such as the bifurcation diagram and Lyapunov exponent, it has shown that the lateral dynamics exhibits complicated motions with the forward speed. Then, a fuzzy control method is applied to the lateral system aiming to convert chaos into periodic motion using the linear-state feedback of an available lateral force with changing tire load. Finally, the rapid control prototyping is built to conduct the real vehicle test. By comparison of time response diagram, phase portraits and Lyapunov exponents at different work conditions, the results on step input and S-shaped road indicate that the slip angle and yaw velocity of lateral dynamics enter into stable domain and the results of test are consistent to the simulation and verified the correctness of simulation. And the Lyapunov exponents of the closed-loop system are becoming from positive to negative. This research proposes a fuzzy control method which has sufficient suppress chaotic motions as an effective active suspension system.

Using Nonlinearity and Contact Lines to Control Fluid Flow in Microgravity

NASA Technical Reports Server (NTRS)

Perlin, M.; Schultz, W. W.; Bian, X.; Agarwal, M.

2002-01-01

Slug flows in a tube are affected by surface tension and contact lines, especially under microgravity. Numerical analyses and experiments are conducted of slug flows in small-diameter tubes with horizontal, inclined and vertical orientations. A PID-controlled, meter-long platform capable of following specified motions is used. An improved understanding of the contact line boundary condition for steady and unsteady contact-line motion is expected. Lastly, a direct fluid-handling method using nonlinear oscillatory motion of a tube is presented.

Synthesis Methods for Robust Passification and Control

NASA Technical Reports Server (NTRS)

Kelkar, Atul G.; Joshi, Suresh M. (Technical Monitor)

2000-01-01

The research effort under this cooperative agreement has been essentially the continuation of the work from previous grants. The ongoing work has primarily focused on developing passivity-based control techniques for Linear Time-Invariant (LTI) systems. During this period, there has been a significant progress made in the area of passivity-based control of LTI systems and some preliminary results have also been obtained for nonlinear systems, as well. The prior work has addressed optimal control design for inherently passive as well as non- passive linear systems. For exploiting the robustness characteristics of passivity-based controllers the passification methodology was developed for LTI systems that are not inherently passive. Various methods of passification were first proposed in and further developed. The robustness of passification was addressed for multi-input multi-output (MIMO) systems for certain classes of uncertainties using frequency-domain methods. For MIMO systems, a state-space approach using Linear Matrix Inequality (LMI)-based formulation was presented, for passification of non-passive LTI systems. An LMI-based robust passification technique was presented for systems with redundant actuators and sensors. The redundancy in actuators and sensors was used effectively for robust passification using the LMI formulation. The passification was designed to be robust to an interval-type uncertainties in system parameters. The passification techniques were used to design a robust controller for Benchmark Active Control Technology wing under parametric uncertainties. The results on passive nonlinear systems, however, are very limited to date. Our recent work in this area was presented, wherein some stability results were obtained for passive nonlinear systems that are affine in control.

Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method.

PubMed

Zhang, Huaguang; Cui, Lili; Zhang, Xin; Luo, Yanhong

2011-12-01

In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

Robot-Arm Dynamic Control by Computer

NASA Technical Reports Server (NTRS)

Bejczy, Antal K.; Tarn, Tzyh J.; Chen, Yilong J.

1987-01-01

Feedforward and feedback schemes linearize responses to control inputs. Method for control of robot arm based on computed nonlinear feedback and state tranformations to linearize system and decouple robot end-effector motions along each of cartesian axes augmented with optimal scheme for correction of errors in workspace. Major new feature of control method is: optimal error-correction loop directly operates on task level and not on joint-servocontrol level.

Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes

ERIC Educational Resources Information Center

Bussolari, Cori J.; Goodell, Judith A.

2009-01-01

Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…

On discrete control of nonlinear systems with applications to robotics

NASA Technical Reports Server (NTRS)

Eslami, Mansour

1989-01-01

Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.

Control of AUVs using differential flatness theory and the derivative-free nonlinear Kalman Filter

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Raffo, Guilerme

2015-12-01

The paper proposes nonlinear control and filtering for Autonomous Underwater Vessels (AUVs) based on differential flatness theory and on the use of the Derivative-free nonlinear Kalman Filter. First, it is shown that the 6-DOF dynamic model of the AUV is a differentially flat one. This enables its transformation into the linear canonical (Brunovsky) form and facilitates the design of a state feedback controller. A problem that has to be dealt with is the uncertainty about the parameters of the AUV's dynamic model, as well the external perturbations which affect its motion. To cope with this, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. The Kalman Filter-based disturbance observer performs simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics. By estimating such disturbances, their compensation is also succeeded through suitable modification of the feedback control input. The efficiency of the proposed AUV control and estimation scheme is confirmed through simulation experiments.

Model-Free Adaptive Control for Unknown Nonlinear Zero-Sum Differential Game.

PubMed

Zhong, Xiangnan; He, Haibo; Wang, Ding; Ni, Zhen

2018-05-01

In this paper, we present a new model-free globalized dual heuristic dynamic programming (GDHP) approach for the discrete-time nonlinear zero-sum game problems. First, the online learning algorithm is proposed based on the GDHP method to solve the Hamilton-Jacobi-Isaacs equation associated with optimal regulation control problem. By setting backward one step of the definition of performance index, the requirement of system dynamics, or an identifier is relaxed in the proposed method. Then, three neural networks are established to approximate the optimal saddle point feedback control law, the disturbance law, and the performance index, respectively. The explicit updating rules for these three neural networks are provided based on the data generated during the online learning along the system trajectories. The stability analysis in terms of the neural network approximation errors is discussed based on the Lyapunov approach. Finally, two simulation examples are provided to show the effectiveness of the proposed method.

An improved synchronous reference frame current control strategy for a photovoltaic grid-connected inverter under unbalanced and nonlinear load conditions.

PubMed

Naderipour, Amirreza; Asuhaimi Mohd Zin, Abdullah; Bin Habibuddin, Mohd Hafiz; Miveh, Mohammad Reza; Guerrero, Josep M

2017-01-01

In recent years, renewable energy sources have been considered the most encouraging resources for grid and off-grid power generation. This paper presents an improved current control strategy for a three-phase photovoltaic grid-connected inverter (GCI) under unbalanced and nonlinear load conditions. It is challenging to suppress the harmonic content in the output current below a pre-set value in the GCI. It is also difficult to compensate for unbalanced loads even when the grid is under disruption due to total harmonic distortion (THD) and unbalanced loads. The primary advantage and objective of this method is to effectively compensate for the harmonic current content of the grid current and microgrid without the use of any compensation devices, such as active and passive filters. This method leads to a very low THD in both the GCI currents and the current exchanged with the grid. The control approach is designed to control the active and reactive power and harmonic current compensation, and it also corrects the system unbalance. The proposed control method features the synchronous reference frame (SRF) method. Simulation results are presented to demonstrate the effective performance of the proposed method.

An improved synchronous reference frame current control strategy for a photovoltaic grid-connected inverter under unbalanced and nonlinear load conditions

PubMed Central

Naderipour, Amirreza; Asuhaimi Mohd Zin, Abdullah; Bin Habibuddin, Mohd Hafiz; Miveh, Mohammad Reza; Guerrero, Josep M.

2017-01-01

In recent years, renewable energy sources have been considered the most encouraging resources for grid and off-grid power generation. This paper presents an improved current control strategy for a three-phase photovoltaic grid-connected inverter (GCI) under unbalanced and nonlinear load conditions. It is challenging to suppress the harmonic content in the output current below a pre-set value in the GCI. It is also difficult to compensate for unbalanced loads even when the grid is under disruption due to total harmonic distortion (THD) and unbalanced loads. The primary advantage and objective of this method is to effectively compensate for the harmonic current content of the grid current and microgrid without the use of any compensation devices, such as active and passive filters. This method leads to a very low THD in both the GCI currents and the current exchanged with the grid. The control approach is designed to control the active and reactive power and harmonic current compensation, and it also corrects the system unbalance. The proposed control method features the synchronous reference frame (SRF) method. Simulation results are presented to demonstrate the effective performance of the proposed method. PMID:28192436

Stokes polarimetry using analysis of the nonlinear voltage-retardance relationship for liquid-crystal variable retarders

DOE Office of Scientific and Technical Information (OSTI.GOV)

López-Téllez, J. M., E-mail: jmlopez@comunidad.unam.mx; Bruce, N. C.

2014-03-15

We present a method for using liquid-crystal variable retarders (LCVR’s) with continually varying voltage to measure the Stokes vector of a light beam. The LCVR's are usually employed with fixed retardance values due to the nonlinear voltage-retardance behavior that they show. The nonlinear voltage-retardance relationship is first measured and then a linear fit of the known retardance terms to the detected signal is performed. We use known waveplates (half-wave and quarter-wave) as devices to provide controlled polarization states to the Stokes polarimeter and we use the measured Stokes parameters as functions of the orientation of the axes of the waveplatesmore » as an indication of the quality of the polarimeter. Results are compared to a Fourier analysis method that does not take into account the nonlinear voltage-retardance relationship and also to a Fourier analysis method that uses experimental voltage values to give a linear retardance function with time. Also, we present results of simulations for comparison.« less

Sum-of-Squares-Based Region of Attraction Analysis for Gain-Scheduled Three-Loop Autopilot

NASA Astrophysics Data System (ADS)

Seo, Min-Won; Kwon, Hyuck-Hoon; Choi, Han-Lim

2018-04-01

A conventional method of designing a missile autopilot is to linearize the original nonlinear dynamics at several trim points, then to determine linear controllers for each linearized model, and finally implement gain-scheduling technique. The validation of such a controller is often based on linear system analysis for the linear closed-loop system at the trim conditions. Although this type of gain-scheduled linear autopilot works well in practice, validation based solely on linear analysis may not be sufficient to fully characterize the closed-loop system especially when the aerodynamic coefficients exhibit substantial nonlinearity with respect to the flight condition. The purpose of this paper is to present a methodology for analyzing the stability of a gain-scheduled controller in a setting close to the original nonlinear setting. The method is based on sum-of-squares (SOS) optimization that can be used to characterize the region of attraction of a polynomial system by solving convex optimization problems. The applicability of the proposed SOS-based methodology is verified on a short-period autopilot of a skid-to-turn missile.

Enhanced optical nonlinearity and fiber-optical frequency comb controlled by a single atom in a whispering-gallery-mode microtoroid resonator

NASA Astrophysics Data System (ADS)

Li, Jiahua; Zhang, Suzhen; Yu, Rong; Zhang, Duo; Wu, Ying

2014-11-01

Based on a single atom coupled to a fiber-coupled, chip-based microresonator [B. Dayan et al., Science 319, 1062 (2008), 10.1126/science.1152261], we put forward a scheme to generate optical frequency combs at driving laser powers as low as a few nanowatts. Using state-of-the-art experimental parameters, we investigate in detail the influences of different atomic positions and taper-resonator coupling regimes on optical-frequency-comb generation. In addition to numerical simulations demonstrating this effect, a physical explanation of the underlying mechanism is presented. We find that the combination of the atom and the resonator can induce a large third-order nonlinearity which is significantly stronger than Kerr nonlinearity in Kerr frequency combs. Such enhanced nonlinearity can be used to generate optical frequency combs if driven with two continuous-wave control and probe lasers and significantly reduce the threshold of nonlinear optical processes. The comb spacing can be well tuned by changing the frequency beating between the driving control and probe lasers. The proposed method is versatile and can be adopted to different types of resonators, such as microdisks, microspheres, microtoroids or microrings.

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

PubMed Central

Mitran, Sorin M.; Forest, M. Gregory; Yao, Lingxing; Lindley, Brandon; Hill, David B.

2009-01-01

The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior. PMID:20011614

Control of nonlinear flexible space structures

NASA Astrophysics Data System (ADS)

Shi, Jianjun

With the advances made in computer technology and efficiency of numerical algorithms over last decade, the MPC strategies have become quite popular among control community. However, application of MPC or GPC to flexible space structure control has not been explored adequately in the literature. The work presented in this thesis primarily focuses on application of GPC to control of nonlinear flexible space structures. This thesis is particularly devoted to the development of various approximate dynamic models, design and assessment of candidate controllers, and extensive numerical simulations for a realistic multibody flexible spacecraft, namely, Jupiter Icy Moons Orbiter (JIMO)---a Prometheus class of spacecraft proposed by NASA for deep space exploratory missions. A stable GPC algorithm is developed for Multi-Input-Multi-Output (MIMO) systems. An end-point weighting (penalty) is used in the GPC cost function to guarantee the nominal stability of the closed-loop system. A method is given to compute the desired end-point state from the desired output trajectory. The methodologies based on Fake Algebraic Riccati Equation (FARE) and constrained nonlinear optimization, are developed for synthesis of state weighting matrix. This makes this formulation more practical. A stable reconfigurable GPC architecture is presented and its effectiveness is demonstrated on both aircraft as well as spacecraft model. A representative in-orbit maneuver is used for assessing the performance of various control strategies using various design models. Different approximate dynamic models used for analysis include linear single body flexible structure, nonlinear single body flexible structure, and nonlinear multibody flexible structure. The control laws evaluated include traditional GPC, feedback linearization-based GPC (FLGPC), reconfigurable GPC, and nonlinear dissipative control. These various control schemes are evaluated for robust stability and robust performance in the presence of parametric uncertainties and input disturbances. Finally, the conclusions are made with regard to the efficacy of these controllers and potential directions for future research.

Linear parameter varying representations for nonlinear control design

NASA Astrophysics Data System (ADS)

Carter, Lance Huntington

Linear parameter varying (LPV) systems are investigated as a framework for gain-scheduled control design and optimal hybrid control. An LPV system is defined as a linear system whose dynamics depend upon an a priori unknown but measurable exogenous parameter. A gain-scheduled autopilot design is presented for a bank-to-turn (BTT) missile. The method is novel in that the gain-scheduled design does not involve linearizations about operating points. Instead, the missile dynamics are brought to LPV form via a state transformation. This idea is applied to the design of a coupled longitudinal/lateral BTT missile autopilot. The pitch and yaw/roll dynamics are separately transformed to LPV form, where the cross axis states are treated as "exogenous" parameters. These are actually endogenous variables, so such a plant is called "quasi-LPV." Once in quasi-LPV form, a family of robust controllers using mu synthesis is designed for both the pitch and yaw/roll channels, using angle-of-attack and roll rate as the scheduling variables. The closed-loop time response is simulated using the original nonlinear model and also using perturbed aerodynamic coefficients. Modeling and control of engine idle speed is investigated using LPV methods. It is shown how generalized discrete nonlinear systems may be transformed into quasi-LPV form. A discrete nonlinear engine model is developed and expressed in quasi-LPV form with engine speed as the scheduling variable. An example control design is presented using linear quadratic methods. Simulations are shown comparing the LPV based controller performance to that using PID control. LPV representations are also shown to provide a setting for hybrid systems. A hybrid system is characterized by control inputs consisting of both analog signals and discrete actions. A solution is derived for the optimal control of hybrid systems with generalized cost functions. This is shown to be computationally intensive, so a suboptimal strategy is proposed that neglects a subset of possible parameter trajectories. A computational algorithm is constructed for this suboptimal solution applied to a class of linear non-quadratic cost functions.

Learning Sequential Composition Control.

PubMed

Najafi, Esmaeil; Babuska, Robert; Lopes, Gabriel A D

2016-11-01

Sequential composition is an effective supervisory control method for addressing control problems in nonlinear dynamical systems. It executes a set of controllers sequentially to achieve a control specification that cannot be realized by a single controller. As these controllers are designed offline, sequential composition cannot address unmodeled situations that might occur during runtime. This paper proposes a learning approach to augment the standard sequential composition framework by using online learning to handle unforeseen situations. New controllers are acquired via learning and added to the existing supervisory control structure. In the proposed setting, learning experiments are restricted to take place within the domain of attraction (DOA) of the existing controllers. This guarantees that the learning process is safe (i.e., the closed loop system is always stable). In addition, the DOA of the new learned controller is approximated after each learning trial. This keeps the learning process short as learning is terminated as soon as the DOA of the learned controller is sufficiently large. The proposed approach has been implemented on two nonlinear systems: 1) a nonlinear mass-damper system and 2) an inverted pendulum. The results show that in both cases a new controller can be rapidly learned and added to the supervisory control structure.

Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach

NASA Technical Reports Server (NTRS)

Arnett, Timothy; Cook, Brandon; Clark, Matthew A.; Rattan, Kuldip

2017-01-01

While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability.

Model-based Acceleration Control of Turbofan Engines with a Hammerstein-Wiener Representation

NASA Astrophysics Data System (ADS)

Wang, Jiqiang; Ye, Zhifeng; Hu, Zhongzhi; Wu, Xin; Dimirovsky, Georgi; Yue, Hong

2017-05-01

Acceleration control of turbofan engines is conventionally designed through either schedule-based or acceleration-based approach. With the widespread acceptance of model-based design in aviation industry, it becomes necessary to investigate the issues associated with model-based design for acceleration control. In this paper, the challenges for implementing model-based acceleration control are explained; a novel Hammerstein-Wiener representation of engine models is introduced; based on the Hammerstein-Wiener model, a nonlinear generalized minimum variance type of optimal control law is derived; the feature of the proposed approach is that it does not require the inversion operation that usually upsets those nonlinear control techniques. The effectiveness of the proposed control design method is validated through a detailed numerical study.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1981-01-01

Research centered on basic topics in the modeling and feedback control of nonlinear dynamical systems is reported. Of special interest were the following topics: (1) the role of series descriptions, especially insofar as they relate to questions of scheduling, in the control of gas turbine engines; (2) the use of algebraic tensor theory as a technique for parameterizing such descriptions; (3) the relationship between tensor methodology and other parts of the nonlinear literature; (4) the improvement of interactive methods for parameter selection within a tensor viewpoint; and (5) study of feedback gain representation as a counterpart to these modeling and parameterization ideas.

Real-Time Adaptive Control Allocation Applied to a High Performance Aircraft

NASA Technical Reports Server (NTRS)

Davidson, John B.; Lallman, Frederick J.; Bundick, W. Thomas

2001-01-01

Abstract This paper presents the development and application of one approach to the control of aircraft with large numbers of control effectors. This approach, referred to as real-time adaptive control allocation, combines a nonlinear method for control allocation with actuator failure detection and isolation. The control allocator maps moment (or angular acceleration) commands into physical control effector commands as functions of individual control effectiveness and availability. The actuator failure detection and isolation algorithm is a model-based approach that uses models of the actuators to predict actuator behavior and an adaptive decision threshold to achieve acceptable false alarm/missed detection rates. This integrated approach provides control reconfiguration when an aircraft is subjected to actuator failure, thereby improving maneuverability and survivability of the degraded aircraft. This method is demonstrated on a next generation military aircraft Lockheed-Martin Innovative Control Effector) simulation that has been modified to include a novel nonlinear fluid flow control control effector based on passive porosity. Desktop and real-time piloted simulation results demonstrate the performance of this integrated adaptive control allocation approach.

Synthesis of nonlinear frequency responses with experimentally extracted nonlinear modes

NASA Astrophysics Data System (ADS)

Peter, Simon; Scheel, Maren; Krack, Malte; Leine, Remco I.

2018-02-01

Determining frequency response curves is a common task in the vibration analysis of nonlinear systems. Measuring nonlinear frequency responses is often challenging and time consuming due to, e.g., coexisting stable or unstable vibration responses and structure-exciter-interaction. The aim of the current paper is to develop a method for the synthesis of nonlinear frequency responses near an isolated resonance, based on data that can be easily and automatically obtained experimentally. The proposed purely experimental approach relies on (a) a standard linear modal analysis carried out at low vibration levels and (b) a phase-controlled tracking of the backbone curve of the considered forced resonance. From (b), the natural frequency and vibrational deflection shape are directly obtained as a function of the vibration level. Moreover, a damping measure can be extracted by power considerations or from the linear modal analysis. In accordance with the single nonlinear mode assumption, the near-resonant frequency response can then be synthesized using this data. The method is applied to a benchmark structure consisting of a cantilevered beam attached to a leaf spring undergoing large deflections. The results are compared with direct measurements of the frequency response. The proposed approach is fast, robust and provides a good estimate for the frequency response. It is also found that direct frequency response measurement is less robust due to bifurcations and using a sine sweep excitation with a conventional force controller leads to underestimation of maximum vibration response.

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric

2018-01-01

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

Designing torus-doubling solutions to discrete time systems by hybrid projective synchronization

NASA Astrophysics Data System (ADS)

Xie, Hui; Wen, Guilin

2013-11-01

Doubling of torus occurs in high dimensional nonlinear systems, which is related to a certain kind of typical second bifurcations. It is a nontrivial task to create a torus-doubling solution with desired dynamical properties based on the classical bifurcation theories. In this paper, dead-beat hybrid projective synchronization is employed to build a novel method for designing stable torus-doubling solutions into discrete time systems with proper properties to achieve the purpose of utilizing bifurcation solutions as well as avoiding the possible conflict of physical meaning of the created solution. Although anti-controls of bifurcation and chaos synchronizations are two different topics in nonlinear dynamics and control, the results imply that it is possible to develop some new interdisciplinary methods between chaos synchronization and anti-controls of bifurcations.

Adaptive sensor-fault tolerant control for a class of multivariable uncertain nonlinear systems.

PubMed

Khebbache, Hicham; Tadjine, Mohamed; Labiod, Salim; Boulkroune, Abdesselem

2015-03-01

This paper deals with the active fault tolerant control (AFTC) problem for a class of multiple-input multiple-output (MIMO) uncertain nonlinear systems subject to sensor faults and external disturbances. The proposed AFTC method can tolerate three additive (bias, drift and loss of accuracy) and one multiplicative (loss of effectiveness) sensor faults. By employing backstepping technique, a novel adaptive backstepping-based AFTC scheme is developed using the fact that sensor faults and system uncertainties (including external disturbances and unexpected nonlinear functions caused by sensor faults) can be on-line estimated and compensated via robust adaptive schemes. The stability analysis of the closed-loop system is rigorously proven using a Lyapunov approach. The effectiveness of the proposed controller is illustrated by two simulation examples. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Spin-orbit optical cross-phase-modulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brasselet, Etienne

2010-12-15

We show experimentally that optical phase singularities (PSs) can be written and erased, locally and in a controllable manner, into a light beam using the giant Kerr optical nonlinearities of liquid crystals. The method relies on the nonlinear optical spin-orbit coupling experienced by a collimated probe beam when a collinear focused pump beam imprints a radial birefringent pattern into a nematic film. In addition, experimental data are quantitatively described, accounting for the elastic anisotropy of the material and its nonlocal spatial response to the pump light field. Since we show that the optical intensity of a light beam (the 'pump')more » controls the phase of another beam (the 'probe') in a singular fashion (i.e., with the generation of a screw PS) via their interaction in a nonlinear medium that involves spin-orbit coupling, we dubbed such a nonlinear optical process as spin-orbit optical cross-phase-modulation.« less

Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities.

Nonlinear adaptive control of grid-connected three-phase inverters for renewable energy applications

NASA Astrophysics Data System (ADS)

Mahdian-Dehkordi, N.; Namvar, M.; Karimi, H.; Piya, P.; Karimi-Ghartemani, M.

2017-01-01

Distributed generation (DG) units are often interfaced to the main grid using power electronic converters including voltage-source converters (VSCs). A VSC offers dc/ac power conversion, high controllability, and fast dynamic response. Because of nonlinearities, uncertainties, and system parameters' changes involved in the nature of a grid-connected renewable DG system, conventional linear control methods cannot completely and efficiently address all control objectives. In this paper, a nonlinear adaptive control scheme based on adaptive backstepping strategy is presented to control the operation of a grid-connected renewable DG unit. As compared to the popular vector control technique, the proposed controller offers smoother transient responses, and lower level of current distortions. The Lyapunov approach is used to establish global asymptotic stability of the proposed control system. Linearisation technique is employed to develop guidelines for parameters tuning of the controller. Extensive time-domain digital simulations are performed and presented to verify the performance of the proposed controller when employed in a VSC to control the operation of a two-stage DG unit and also that of a single-stage solar photovoltaic system. Desirable and superior performance of the proposed controller is observed.

Sub-optimal control of unsteady boundary layer separation and optimal control of Saltzman-Lorenz model

NASA Astrophysics Data System (ADS)

Sardesai, Chetan R.

The primary objective of this research is to explore the application of optimal control theory in nonlinear, unsteady, fluid dynamical settings. Two problems are considered: (1) control of unsteady boundary-layer separation, and (2) control of the Saltzman-Lorenz model. The unsteady boundary-layer equations are nonlinear partial differential equations that govern the eruptive events that arise when an adverse pressure gradient acts on a boundary layer at high Reynolds numbers. The Saltzman-Lorenz model consists of a coupled set of three nonlinear ordinary differential equations that govern the time-dependent coefficients in truncated Fourier expansions of Rayleigh-Renard convection and exhibit deterministic chaos. Variational methods are used to derive the nonlinear optimal control formulations based on cost functionals that define the control objective through a performance measure and a penalty function that penalizes the cost of control. The resulting formulation consists of the nonlinear state equations, which must be integrated forward in time, and the nonlinear control (adjoint) equations, which are integrated backward in time. Such coupled forward-backward time integrations are computationally demanding; therefore, the full optimal control problem for the Saltzman-Lorenz model is carried out, while the more complex unsteady boundary-layer case is solved using a sub-optimal approach. The latter is a quasi-steady technique in which the unsteady boundary-layer equations are integrated forward in time, and the steady control equation is solved at each time step. Both sub-optimal control of the unsteady boundary-layer equations and optimal control of the Saltzman-Lorenz model are found to be successful in meeting the control objectives for each problem. In the case of boundary-layer separation, the control results indicate that it is necessary to eliminate the recirculation region that is a precursor to the unsteady boundary-layer eruptions. In the case of the Saltzman-Lorenz model, it is possible to control the system about either of the two unstable equilibrium points representing clockwise and counterclockwise rotation of the convection roles in a parameter regime for which the uncontrolled solution would exhibit deterministic chaos.

Analysis of Nonlinear Periodic and Aperiodic Media: Application to Optical Logic Gates

NASA Astrophysics Data System (ADS)

Yu, Yisheng

This dissertation is about the analysis of nonlinear periodic and aperiodic media and their application to the design of intensity controlled all optical logic gates: AND, OR, and NOT. A coupled nonlinear differential equation that characterizes the electromagnetic wave propagation in a nonlinear periodic (and aperiodic) medium has been derived from the first principle. The equations are general enough that it reflects the effect of transverse modal fields and can be used to analyze both co-propagating and counter propagating waves. A numerical technique based on the finite differences method and absorbing boundary condition has been developed to solve the coupled differential equations here. The numerical method is simple and accurate. Unlike the method based on characteristics that has been reported in the literature, this method does not involve integration and step sizes of time and space coordinates are decoupled. The decoupling provides independent choice for time and space step sizes. The concept of "gap soliton" has also been re-examined. The dissertation consists of four manuscripts. Manuscript I reports on the design of all optical logic gates: AND, OR, and NOT based on the bistability property of nonlinear periodic and aperiodic waveguiding structures. The functioning of the logic gates has been shown by analysis. The numerical technique that has been developed to solve the nonlinear differential equations are addressed in manuscript II. The effect of transverse modal fields on the bistable property of nonlinear periodic medium is reported in manuscript III. The concept of "gap soliton" that are generated in a nonlinear periodic medium has been re-examined. The details on the finding of the re-examination are discussed in manuscript IV.

Comparison of some optimal control methods for the design of turbine blades

NASA Technical Reports Server (NTRS)

Desilva, B. M. E.; Grant, G. N. C.

1977-01-01

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Spacecraft nonlinear control

NASA Technical Reports Server (NTRS)

Sheen, Jyh-Jong; Bishop, Robert H.

1992-01-01

The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.

A fuzzy controller with nonlinear control rules is the sum of a global nonlinear controller and a local nonlinear PI-like controller

NASA Technical Reports Server (NTRS)

Ying, Hao

1993-01-01

The fuzzy controllers studied in this paper are the ones that employ N trapezoidal-shaped members for input fuzzy sets, Zadeh fuzzy logic and a centroid defuzzification algorithm for output fuzzy set. The author analytically proves that the structure of the fuzzy controllers is the sum of a global nonlinear controller and a local nonlinear proportional-integral-like controller. If N approaches infinity, the global controller becomes a nonlinear controller while the local controller disappears. If linear control rules are used, the global controller becomes a global two-dimensional multilevel relay which approaches a global linear proportional-integral (PI) controller as N approaches infinity.

Nonlinear magneto-plasmonics

DOE PAGES

Zheng, Wei; Liu, Xiao; Hanbicki, Aubrey T.; ...

2015-10-19

Nonlinear magneto-plasmonics (NMP) describes systems where nonlinear optics, magnetics and plasmonics are all involved. In such systems, nonlinear magneto-optical Kerr effect (nonlinear MOKE) plays an important role as a characterization method, and Surface Plasmons (SPs) work as catalyst to induce many new effects. Magnetization-induced second-harmonic generation (MSHG) is the major nonlinear magneto-optical process involved. The new effects include enhanced MSHG, controlled and enhanced magnetic contrast, etc. Nanostructures such as thin films, nanoparticles, nanogratings, and nanoarrays are critical for the excitation of SPs, which makes NMP an interdisciplinary research field in nanoscience and nanotechnology. In this review article, we organize recentmore » work in this field into two categories: surface plasmon polaritons (SPPs) representing propagating surface plasmons, and localized surface plasmons (LSPs), also called particle plasmons. We review the structures, experiments, findings, and the applications of NMP from various groups.« less

Nonlinear Control Systems

DTIC Science & Technology

2009-11-18

J.M. Schumacher, Finite -dimensional regulators for a class of infinite dimensional systems . Systems and Control Letters, 3 (1983), 7-12. [39J J.M...for the control of certain examples or system classes us- ing particular feedback design methods ([20, 21, 16, 17, 19, 18]). Still, the control of...long time existence and asymptotic behavior for certain examples or system classes using particular feedback design methods (see, e.g., [20, 21, 16, 17

Generalized Predictive and Neural Generalized Predictive Control of Aerospace Systems

NASA Technical Reports Server (NTRS)

Kelkar, Atul G.

2000-01-01

The research work presented in this thesis addresses the problem of robust control of uncertain linear and nonlinear systems using Neural network-based Generalized Predictive Control (NGPC) methodology. A brief overview of predictive control and its comparison with Linear Quadratic (LQ) control is given to emphasize advantages and drawbacks of predictive control methods. It is shown that the Generalized Predictive Control (GPC) methodology overcomes the drawbacks associated with traditional LQ control as well as conventional predictive control methods. It is shown that in spite of the model-based nature of GPC it has good robustness properties being special case of receding horizon control. The conditions for choosing tuning parameters for GPC to ensure closed-loop stability are derived. A neural network-based GPC architecture is proposed for the control of linear and nonlinear uncertain systems. A methodology to account for parametric uncertainty in the system is proposed using on-line training capability of multi-layer neural network. Several simulation examples and results from real-time experiments are given to demonstrate the effectiveness of the proposed methodology.

Nonlinear Dynamics and Control of Flexible Structures

DTIC Science & Technology

1991-03-01

of which might be used for space applications. This project was a collaborative one involving structural, electrical and mechanical engineers and...methods for vibration analysis and new models to analyze chaotic dynamics in nonlinear structures with large deformations and friction forces. Finally... electrical and mechanical engineers and resulted in nine doctoral dissertations and two masters theses wholly or partially supported by this grant

Elegant anti-disturbance control for discrete-time stochastic systems with nonlinearity and multiple disturbances

NASA Astrophysics Data System (ADS)

Wei, Xinjiang; Sun, Shixiang

2018-03-01

An elegant anti-disturbance control (EADC) strategy for a class of discrete-time stochastic systems with both nonlinearity and multiple disturbances, which include the disturbance with partially known information and a sequence of random vectors, is proposed in this paper. A stochastic disturbance observer is constructed to estimate the disturbance with partially known information, based on which, an EADC scheme is proposed by combining pole placement and linear matrix inequality methods. It is proved that the two different disturbances can be rejected and attenuated, and the corresponding desired performances can be guaranteed for discrete-time stochastic systems with known and unknown nonlinear dynamics, respectively. Simulation examples are given to demonstrate the effectiveness of the proposed schemes compared with some existing results.

Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification

PubMed Central

Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.

2016-01-01

The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities. PMID:27108814

Nonlinear Characterization of Half and Full Wavelength Power Ultrasonic Devices

NASA Astrophysics Data System (ADS)

Mathieson, Andrew; Cerisola, Niccolò; Cardoni, Andrea

It is well known that power ultrasonic devices whilst driven under elevated excitation levels exhibit nonlinear behaviors. If no attempt is made to understand and subsequently control these behaviors, these devices can exhibit poor performance or even suffer premature failure. This paper presents an experimental method for the dynamic characterization of a commercial ultrasonic transducer for bone cutting applications (Piezosurgery® Device) operated together with a variety of rod horns that are tuned to operate in a longitudinal mode of vibration. Near resonance responses, excited via a burst sine sweep method were used to identify nonlinear responses exhibited by the devices, while experimental modal analysis was performed to identify the modal parameters of the longitudinal modes of vibration of the assemblies between 0-80 kHz. This study tries to provide an understanding of the effects that geometry and material choices may have on the nonlinear behavior of a tuned device.

Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

2018-03-01

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction.

PubMed

Wei, Jianming; Zhang, Youan; Sun, Meimei; Geng, Baoliang

2017-09-01

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Constrained tracking control for nonlinear systems.

PubMed

Khani, Fatemeh; Haeri, Mohammad

2017-09-01

This paper proposes a tracking control strategy for nonlinear systems without needing a prior knowledge of the reference trajectory. The proposed method consists of a set of local controllers with appropriate overlaps in their stability regions and an on-line switching strategy which implements these controllers and uses some augmented intermediate controllers to ensure steering the system states to the desired set points without needing to redesign the controller for each value of set point changes. The proposed approach provides smooth transient responses despite switching among the local controllers. It should be mentioned that the stability regions of the proposed controllers could be estimated off-line for a range of set-point changes. The efficiencies of the proposed algorithm are illustrated via two example simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Sliding mode control of magnetic suspensions for precision pointing and tracking applications

NASA Technical Reports Server (NTRS)

Misovec, Kathleen M.; Flynn, Frederick J.; Johnson, Bruce G.; Hedrick, J. Karl

1991-01-01

A recently developed nonlinear control method, sliding mode control, is examined as a means of advancing the achievable performance of space-based precision pointing and tracking systems that use nonlinear magnetic actuators. Analytic results indicate that sliding mode control improves performance compared to linear control approaches. In order to realize these performance improvements, precise knowledge of the plant is required. Additionally, the interaction of an estimating scheme and the sliding mode controller has not been fully examined in the literature. Estimation schemes were designed for use with this sliding mode controller that do not seriously degrade system performance. The authors designed and built a laboratory testbed to determine the feasibility of utilizing sliding mode control in these types of applications. Using this testbed, experimental verification of the authors' analyses is ongoing.

Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode

NASA Astrophysics Data System (ADS)

Zhang, Wei-Ya; Li, Yong-Li; Chang, Xiao-Yong; Wang, Nan

2013-09-01

In this paper, the dynamic behavior analysis of the electromechanical coupling characteristics of a flywheel energy storage system (FESS) with a permanent magnet (PM) brushless direct-current (DC) motor (BLDCM) is studied. The Hopf bifurcation theory and nonlinear methods are used to investigate the generation process and mechanism of the coupled dynamic behavior for the average current controlled FESS in the charging mode. First, the universal nonlinear dynamic model of the FESS based on the BLDCM is derived. Then, for a 0.01 kWh/1.6 kW FESS platform in the Key Laboratory of the Smart Grid at Tianjin University, the phase trajectory of the FESS from a stable state towards chaos is presented using numerical and stroboscopic methods, and all dynamic behaviors of the system in this process are captured. The characteristics of the low-frequency oscillation and the mechanism of the Hopf bifurcation are investigated based on the Routh stability criterion and nonlinear dynamic theory. It is shown that the Hopf bifurcation is directly due to the loss of control over the inductor current, which is caused by the system control parameters exceeding certain ranges. This coupling nonlinear process of the FESS affects the stability of the motor running and the efficiency of energy transfer. In this paper, we investigate into the effects of control parameter change on the stability and the stability regions of these parameters based on the averaged-model approach. Furthermore, the effect of the quantization error in the digital control system is considered to modify the stability regions of the control parameters. Finally, these theoretical results are verified through platform experiments.

Loudspeakers: Modeling and control

NASA Astrophysics Data System (ADS)

Al-Ali, Khalid Mohammad

This thesis documented a comprehensive study of loudspeaker modeling and control. A lumped-parameter model for a voice-coil loudspeaker in a vented enclosure was presented that derived from a consideration of physical principles. In addition, a low-frequency (20 Hz to 100 Hz), feedback control method designed to improve the nonlinear performance of the loudspeaker and a suitable performance measure for use in design and evaluation were proposed. Data from experiments performed on a variety of actual loudspeakers confirmed the practicality of the theory developed in this work. The lumped-parameter loudspeaker model, although simple, captured much of the nonlinear behavior of the loudspeaker. In addition, the model formulation allowed a straightforward application of modern control system methods and lent itself well to modern parametric identification techniques. The nonlinear performance of the loudspeaker system was evaluated using a suitable distortion measure that was proposed and compared with other distortion measures currently used in practice. Furthermore, the linearizing effect of feedback using a linear controller (both static and dynamic) was studied on a class of nonlinear systems. The results illustrated that the distortion reduction was potentially significant and a useful upper bound on the closed-loop distortion was found based on the sensitivity function of the system's linearization. A feedback scheme based on robust control theory was chosen for application to the loudspeaker system. Using the pressure output of the loudspeaker system for feedback, the technique offered significant advantages over those previously attempted. Illustrative examples were presented that proved the applicability of the theory developed in this dissertation to a variety of loudspeaker systems. The examples included a vented loudspeaker model and actual loudspeakers enclosed in both vented and sealed configurations. In each example, predictable and measurable distortion reduction at the output of the closed-loop system was recorded.

Fuzzy self-learning control for magnetic servo system

NASA Technical Reports Server (NTRS)

Tarn, J. H.; Kuo, L. T.; Juang, K. Y.; Lin, C. E.

1994-01-01

It is known that an effective control system is the key condition for successful implementation of high-performance magnetic servo systems. Major issues to design such control systems are nonlinearity; unmodeled dynamics, such as secondary effects for copper resistance, stray fields, and saturation; and that disturbance rejection for the load effect reacts directly on the servo system without transmission elements. One typical approach to design control systems under these conditions is a special type of nonlinear feedback called gain scheduling. It accommodates linear regulators whose parameters are changed as a function of operating conditions in a preprogrammed way. In this paper, an on-line learning fuzzy control strategy is proposed. To inherit the wealth of linear control design, the relations between linear feedback and fuzzy logic controllers have been established. The exercise of engineering axioms of linear control design is thus transformed into tuning of appropriate fuzzy parameters. Furthermore, fuzzy logic control brings the domain of candidate control laws from linear into nonlinear, and brings new prospects into design of the local controllers. On the other hand, a self-learning scheme is utilized to automatically tune the fuzzy rule base. It is based on network learning infrastructure; statistical approximation to assign credit; animal learning method to update the reinforcement map with a fast learning rate; and temporal difference predictive scheme to optimize the control laws. Different from supervised and statistical unsupervised learning schemes, the proposed method learns on-line from past experience and information from the process and forms a rule base of an FLC system from randomly assigned initial control rules.

Proceedings of the Non-Linear Aero Prediction Requirements Workshop

NASA Technical Reports Server (NTRS)

Logan, Michael J. (Editor)

1994-01-01

The purpose of the Non-Linear Aero Prediction Requirements Workshop, held at NASA Langley Research Center on 8-9 Dec. 1993, was to identify and articulate requirements for non-linear aero prediction capabilities during conceptual/preliminary design. The attendees included engineers from industry, government, and academia in a variety of aerospace disciplines, such as advanced design, aerodynamic performance analysis, aero methods development, flight controls, and experimental and theoretical aerodynamics. Presentations by industry and government organizations were followed by panel discussions. This report contains copies of the presentations and the results of the panel discussions.

Nonlinear integrable model of Frenkel-like excitations on a ribbon of triangular lattice

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2015-03-01

Following the considerable progress in nanoribbon technology, we propose to model the nonlinear Frenkel-like excitations on a triangular-lattice ribbon by the integrable nonlinear ladder system with the background-controlled intersite resonant coupling. The system of interest arises as a proper reduction of first general semidiscrete integrable system from an infinite hierarchy. The most significant local conservation laws related to the first general integrable system are found explicitly in the framework of generalized recursive approach. The obtained general local densities are equally applicable to any general semidiscrete integrable system from the respective infinite hierarchy. Using the recovered second densities, the Hamiltonian formulation of integrable nonlinear ladder system with background-controlled intersite resonant coupling is presented. In doing so, the relevant Poisson structure turns out to be essentially nontrivial. The Darboux transformation scheme as applied to the first general semidiscrete system is developed and the key role of Bäcklund transformation in justification of its self-consistency is pointed out. The spectral properties of Darboux matrix allow to restore the whole Darboux matrix thus ensuring generation one more soliton as compared with a priori known seed solution of integrable nonlinear system. The power of Darboux-dressing method is explicitly demonstrated in generating the multicomponent one-soliton solution to the integrable nonlinear ladder system with background-controlled intersite resonant coupling.

Neural control of fast nonlinear systems--application to a turbocharged SI engine with VCT.

PubMed

Colin, Guillaume; Chamaillard, Yann; Bloch, Gérard; Corde, Gilles

2007-07-01

Today, (engine) downsizing using turbocharging appears as a major way in reducing fuel consumption and pollutant emissions of spark ignition (SI) engines. In this context, an efficient control of the air actuators [throttle, turbo wastegate, and variable camshaft timing (VCT)] is needed for engine torque control. This paper proposes a nonlinear model-based control scheme which combines separate, but coordinated, control modules. Theses modules are based on different control strategies: internal model control (IMC), model predictive control (MPC), and optimal control. It is shown how neural models can be used at different levels and included in the control modules to replace physical models, which are too complex to be online embedded, or to estimate nonmeasured variables. The results obtained from two different test benches show the real-time applicability and good control performance of the proposed methods.

Distributed ESO based cooperative tracking control for high-order nonlinear multiagent systems with lumped disturbance and application in multi flight simulators systems.

PubMed

Cong, Zhang

2018-03-01

Based on extended state observer, a novel and practical design method is developed to solve the distributed cooperative tracking problem of higher-order nonlinear multiagent systems with lumped disturbance in a fixed communication topology directed graph. The proposed method is designed to guarantee all the follower nodes ultimately and uniformly converge to the leader node with bounded residual errors. The leader node, modeled as a higher-order non-autonomous nonlinear system, acts as a command generator giving commands only to a small portion of the networked follower nodes. Extended state observer is used to estimate the local states and lumped disturbance of each follower node. Moreover, each distributed controller can work independently only requiring the relative states and/or the estimated relative states information between itself and its neighbors. Finally an engineering application of multi flight simulators systems is demonstrated to test and verify the effectiveness of the proposed algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear dynamical systems for theory and research in ergonomics.

PubMed

Guastello, Stephen J

2017-02-01

Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn; Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin; Zhang, W. D., E-mail: zhangwenditju@126.com

2014-03-15

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposedmore » in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.« less

A sequential linear optimization approach for controller design

NASA Technical Reports Server (NTRS)

Horta, L. G.; Juang, J.-N.; Junkins, J. L.

1985-01-01

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.

PubMed

Herzallah, Randa

2015-03-01

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained. Copyright © 2014 Elsevier Ltd. All rights reserved.

Control Relevant Modeling and Design of Scramjet-Powered Hypersonic Vehicles

NASA Astrophysics Data System (ADS)

Dickeson, Jeffrey James

This report provides an overview of scramjet-powered hypersonic vehicle modeling and control challenges. Such vehicles are characterized by unstable non-minimum phase dynamics with significant coupling and low thrust margins. Recent trends in hypersonic vehicle research are summarized. To illustrate control relevant design issues and tradeoffs, a generic nonlinear 3DOF longitudinal dynamics model capturing aero-elastic-propulsive interactions for wedge-shaped vehicle is used. Limitations of the model are discussed and numerous modifications have been made to address control relevant needs. Two different baseline configurations are examined over a two-stage to orbit ascent trajectory. The report highlights how vehicle level-flight static (trim) and dynamic properties change over the trajectory. Thermal choking constraints are imposed on control system design as a direct consequence of having a finite FER margin. The implication of this state-dependent nonlinear FER margin constraint, the right half plane (RHP) zero, and lightly damped flexible modes, on control system bandwidth (BW) and FPA tracking has been discussed. A control methodology has been proposed that addresses the above dynamics while providing some robustness to modeling uncertainty. Vehicle closure (the ability to fly a trajectory segment subject to constraints) is provided through a proposed vehicle design methodology. The design method attempts to use open loop metrics whenever possible to design the vehicle. The design method is applied to a vehicle/control law closed loop nonlinear simulation for validation. The 3DOF longitudinal modeling results are validated against a newly released NASA 6DOF code.

Decentralized Interleaving of Paralleled Dc-Dc Buck Converters: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Brian B; Rodriguez, Miguel; Sinha, Mohit

We present a decentralized control strategy that yields switch interleaving among parallel connected dc-dc buck converters without communication. The proposed method is based on the digital implementation of the dynamics of a nonlinear oscillator circuit as the controller. Each controller is fully decentralized, i.e., it only requires the locally measured output current to synthesize the pulse width modulation (PWM) carrier waveform. By virtue of the intrinsic electrical coupling between converters, the nonlinear oscillator-based controllers converge to an interleaved state with uniform phase-spacing across PWM carriers. To the knowledge of the authors, this work represents the first fully decentralized strategy formore » switch interleaving of paralleled dc-dc buck converters.« less

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

NASA Technical Reports Server (NTRS)

Whiffen, Gregory J.

2006-01-01

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

Investigation of chaos and its control in a Duffing-type nano beam model

NASA Astrophysics Data System (ADS)

Jha, Abhishek Kumar; Dasgupta, Sovan Sundar

2018-04-01

The prediction of chaos of a nano beam with harmonic excitation is investigated. Using the Galerkin method the nonlinear lumped model of a clamped-clamped nano beam with nonlinear cubic stiffness is obtained. This is a Duffing system with hardening type of nonlinearity. Based on the energy function and the phase portrait of the system, the resonator dynamics is categorized into four situations in which Using Malnikov function, an analytical criterion for homoclinic intersection in the form of inequality is written in terms of the system parameters. A numerical study including largest lyapunov exponent, Poincare diagram and phase portrait confirm the analytical prediction of chaos and effect of forcing amplitude. Subsequently, a linear velocity feedback controller is introduced into the system to successfully control the chaotic motion of the system at a faster rate at larger value of gain parameter.

Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints

NASA Astrophysics Data System (ADS)

Yang, Xiong; Liu, Derong; Wang, Ding

2014-03-01

In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.

Idempotent Methods for Continuous Time Nonlinear Stochastic Control

DTIC Science & Technology

2012-09-13

AND ADDRESS(ES) dba AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Stochastech Corporation dba Tempest Technologies 8939 S...Stochastic Control Problems Ben G. Fitzpatrick Tempest Technologies 8939 S. Sepulveda Boulevard, Suite 506 Los Angeles, CA 90045 Sponsored by

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Modeling and Designing of A Nonlineartemperature-Humidity Controller Using Inmushroom-Drying Machine

NASA Astrophysics Data System (ADS)

Wu, Xiuhua; Luo, Haiyan; Shi, Minhui

Drying-process of many kinds of farm produce in a close room, such as mushroom-drying machine, is generally a complicated nonlinear and timedelay cause, in which the temperature and the humidity are the main controlled elements. The accurate controlling of the temperature and humidity is always an interesting problem. It's difficult and very important to make a more accurate mathematical model about the varying of the two. A math model was put forward after considering many aspects and analyzing the actual working circumstance in this paper. Form the model it can be seen that the changes of temperature and humidity in drying machine are not simple linear but an affine nonlinear process. Controlling the process exactly is the key that influences the quality of the dried mushroom. In this paper, the differential geometry theories and methods are used to analyze and solve the model of these smallenvironment elements. And at last a kind of nonlinear controller which satisfied the optimal quadratic performance index is designed. It can be proved more feasible and practical than the conventional controlling.

Model Predictive Control of the Current Profile and the Internal Energy of DIII-D Plasmas

NASA Astrophysics Data System (ADS)

Lauret, M.; Wehner, W.; Schuster, E.

2015-11-01

For efficient and stable operation of tokamak plasmas it is important that the current density profile and the internal energy are jointly controlled by using the available heating and current-drive (H&CD) sources. The proposed approach is a version of nonlinear model predictive control in which the input set is restricted in size by the possible combinations of the H&CD on/off states. The controller uses real-time predictions over a receding-time horizon of both the current density profile (nonlinear partial differential equation) and the internal energy (nonlinear ordinary differential equation) evolutions. At every time instant the effect of every possible combination of H&CD sources on the current profile and internal energy is evaluated over the chosen time horizon. The combination that leads to the best result, which is assessed by a user-defined cost function, is then applied up until the next time instant. Simulations results based on a control-oriented transport code illustrate the effectiveness of the proposed control method. Supported by the US DOE under DE-FC02-04ER54698 & DE-SC0010661.

Rapid assessment of nonlinear optical propagation effects in dielectrics

PubMed Central

Hoyo, J. del; de la Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process. PMID:25564243

Rapid assessment of nonlinear optical propagation effects in dielectrics.

PubMed

del Hoyo, J; de la Cruz, A Ruiz; Grace, E; Ferrer, A; Siegel, J; Pasquazi, A; Assanto, G; Solis, J

2015-01-07

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Rapid assessment of nonlinear optical propagation effects in dielectrics

NASA Astrophysics Data System (ADS)

Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

A nonlinear optimal control approach to stabilization of a macroeconomic development model

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.

Decentralized Interleaving of Paralleled Dc-Dc Buck Converters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Brian B; Rodriguez, Miguel; Sinha, Mohit

We present a decentralized control strategy that yields switch interleaving among parallel-connected dc-dc buck converters. The proposed method is based on the digital implementation of the dynamics of a nonlinear oscillator circuit as the controller. Each controller is fully decentralized, i.e., it only requires the locally measured output current to synthesize the pulse width modulation (PWM) carrier waveform and no communication between different controllers is needed. By virtue of the intrinsic electrical coupling between converters, the nonlinear oscillator-based controllers converge to an interleaved state with uniform phase-spacing across PWM carriers. To the knowledge of the authors, this work presents themore » first fully decentralized strategy for switch interleaving in paralleled dc-dc buck converters.« less

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

NASA Technical Reports Server (NTRS)

Wen, J. T.; Bayard, D. S.

1987-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.

Classifying depression patients and normal subjects using machine learning techniques and nonlinear features from EEG signal.

PubMed

Hosseinifard, Behshad; Moradi, Mohammad Hassan; Rostami, Reza

2013-03-01

Diagnosing depression in the early curable stages is very important and may even save the life of a patient. In this paper, we study nonlinear analysis of EEG signal for discriminating depression patients and normal controls. Forty-five unmedicated depressed patients and 45 normal subjects were participated in this study. Power of four EEG bands and four nonlinear features including detrended fluctuation analysis (DFA), higuchi fractal, correlation dimension and lyapunov exponent were extracted from EEG signal. For discriminating the two groups, k-nearest neighbor, linear discriminant analysis and logistic regression as the classifiers are then used. Highest classification accuracy of 83.3% is obtained by correlation dimension and LR classifier among other nonlinear features. For further improvement, all nonlinear features are combined and applied to classifiers. A classification accuracy of 90% is achieved by all nonlinear features and LR classifier. In all experiments, genetic algorithm is employed to select the most important features. The proposed technique is compared and contrasted with the other reported methods and it is demonstrated that by combining nonlinear features, the performance is enhanced. This study shows that nonlinear analysis of EEG can be a useful method for discriminating depressed patients and normal subjects. It is suggested that this analysis may be a complementary tool to help psychiatrists for diagnosing depressed patients. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Optical Quasi-Soliton Solutions for the Cubic-Quintic Nonlinear SCHRÖDINGER Equation with Variable Coefficients

NASA Astrophysics Data System (ADS)

Yang, Qin; Zhang, Jie-Fang

Optical quasi-soliton solutions for the cubic-quintic nonlinear Schrödinger equation (CQNLSE) with variable coefficients are considered. Based on the extended tanh-function method, we not only successfully obtained bright and dark quasi-soliton solutions, but also obtained the kink quasi-soliton solutions under certain parametric conditions. We conclude that the quasi-solitons induced by the combined effects of the group velocity dispersion (GVD) distribution, the nonlinearity distribution, higher-order nonlinearity distribution, and the amplification or absorption coefficient are quite different from those of the solitons induced only by the combined effects of the GVD, the nonlinearity distribution, and the amplification or absorption coefficient without considering the higher-order nonlinearity distribution (i.e. α(z)=0). Furthermore, we choose appropriate optical fiber parameters D(z) and R(z) to control the velocity of quasi-soliton and time shift, and discuss the evolution behavior of the special quasi-soliton.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

NASA Astrophysics Data System (ADS)

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-05-01

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m-3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

A robust direct-integration method for rotorcraft maneuver and periodic response

NASA Technical Reports Server (NTRS)

Panda, Brahmananda

1992-01-01

The Newmark-Beta method and the Newton-Raphson iteration scheme are combined to develop a direct-integration method for evaluating the maneuver and periodic-response expressions for rotorcraft. The method requires the generation of Jacobians and includes higher derivatives in the formulation of the geometric stiffness matrix to enhance the convergence of the system. The method leads to effective convergence with nonlinear structural dynamics and aerodynamic terms. Singularities in the matrices can be addressed with the method as they arise from a Lagrange multiplier approach for coupling equations with nonlinear constraints. The method is also shown to be general enough to handle singularities from quasisteady control-system models. The method is shown to be more general and robust than the similar 2GCHAS method for analyzing rotorcraft dynamics.

Adaptive non-predictor control of lower triangular uncertain nonlinear systems with an unknown time-varying delay in the input

NASA Astrophysics Data System (ADS)

Koo, Min-Sung; Choi, Ho-Lim

2018-01-01

In this paper, we consider a control problem for a class of uncertain nonlinear systems in which there exists an unknown time-varying delay in the input and lower triangular nonlinearities. Usually, in the existing results, input delays have been coupled with feedforward (or upper triangular) nonlinearities; in other words, the combination of lower triangular nonlinearities and input delay has been rare. Motivated by the existing controller for input-delayed chain of integrators with nonlinearity, we show that the control of input-delayed nonlinear systems with two particular types of lower triangular nonlinearities can be done. As a control solution, we propose a newly designed feedback controller whose main features are its dynamic gain and non-predictor approach. Three examples are given for illustration.

Nonlinear Control of Large Disturbances in Magnetic Bearing Systems

NASA Technical Reports Server (NTRS)

Jiang, Yuhong; Zmood, R. B.

1996-01-01

In this paper, the nonlinear operation of magnetic bearing control methods is reviewed. For large disturbances, the effects of displacement constraints and power amplifier current and di/dt limits on bearing control system performance are analyzed. The operation of magnetic bearings exhibiting self-excited large scale oscillations have been studied both experimentally and by simulation. The simulation of the bearing system has been extended to include the effects of eddy currents in the actuators, so as to improve the accuracy of the simulation results. The results of these experiments and simulations are compared, and some useful conclusions are drawn for improving bearing system robustness.

Materials for Adaptive Structural Acoustic Control. Volume 2

DTIC Science & Technology

1994-04-11

Cross. Effects of Electrodes and Elecu’oding Methods on Fatigue Behavior in Ferroelectric Materials. Ferroelectrics: Proceedings of IMF8, Gaithersburg...describe the linear piezoelectric behavior of ferroelectric ceramics. We have generalized this model to describe the nonlinear effects resulting from...report some of the nonlinear effects under resonant conditions for a PZT-501A ceramic. Figure 8 shows the complex admittance circles at different

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

NASA Astrophysics Data System (ADS)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Leake, R. J.; Sain, M. K.

1978-01-01

General goals of the research were classified into two categories. The first category involves the use of modern multivariable frequency domain methods for control of engine models in the neighborhood of a quiescent point. The second category involves the use of nonlinear modelling and optimization techniques for control of engine models over a more extensive part of the flight envelope. In the frequency domain category, works were published in the areas of low-interaction design, polynomial design, and multiple setpoint studies. A number of these ideas progressed to the point at which they are starting to attract practical interest. In the nonlinear category, advances were made both in engine modelling and in the details associated with software for determination of time optimal controls. Nonlinear models for a two spool turbofan engine were expanded and refined; and a promising new approach to automatic model generation was placed under study. A two time scale scheme was developed to do two-dimensional dynamic programming, and an outward spiral sweep technique has greatly speeded convergence times in time optimal calculations.

Improved prescribed performance control for air-breathing hypersonic vehicles with unknown deadzone input nonlinearity.

PubMed

Wang, Yingyang; Hu, Jianbo

2018-05-19

An improved prescribed performance controller is proposed for the longitudinal model of an air-breathing hypersonic vehicle (AHV) subject to uncertain dynamics and input nonlinearity. Different from the traditional non-affine model requiring non-affine functions to be differentiable, this paper utilizes a semi-decomposed non-affine model with non-affine functions being locally semi-bounded and possibly in-differentiable. A new error transformation combined with novel prescribed performance functions is proposed to bypass complex deductions caused by conventional error constraint approaches and circumvent high frequency chattering in control inputs. On the basis of backstepping technique, the improved prescribed performance controller with low structural and computational complexity is designed. The methodology guarantees the altitude and velocity tracking error within transient and steady state performance envelopes and presents excellent robustness against uncertain dynamics and deadzone input nonlinearity. Simulation results demonstrate the efficacy of the proposed method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Phase walk analysis of leptokurtic time series.

PubMed

Schreiber, Korbinian; Modest, Heike I; Räth, Christoph

2018-06-01

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases. The method, being called phase walk analysis, is based on well established measures from random walk analysis, which are now applied to the unwrapped Fourier phases of time series. We provide an analytical description of its functionality and demonstrate its capabilities on systematically controlled leptokurtic noise. Hereby, we investigate the properties of leptokurtic time series and their influence on the Fourier phases of time series. The phase walk analysis is applied to measured and simulated intermittent time series, whose probability density distribution is approximated by power laws. We use the day-to-day returns of the Dow-Jones industrial average, a synthetic time series with tailored nonlinearities mimicing the power law behavior of the Dow-Jones and the acceleration of the wind at an Atlantic offshore site. Testing for nonlinearities by means of surrogates shows that the new method yields strong significances for nonlinear behavior. Due to the drastically decreased computing time as compared to embedding space methods, the number of surrogate realizations can be increased by orders of magnitude. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities.

Robust gaze-steering of an active vision system against errors in the estimated parameters

NASA Astrophysics Data System (ADS)

Han, Youngmo

2015-01-01

Gaze-steering is often used to broaden the viewing range of an active vision system. Gaze-steering procedures are usually based on estimated parameters such as image position, image velocity, depth and camera calibration parameters. However, there may be uncertainties in these estimated parameters because of measurement noise and estimation errors. In this case, robust gaze-steering cannot be guaranteed. To compensate for such problems, this paper proposes a gaze-steering method based on a linear matrix inequality (LMI). In this method, we first propose a proportional derivative (PD) control scheme on the unit sphere that does not use depth parameters. This proposed PD control scheme can avoid uncertainties in the estimated depth and camera calibration parameters, as well as inconveniences in their estimation process, including the use of auxiliary feature points and highly non-linear computation. Furthermore, the control gain of the proposed PD control scheme on the unit sphere is designed using LMI such that the designed control is robust in the presence of uncertainties in the other estimated parameters, such as image position and velocity. Simulation results demonstrate that the proposed method provides a better compensation for uncertainties in the estimated parameters than the contemporary linear method and steers the gaze of the camera more steadily over time than the contemporary non-linear method.

Control-oriented modeling and adaptive backstepping control for a nonminimum phase hypersonic vehicle.

PubMed

Ye, Linqi; Zong, Qun; Tian, Bailing; Zhang, Xiuyun; Wang, Fang

2017-09-01

In this paper, the nonminimum phase problem of a flexible hypersonic vehicle is investigated. The main challenge of nonminimum phase is the prevention of dynamic inversion methods to nonlinear control design. To solve this problem, we make research on the relationship between nonminimum phase and backstepping control, finding that a stable nonlinear controller can be obtained by changing the control loop on the basis of backstepping control. By extending the control loop to cover the internal dynamics in it, the internal states are directly controlled by the inputs and simultaneously serve as virtual control for the external states, making it possible to guarantee output tracking as well as internal stability. Then, based on the extended control loop, a simplified control-oriented model is developed to enable the applicability of adaptive backstepping method. It simplifies the design process and releases some limitations caused by direct use of the no simplified control-oriented model. Next, under proper assumptions, asymptotic stability is proved for constant commands, while bounded stability is proved for varying commands. The proposed method is compared with approximate backstepping control and dynamic surface control and is shown to have superior tracking accuracy as well as robustness from the simulation results. This paper may also provide a beneficial guidance for control design of other complex systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Design of Linear Control System for Wind Turbine Blade Fatigue Testing

NASA Astrophysics Data System (ADS)

Toft, Anders; Roe-Poulsen, Bjarke; Christiansen, Rasmus; Knudsen, Torben

2016-09-01

This paper proposes a linear method for wind turbine blade fatigue testing at Siemens Wind Power. The setup consists of a blade, an actuator (motor and load mass) that acts on the blade with a sinusoidal moment, and a distribution of strain gauges to measure the blade flexure. Based on the frequency of the sinusoidal input, the blade will start oscillating with a given gain, hence the objective of the fatigue test is to make the blade oscillate with a controlled amplitude. The system currently in use is based on frequency control, which involves some non-linearities that make the system difficult to control. To make a linear controller, a different approach has been chosen, namely making a controller which is not regulating on the input frequency, but on the input amplitude. A non-linear mechanical model for the blade and the motor has been constructed. This model has been simplified based on the desired output, namely the amplitude of the blade. Furthermore, the model has been linearised to make it suitable for linear analysis and control design methods. The controller is designed based on a simplified and linearised model, and its gain parameter determined using pole placement. The model variants have been simulated in the MATLAB toolbox Simulink, which shows that the controller design based on the simple model performs adequately with the non-linear model. Moreover, the developed controller solves the robustness issue found in the existent solution and also reduces the needed energy for actuation as it always operates at the blade eigenfrequency.

System and method for generating 3D images of non-linear properties of rock formation using surface seismic or surface to borehole seismic or both

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vu, Cung Khac; Nihei, Kurt Toshimi; Johnson, Paul A.

A system and method of characterizing properties of a medium from a non-linear interaction are include generating, by first and second acoustic sources disposed on a surface of the medium on a first line, first and second acoustic waves. The first and second acoustic sources are controllable such that trajectories of the first and second acoustic waves intersect in a mixing zone within the medium. The method further includes receiving, by a receiver positioned in a plane containing the first and second acoustic sources, a third acoustic wave generated by a non-linear mixing process from the first and second acousticmore » waves in the mixing zone; and creating a first two-dimensional image of non-linear properties or a first ratio of compressional velocity and shear velocity, or both, of the medium in a first plane generally perpendicular to the surface and containing the first line, based on the received third acoustic wave.« less

YIP Formal Synthesis of Software-Based Control Protocols for Fractionated,Composable Autonomous Systems

DTIC Science & Technology

2016-07-08

Systems Using Automata Theory and Barrier Certifi- cates We developed a sound but incomplete method for the computational verification of specifications...method merges ideas from automata -based model checking with those from control theory including so-called barrier certificates and optimization-based... Automata theory meets barrier certificates: Temporal logic verification of nonlinear systems,” IEEE Transactions on Automatic Control, 2015. [J2] R

Predicting radiotherapy outcomes using statistical learning techniques

NASA Astrophysics Data System (ADS)

El Naqa, Issam; Bradley, Jeffrey D.; Lindsay, Patricia E.; Hope, Andrew J.; Deasy, Joseph O.

2009-09-01

Radiotherapy outcomes are determined by complex interactions between treatment, anatomical and patient-related variables. A common obstacle to building maximally predictive outcome models for clinical practice is the failure to capture potential complexity of heterogeneous variable interactions and applicability beyond institutional data. We describe a statistical learning methodology that can automatically screen for nonlinear relations among prognostic variables and generalize to unseen data before. In this work, several types of linear and nonlinear kernels to generate interaction terms and approximate the treatment-response function are evaluated. Examples of institutional datasets of esophagitis, pneumonitis and xerostomia endpoints were used. Furthermore, an independent RTOG dataset was used for 'generalizabilty' validation. We formulated the discrimination between risk groups as a supervised learning problem. The distribution of patient groups was initially analyzed using principle components analysis (PCA) to uncover potential nonlinear behavior. The performance of the different methods was evaluated using bivariate correlations and actuarial analysis. Over-fitting was controlled via cross-validation resampling. Our results suggest that a modified support vector machine (SVM) kernel method provided superior performance on leave-one-out testing compared to logistic regression and neural networks in cases where the data exhibited nonlinear behavior on PCA. For instance, in prediction of esophagitis and pneumonitis endpoints, which exhibited nonlinear behavior on PCA, the method provided 21% and 60% improvements, respectively. Furthermore, evaluation on the independent pneumonitis RTOG dataset demonstrated good generalizabilty beyond institutional data in contrast with other models. This indicates that the prediction of treatment response can be improved by utilizing nonlinear kernel methods for discovering important nonlinear interactions among model variables. These models have the capacity to predict on unseen data. Part of this work was first presented at the Seventh International Conference on Machine Learning and Applications, San Diego, CA, USA, 11-13 December 2008.

Quad-rotor flight path energy optimization

NASA Astrophysics Data System (ADS)

Kemper, Edward

Quad-Rotor unmanned areal vehicles (UAVs) have been a popular area of research and development in the last decade, especially with the advent of affordable microcontrollers like the MSP 430 and the Raspberry Pi. Path-Energy Optimization is an area that is well developed for linear systems. In this thesis, this idea of path-energy optimization is extended to the nonlinear model of the Quad-rotor UAV. The classical optimization technique is adapted to the nonlinear model that is derived for the problem at hand, coming up with a set of partial differential equations and boundary value conditions to solve these equations. Then, different techniques to implement energy optimization algorithms are tested using simulations in Python. First, a purely nonlinear approach is used. This method is shown to be computationally intensive, with no practical solution available in a reasonable amount of time. Second, heuristic techniques to minimize the energy of the flight path are tested, using Ziegler-Nichols' proportional integral derivative (PID) controller tuning technique. Finally, a brute force look-up table based PID controller is used. Simulation results of the heuristic method show that both reliable control of the system and path-energy optimization are achieved in a reasonable amount of time.

Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

PubMed

Wu, Huai-Ning; Luo, Biao

2012-12-01

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

Non-linear Heart Rate Variability as a Discriminator of Internalizing Psychopathology and Negative Affect in Children With Internalizing Problems and Healthy Controls

PubMed Central

Fiskum, Charlotte; Andersen, Tonje G.; Bornas, Xavier; Aslaksen, Per M.; Flaten, Magne A.; Jacobsen, Karl

2018-01-01

Background: Internalizing psychopathology and dysregulated negative affect are characterized by dysregulation in the autonomic nervous system and reduced heart rate variability (HRV) due to increases in sympathetic activity alongside reduced vagal tone. The neurovisceral system is however, a complex nonlinear system, and nonlinear indices related to psychopathology are so far less studied in children. Essential nonlinear properties of a system can be found in two main domains: the informational domain and the invariant domain. sample entropy (SampEn) is a much-used method from the informational domain, while detrended fluctuation analysis (DFA) represents a widely-used method from the invariant domain. To see if nonlinear HRV can provide information beyond linear indices of autonomic activation, this study investigated SampEn and DFA as discriminators of internalizing psychopathology and negative affect alongside measures of vagally-mediated HRV and sympathetic activation. Material and Methods: Thirty-Two children with internalizing difficulties and 25 healthy controls (aged 9–13) were assessed with the Child Behavior Checklist and the Early Adolescent Temperament Questionnaire, Revised, giving an estimate of internalizing psychopathology, negative affect and effortful control, a protective factor against psychopathology. Five minute electrocardiogram and impedance cardiography recordings were collected during a resting baseline, giving estimates of SampEn, DFA short-term scaling exponent α1, root mean square of successive differences (RMSSD), and pre-ejection period (PEP). Between-group differences and correlations were assessed with parametric and non-parametric tests, and the relationships between cardiac variables, psychopathology and negative affect were assessed using generalized linear modeling. Results: SampEn and DFA were not significantly different between the groups. SampEn was weakly negatively related to heart rate (HR) in the controls, while DFA was moderately negatively related to RMSSD in both groups, and moderately positively related to HR in the clinical sample. SampEn was significantly associated with internalizing psychopathology and negative affect. DFA was significantly related to internalizing psychopathology. Conclusions: Higher invariant self-similarity was linked to less psychopathology. Higher informational entropy was related to less psychopathology and less negative affect, and may provide an index of the organizational flexibility of the neurovisceral system. PMID:29875679

Non-linear Heart Rate Variability as a Discriminator of Internalizing Psychopathology and Negative Affect in Children With Internalizing Problems and Healthy Controls.

PubMed

Fiskum, Charlotte; Andersen, Tonje G; Bornas, Xavier; Aslaksen, Per M; Flaten, Magne A; Jacobsen, Karl

2018-01-01

Background: Internalizing psychopathology and dysregulated negative affect are characterized by dysregulation in the autonomic nervous system and reduced heart rate variability (HRV) due to increases in sympathetic activity alongside reduced vagal tone. The neurovisceral system is however, a complex nonlinear system, and nonlinear indices related to psychopathology are so far less studied in children. Essential nonlinear properties of a system can be found in two main domains: the informational domain and the invariant domain. sample entropy (SampEn) is a much-used method from the informational domain, while detrended fluctuation analysis (DFA) represents a widely-used method from the invariant domain. To see if nonlinear HRV can provide information beyond linear indices of autonomic activation, this study investigated SampEn and DFA as discriminators of internalizing psychopathology and negative affect alongside measures of vagally-mediated HRV and sympathetic activation. Material and Methods: Thirty-Two children with internalizing difficulties and 25 healthy controls (aged 9-13) were assessed with the Child Behavior Checklist and the Early Adolescent Temperament Questionnaire, Revised, giving an estimate of internalizing psychopathology, negative affect and effortful control, a protective factor against psychopathology. Five minute electrocardiogram and impedance cardiography recordings were collected during a resting baseline, giving estimates of SampEn, DFA short-term scaling exponent α 1 , root mean square of successive differences (RMSSD), and pre-ejection period (PEP). Between-group differences and correlations were assessed with parametric and non-parametric tests, and the relationships between cardiac variables, psychopathology and negative affect were assessed using generalized linear modeling. Results: SampEn and DFA were not significantly different between the groups. SampEn was weakly negatively related to heart rate (HR) in the controls, while DFA was moderately negatively related to RMSSD in both groups, and moderately positively related to HR in the clinical sample. SampEn was significantly associated with internalizing psychopathology and negative affect. DFA was significantly related to internalizing psychopathology. Conclusions: Higher invariant self-similarity was linked to less psychopathology. Higher informational entropy was related to less psychopathology and less negative affect, and may provide an index of the organizational flexibility of the neurovisceral system.

Interaction model between capsule robot and intestine based on nonlinear viscoelasticity.

PubMed

Zhang, Cheng; Liu, Hao; Tan, Renjia; Li, Hongyi

2014-03-01

Active capsule endoscope could also be called capsule robot, has been developed from laboratory research to clinical application. However, the system still has defects, such as poor controllability and failing to realize automatic checks. The imperfection of the interaction model between capsule robot and intestine is one of the dominating reasons causing the above problems. A model is hoped to be established for the control method of the capsule robot in this article. It is established based on nonlinear viscoelasticity. The interaction force of the model consists of environmental resistance, viscous resistance and Coulomb friction. The parameters of the model are identified by experimental investigation. Different methods are used in the experiment to obtain different values of the same parameter at different velocities. The model is proved to be valid by experimental verification. The achievement in this article is the attempted perfection of an interaction model. It is hoped that the model can optimize the control method of the capsule robot in the future.

Modification of a method-of-characteristics solute-transport model to incorporate decay and equilibrium-controlled sorption or ion exchange

USGS Publications Warehouse

Goode, D.J.; Konikow, Leonard F.

1989-01-01

The U.S. Geological Survey computer model of two-dimensional solute transport and dispersion in ground water (Konikow and Bredehoeft, 1978) has been modified to incorporate the following types of chemical reactions: (1) first-order irreversible rate-reaction, such as radioactive decay; (2) reversible equilibrium-controlled sorption with linear, Freundlich, or Langmuir isotherms; and (3) reversible equilibrium-controlled ion exchange for monovalent or divalent ions. Numerical procedures are developed to incorporate these processes in the general solution scheme that uses method-of- characteristics with particle tracking for advection and finite-difference methods for dispersion. The first type of reaction is accounted for by an exponential decay term applied directly to the particle concentration. The second and third types of reactions are incorporated through a retardation factor, which is a function of concentration for nonlinear cases. The model is evaluated and verified by comparison with analytical solutions for linear sorption and decay, and by comparison with other numerical solutions for nonlinear sorption and ion exchange.

Linear matrix inequality-based nonlinear adaptive robust control with application to unmanned aircraft systems

NASA Astrophysics Data System (ADS)

Kun, David William

Unmanned aircraft systems (UASs) are gaining popularity in civil and commercial applications as their lightweight on-board computers become more powerful and affordable, their power storage devices improve, and the Federal Aviation Administration addresses the legal and safety concerns of integrating UASs in the national airspace. Consequently, many researchers are pursuing novel methods to control UASs in order to improve their capabilities, dependability, and safety assurance. The nonlinear control approach is a common choice as it offers several benefits for these highly nonlinear aerospace systems (e.g., the quadrotor). First, the controller design is physically intuitive and is derived from well known dynamic equations. Second, the final control law is valid in a larger region of operation, including far from the equilibrium states. And third, the procedure is largely methodical, requiring less expertise with gain tuning, which can be arduous for a novice engineer. Considering these facts, this thesis proposes a nonlinear controller design method that combines the advantages of adaptive robust control (ARC) with the powerful design tools of linear matrix inequalities (LMI). The ARC-LMI controller is designed with a discontinuous projection-based adaptation law, and guarantees a prescribed transient and steady state tracking performance for uncertain systems in the presence of matched disturbances. The norm of the tracking error is bounded by a known function that depends on the controller design parameters in a known form. Furthermore, the LMI-based part of the controller ensures the stability of the system while overcoming polytopic uncertainties, and minimizes the control effort. This can reduce the number of parameters that require adaptation, and helps to avoid control input saturation. These desirable characteristics make the ARC-LMI control algorithm well suited for the quadrotor UAS, which may have unknown parameters and may encounter external disturbances such as wind gusts and turbulence. This thesis develops the ARC-LMI attitude and position controllers for an X-configuration quadrotor helicopter. The inner-loop of the autopilot controls the attitude and altitude of the quadrotor, and the outer-loop controls its position in the earth-fixed coordinate frame. Furthermore, by intelligently generating a smooth trajectory from the given reference coordinates (waypoints), the transient performance is improved. The simulation results indicate that the ARC-LMI controller design is useful for a variety of quadrotor applications, including precise trajectory tracking, autonomous waypoint navigation in the presence of disturbances, and package delivery without loss of performance.

Approximately adaptive neural cooperative control for nonlinear multiagent systems with performance guarantee

NASA Astrophysics Data System (ADS)

Wang, Jing; Yang, Tianyu; Staskevich, Gennady; Abbe, Brian

2017-04-01

This paper studies the cooperative control problem for a class of multiagent dynamical systems with partially unknown nonlinear system dynamics. In particular, the control objective is to solve the state consensus problem for multiagent systems based on the minimisation of certain cost functions for individual agents. Under the assumption that there exist admissible cooperative controls for such class of multiagent systems, the formulated problem is solved through finding the optimal cooperative control using the approximate dynamic programming and reinforcement learning approach. With the aid of neural network parameterisation and online adaptive learning, our method renders a practically implementable approximately adaptive neural cooperative control for multiagent systems. Specifically, based on the Bellman's principle of optimality, the Hamilton-Jacobi-Bellman (HJB) equation for multiagent systems is first derived. We then propose an approximately adaptive policy iteration algorithm for multiagent cooperative control based on neural network approximation of the value functions. The convergence of the proposed algorithm is rigorously proved using the contraction mapping method. The simulation results are included to validate the effectiveness of the proposed algorithm.

Chaotic operation and chaos control of travelling wave ultrasonic motor.

PubMed

Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

2013-08-01

The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

Research leading to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle of attack aircraft such as the F-18 is discussed. The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis, and simulation were studied in some detail as well. Studies indicated that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in angle of attack. Included here are studies on nonlinear model algorithmic controller design and an analysis of nonlinear system stability using robust stability analysis for linear systems.

IR Li2Ga2GeS6 nanocrystallized GeS2-Ga2S3-Li2S electroconductive chalcogenide glass with good nonlinearity

PubMed Central

Liu, Qiming; Zhang, Peng

2014-01-01

GeS2-Ga2S3-Li2S electroconductive glasses were prepared by the conventional melt-quenching method through carefully controlling the heating rate. Comparing with the reference of glass-forming region, our investigated GeS2-Ga2S3-Li2S system was extended to the cation ratio of 0–20% Li with around 40% Ga. GeS2-Ga2S3-Li2S glass-ceramics containing IR Li2Ga2GeS6 nonlinear nanocrystals were obtained by the more carefully controlled heating rate. Its optical nonlinearity was investigated by the Maker fringe measurements, the maximum second harmonic intensity was observed to be 0.35 of the reference Z-cut quartz. IR Li2Ga2GeS6 nonlinear crystals were directly obtained at the composition of 40GeS2-30GaS1.5-30LiS0.5. PMID:25030713

Active and passive controls of Jeffrey nanofluid flow over a nonlinear stretching surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

This communication explores magnetohydrodynamic (MHD) boundary-layer flow of Jeffrey nanofluid over a nonlinear stretching surface with active and passive controls of nanoparticles. A nonlinear stretching surface generates the flow. Effects of thermophoresis and Brownian diffusion are considered. Jeffrey fluid is electrically conducted subject to non-uniform magnetic field. Low magnetic Reynolds number and boundary-layer approximations have been considered in mathematical modelling. The phenomena of impulsing the particles away from the surface in combination with non-zero mass flux condition is known as the condition of zero mass flux. Convergent series solutions for the nonlinear governing system are established through optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the temperature and concentration distributions are affected by distinct physical flow parameters. Skin friction coefficient and local Nusselt and Sherwood numbers are also computed and analyzed. Our findings show that the temperature and concentration distributions are increasing functions of Hartman number and thermophoresis parameter.

Improved stability of the induced second-order nonlinearity in soft glass by thermal poling

NASA Astrophysics Data System (ADS)

Moura, A. L.; de Araujo, M. T.; Vermelho, M. V. D.; Aitchison, J. S.

2006-08-01

Stable and intense second-order nonlinearity in soda lime glass is investigated tailoring the induced electric current. This procedure allows the determination of the relative contributions of the dipole orientation as well as the ionic contributions to the poling process. The experiments are developed in the light of multiple-carrier models controlling the output power supply applied current to tailor the frozen-in induced electric field — Edc. This method permits the induction of the stable nonlinearity for applied electric fields above ˜5kV/cm and temperatures ˜250°C. It is also possible to reach higher temperatures than the ones used in normal poling procedures avoiding the electric current breakdown. The controlled Edc formation enables it to participate in essential chemical reactions that determine the intensity and stability of the nonlinearity. The induced d33 of ˜0.41pm/V measured 20 days after poling reduced only ˜50% during the next seven months.

Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

NASA Technical Reports Server (NTRS)

Mukhopadhyay, A. K.

1975-01-01

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

Gradient optimization and nonlinear control

NASA Technical Reports Server (NTRS)

Hasdorff, L.

1976-01-01

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

Coordinated control of active and reactive power of distribution network with distributed PV cluster via model predictive control

NASA Astrophysics Data System (ADS)

Ji, Yu; Sheng, Wanxing; Jin, Wei; Wu, Ming; Liu, Haitao; Chen, Feng

2018-02-01

A coordinated optimal control method of active and reactive power of distribution network with distributed PV cluster based on model predictive control is proposed in this paper. The method divides the control process into long-time scale optimal control and short-time scale optimal control with multi-step optimization. The models are transformed into a second-order cone programming problem due to the non-convex and nonlinear of the optimal models which are hard to be solved. An improved IEEE 33-bus distribution network system is used to analyse the feasibility and the effectiveness of the proposed control method

DAST single-nanometer crystal preparation using a substrate-supported rapid evaporation crystallization method.

PubMed

Tian, Tian; Cai, Bin; Sugihara, Okihiro

2016-12-07

A substrate-supported rapid evaporation crystallization (SSREC) method was used to develop a highly nonlinear optical material, 4-N,N-dimethylamino-4'-N'-methyl-stilbazolium tosylate (DAST), which satisfies the Rayleigh scattering requirement for the fabrication of highly transparent composites. DAST nanocrystals have a second harmonic generation active crystal structure and a high signal-to-noise ratio second harmonic generation signal when excited by using a 1064 nm cw laser. The nanocrystals also possess size-dependent UV-vis absorption and fluorescence behavior which is not seen in the bulk state. SSREC offers a very convenient means of nanocrystal size control for fabricating nonlinear optical nanomaterials, and the unique properties of these DAST NCs provide potential applications in the fields of lasing, fluorescence probes, and other nonlinear optical photonics.

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

An LMI approach to design H(infinity) controllers for discrete-time nonlinear systems based on unified models.

PubMed

Liu, Meiqin; Zhang, Senlin

2008-10-01

A unified neural network model termed standard neural network model (SNNM) is advanced. Based on the robust L(2) gain (i.e. robust H(infinity) performance) analysis of the SNNM with external disturbances, a state-feedback control law is designed for the SNNM to stabilize the closed-loop system and eliminate the effect of external disturbances. The control design constraints are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms (e.g. interior-point algorithms) to determine the control law. Most discrete-time recurrent neural network (RNNs) and discrete-time nonlinear systems modelled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be robust H(infinity) performance analyzed or robust H(infinity) controller synthesized in a unified SNNM's framework. Finally, some examples are presented to illustrate the wide application of the SNNMs to the nonlinear systems, and the proposed approach is compared with related methods reported in the literature.

Application of dynamical systems theory to nonlinear aircraft dynamics

NASA Technical Reports Server (NTRS)

Culick, Fred E. C.; Jahnke, Craig C.

1988-01-01

Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

Nonlinear frequency response based adaptive vibration controller design for a class of nonlinear systems

NASA Astrophysics Data System (ADS)

Thenozhi, Suresh; Tang, Yu

2018-01-01

Frequency response functions (FRF) are often used in the vibration controller design problems of mechanical systems. Unlike linear systems, the FRF derivation for nonlinear systems is not trivial due to their complex behaviors. To address this issue, the convergence property of nonlinear systems can be studied using convergence analysis. For a class of time-invariant nonlinear systems termed as convergent systems, the nonlinear FRF can be obtained. The present paper proposes a nonlinear FRF based adaptive vibration controller design for a mechanical system with cubic damping nonlinearity and a satellite system. Here the controller gains are tuned such that a desired closed-loop frequency response for a band of harmonic excitations is achieved. Unlike the system with cubic damping, the satellite system is not convergent, therefore an additional controller is utilized to achieve the convergence property. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller.

An approach to simultaneous control of trajectory and interaction forces in dual-arm configurations

NASA Technical Reports Server (NTRS)

Yun, Xiaoping; Kumar, Vijay R.

1991-01-01

An approach to the control of constrained dynamic systems such as multiple arm systems, multifingered grippers, and walking vehicles is described. The basic philosophy is to utilize a minimal set of inputs to control the trajectory and the surplus input to control the constraint or interaction forces and moments in the closed chain. A dynamic control model for the closed chain is derived that is suitable for designing a controller in which the trajectory and the interaction forces and moments are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. These ideas are illustrated through a planar example in which two arms are used for cooperative manipulation. Results from a simulation are used to illustrate the efficacy of the method.

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

NASA Astrophysics Data System (ADS)

Sandhu, Amit

A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

Suppression of chaotic vibrations in a nonlinear half-car model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tusset, Ângelo Marcelo, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com; Piccirillo, Vinícius, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com; Janzen, Frederic Conrad, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com

The present work investigates the nonlinear response of a half-car model. The disturbances of the road are assumed to be sinusoidal. After constructing the bifurcation diagram, we using the 0-1 test for identify the chaotic motion. The principal objective of this study is to eliminate the chaotic behaviour of the chassis and reduce its vibration, and for this reason a control system for semi-active vehicle suspension with magnetorheological damper is proposed. The control mechanism is designed based on SDRE technique, where the control parameter is the voltage applied to the coil of the damper. Numerical results show that the proposedmore » control method is effective in significantly reducing of the chassis vibration, increasing therefore, passenger comfort.« less

A survey of methods of feasible directions for the solution of optimal control problems

NASA Technical Reports Server (NTRS)

Polak, E.

1972-01-01

Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category.

The Application of Linear and Nonlinear Water Tanks Case Study in Teaching of Process Control

NASA Astrophysics Data System (ADS)

Li, Xiangshun; Li, Zhiang

2018-02-01

In the traditional process control teaching, the importance of passing knowledge is emphasized while the development of creative and practical abilities of students is ignored. Traditional teaching methods are not very helpful to breed a good engineer. Case teaching is a very useful way to improve students’ innovative and practical abilities. In the traditional case teaching, knowledge points are taught separately based on different examples or no examples, thus it is very hard to setup the whole knowledge structure. Though all the knowledge is learned, how to use the knowledge to solve engineering problems keeps challenging for students. In this paper, the linear and nonlinear tanks are taken as illustrative examples which involves several knowledge points of process control. The application method of each knowledge point is discussed in detail and simulated. I believe the case-based study will be helpful for students.

On the new method for the control of discrete nonlinear dynamic systems using neural networks.

PubMed

Deng, Hua; Li, Han-Xiong

2006-03-01

This correspondence points out an incorrect statement in Adetona et al, 2000, and Adetona et al., 2004, about the application of the proposed control law to nonminimum phase systems. A counterexample shows the limitations of the control law and, furthermore, its control capability to nonminimum phase systems is explained.

Integral reinforcement learning for continuous-time input-affine nonlinear systems with simultaneous invariant explorations.

PubMed

Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2015-05-01

This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods.

Force-controlled absorption in a fully-nonlinear numerical wave tank

NASA Astrophysics Data System (ADS)

Spinneken, Johannes; Christou, Marios; Swan, Chris

2014-09-01

An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank. In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain. The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.

Data based identification and prediction of nonlinear and complex dynamical systems

NASA Astrophysics Data System (ADS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods outlined in this Review are principled on various concepts in complexity science and engineering such as phase transitions, bifurcations, stabilities, and robustness. The methodologies have the potential to significantly improve our ability to understand a variety of complex dynamical systems ranging from gene regulatory systems to social networks toward the ultimate goal of controlling such systems.

Active Nonlinear Feedback Control for Aerospace Systems. Processor

DTIC Science & Technology

1990-12-01

relating to the role of nonlinearities in feedback control. These area include Lyapunov function theory, chaotic controllers, statistical energy analysis , phase robustness, and optimal nonlinear control theory.

Prediction of jump phenomena in roll-coupled maneuvers of airplanes

NASA Technical Reports Server (NTRS)

Schy, A. A.; Hannah, M. E.

1976-01-01

An easily computerized analytical method is developed for identifying critical airplane maneuvers in which nonlinear rotational coupling effects may cause sudden jumps in the response to pilot's control inputs. Fifth and ninth degree polynomials for predicting multiple pseudo-steady states of roll-coupled maneuvers are derived. The program calculates the pseudo-steady solutions and their stability. The occurrence of jump-like responses for several airplanes and a variety of maneuvers is shown to correlate well with the appearance of multiple stable solutions for critical control combinations. The analysis is extended to include aerodynamics nonlinear in angle of attack.

Maximizing entanglement in bosonic Josephson junctions using shortcuts to adiabaticity and optimal control

NASA Astrophysics Data System (ADS)

Stefanatos, Dionisis; Paspalakis, Emmanuel

2018-05-01

In this article we consider a bosonic Josephson junction, a model system composed by two coupled nonlinear quantum oscillators which can be implemented in various physical contexts, initially prepared in a product of weakly populated coherent states. We quantify the maximum achievable entanglement between the modes of the junction and then use shortcuts to adiabaticity, a method developed to speed up adiabatic quantum dynamics, as well as numerical optimization, to find time-dependent controls (the nonlinearity and the coupling of the junction) which bring the system to a maximally entangled state.

A Criterion to Control Nonlinear Error in the Mixed-Mode Bending Test

NASA Technical Reports Server (NTRS)

Reeder, James R.

2002-01-01

The mixed-mode bending test ha: been widely used to measure delamination toughness and was recently standardized by ASTM as Standard Test Method D6671-01. This simple test is a combination of the standard Mode I (opening) test and a Mode II (sliding) test. This test uses a unidirectional composite test specimen with an artificial delamination subjected to bending loads to characterize when a delamination will extend. When the displacements become large, the linear theory used to analyze the results of the test yields errors in the calcu1ated toughness values. The current standard places no limit on the specimen loading and therefore test data can be created using the standard that are significantly in error. A method of limiting the error that can be incurred in the calculated toughness values is needed. In this paper, nonlinear models of the MMB test are refined. One of the nonlinear models is then used to develop a simple criterion for prescribing conditions where thc nonlinear error will remain below 5%.

Transient response of an active nonlinear sandwich piezolaminated plate

NASA Astrophysics Data System (ADS)

Oveisi, Atta; Nestorović, Tamara

2017-04-01

In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

Further developments in the controlled growth approach for optimal structural synthesis

NASA Technical Reports Server (NTRS)

Hajela, P.

1982-01-01

It is pointed out that the use of nonlinear programming methods in conjunction with finite element and other discrete analysis techniques have provided a powerful tool in the domain of optimal structural synthesis. The present investigation is concerned with new strategies which comprise an extension to the controlled growth method considered by Hajela and Sobieski-Sobieszczanski (1981). This method proposed an approach wherein the standard nonlinear programming (NLP) methodology of working with a very large number of design variables was replaced by a sequence of smaller optimization cycles, each involving a single 'dominant' variable. The current investigation outlines some new features. Attention is given to a modified cumulative constraint representation which is defined in both the feasible and infeasible domain of the design space. Other new features are related to the evaluation of the 'effectiveness measure' on which the choice of the dominant variable and the linking strategy is based.

Triggered instabilities in rocket motors and active combustion control for an incinerator afterburner

NASA Astrophysics Data System (ADS)

Wicker, Josef M.

1999-11-01

Two branches of research are conducted in this thesis. The first deals with nonlinear combustion response as a mechanism for triggering combustion instabilities in solid rocket motors. A nonlinear wave equation is developed to study a wide class of combustion response functions to second-order in fluctuation amplitude. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be how the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse. Also, dependence of nonlinear stability upon system parameters is considered. The second part of this thesis presents research for a controller to improve the emissions of an incinerator afterburner. The developed controller was experimentally tested at the Naval Air Warfare Center (NAWC), on a 50kW-scale model of an afterburner for Naval shipboard incinerator applications. Acoustic forcing of the combustor's reacting shear layer is used to control the formation of coherent vortical structures, within which favorable fuel-air mixing and efficient combustion can occur. Laser-based measurements of CO emissions are used as the performance indicator for the combustor. The controller algorithm is based on the downhill simplex method and adjusts the shear layer forcing parameters in order to minimize the CO emissions. The downhill simplex method was analyzed with respect to its behavior in the face of time-variation of the plant and noise in the sensor signal, and was modified to account for these difficulties. The control system has experimentally demonstrated the ability (1) to find optimal control action for single- and multi-variable control, (2) to maintain optimal control for time-varying operating states, and (3) to automatically adjust auxiliary fuel in response to changing stoichiometry of the incoming waste pyrolysis gas. Also presented but not tested in the experiments are an expert-type model-guidance feature to aid convergence of the controller to optimum control, and methodology for maintaining flammability.

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

NASA Astrophysics Data System (ADS)

Huang, Rui; Hu, Haiyan; Zhao, Yonghui

2013-10-01

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.

Nonlinear Markov Control Processes and Games

DTIC Science & Technology

2012-11-15

the analysis of a new class of stochastic games , nonlinear Markov games , as they arise as a ( competitive ) controlled version of nonlinear Markov... competitive interests) a nonlinear Markov game that we are investigating. I 0. :::tUt::JJt:.l.. I I t:t11VI;:, nonlinear Markov game , nonlinear Markov...corresponding stochastic game Γ+(T, h). In a slightly different setting one can assume that changes in a competitive control process occur as a

Algebraic and adaptive learning in neural control systems

NASA Astrophysics Data System (ADS)

Ferrari, Silvia

A systematic approach is developed for designing adaptive and reconfigurable nonlinear control systems that are applicable to plants modeled by ordinary differential equations. The nonlinear controller comprising a network of neural networks is taught using a two-phase learning procedure realized through novel techniques for initialization, on-line training, and adaptive critic design. A critical observation is that the gradients of the functions defined by the neural networks must equal corresponding linear gain matrices at chosen operating points. On-line training is based on a dual heuristic adaptive critic architecture that improves control for large, coupled motions by accounting for actual plant dynamics and nonlinear effects. An action network computes the optimal control law; a critic network predicts the derivative of the cost-to-go with respect to the state. Both networks are algebraically initialized based on prior knowledge of satisfactory pointwise linear controllers and continue to adapt on line during full-scale simulations of the plant. On-line training takes place sequentially over discrete periods of time and involves several numerical procedures. A backpropagating algorithm called Resilient Backpropagation is modified and successfully implemented to meet these objectives, without excessive computational expense. This adaptive controller is as conservative as the linear designs and as effective as a global nonlinear controller. The method is successfully implemented for the full-envelope control of a six-degree-of-freedom aircraft simulation. The results show that the on-line adaptation brings about improved performance with respect to the initialization phase during aircraft maneuvers that involve large-angle and coupled dynamics, and parameter variations.

SDRE controller for motion design of cable-suspended robot with uncertainties and moving obstacles

NASA Astrophysics Data System (ADS)

Behboodi, Ahad; Salehi, Seyedmohammad

2017-10-01

In this paper an optimal control approach for nonlinear dynamical systems was proposed based on State Dependent Riccati Equation (SDRE) and its robustness against uncertainties is shown by simulation results. The proposed method was applied on a spatial six-cable suspended robot, which was designed to carry loads or perform different tasks in huge workspaces. Motion planning for cable-suspended robots in such a big workspace is subjected to uncertainties and obstacles. First, we emphasized the ability of SDRE to construct a systematic basis and efficient design of controller for wide variety of nonlinear dynamical systems. Then we showed how this systematic design improved the robustness of the system and facilitated the integration of motion planning techniques with the controller. In particular, obstacle avoidance technique based on artificial potential field (APF) can be easily combined with SDRE controller with efficient performance. Due to difficulties of exact solution for SDRE, an approximation method was used based on power series expansion. The efficiency and robustness of the SDRE controller was illustrated on a six-cable suspended robot with proper simulations.

An enhanced nonlinear damping approach accounting for system constraints in active mass dampers

NASA Astrophysics Data System (ADS)

Venanzi, Ilaria; Ierimonti, Laura; Ubertini, Filippo

2015-11-01

Active mass dampers are a viable solution for mitigating wind-induced vibrations in high-rise buildings and improve occupants' comfort. Such devices suffer particularly when they reach force saturation of the actuators and maximum extension of their stroke, which may occur in case of severe loading conditions (e.g. wind gust and earthquake). Exceeding actuators' physical limits can impair the control performance of the system or even lead to devices damage, with consequent need for repair or substitution of part of the control system. Controllers for active mass dampers should account for their technological limits. Prior work of the authors was devoted to stroke issues and led to the definition of a nonlinear damping approach, very easy to implement in practice. It consisted of a modified skyhook algorithm complemented with a nonlinear braking force to reverse the direction of the mass before reaching the stroke limit. This paper presents an enhanced version of this approach, also accounting for force saturation of the actuator and keeping the simplicity of implementation. This is achieved by modulating the control force by a nonlinear smooth function depending on the ratio between actuator's force and saturation limit. Results of a numerical investigation show that the proposed approach provides similar results to the method of the State Dependent Riccati Equation, a well-established technique for designing optimal controllers for constrained systems, yet very difficult to apply in practice.

Fuzzy controller training using particle swarm optimization for nonlinear system control.

PubMed

Karakuzu, Cihan

2008-04-01

This paper proposes and describes an effective utilization of particle swarm optimization (PSO) to train a Takagi-Sugeno (TS)-type fuzzy controller. Performance evaluation of the proposed fuzzy training method using the obtained simulation results is provided with two samples of highly nonlinear systems: a continuous stirred tank reactor (CSTR) and a Van der Pol (VDP) oscillator. The superiority of the proposed learning technique is that there is no need for a partial derivative with respect to the parameter for learning. This fuzzy learning technique is suitable for real-time implementation, especially if the system model is unknown and a supervised training cannot be run. In this study, all parameters of the controller are optimized with PSO in order to prove that a fuzzy controller trained by PSO exhibits a good control performance.

Adaptive Neural Output Feedback Control for Nonstrict-Feedback Stochastic Nonlinear Systems With Unknown Backlash-Like Hysteresis and Unknown Control Directions.

PubMed

Yu, Zhaoxu; Li, Shugang; Yu, Zhaosheng; Li, Fangfei

2018-04-01

This paper investigates the problem of output feedback adaptive stabilization for a class of nonstrict-feedback stochastic nonlinear systems with both unknown backlashlike hysteresis and unknown control directions. A new linear state transformation is applied to the original system, and then, control design for the new system becomes feasible. By combining the neural network's (NN's) parameterization, variable separation technique, and Nussbaum gain function method, an input-driven observer-based adaptive NN control scheme, which involves only one parameter to be updated, is developed for such systems. All closed-loop signals are bounded in probability and the error signals remain semiglobally bounded in the fourth moment (or mean square). Finally, the effectiveness and the applicability of the proposed control design are verified by two simulation examples.

Adaptive control of Parkinson's state based on a nonlinear computational model with unknown parameters.

PubMed

Su, Fei; Wang, Jiang; Deng, Bin; Wei, Xi-Le; Chen, Ying-Yuan; Liu, Chen; Li, Hui-Yan

2015-02-01

The objective here is to explore the use of adaptive input-output feedback linearization method to achieve an improved deep brain stimulation (DBS) algorithm for closed-loop control of Parkinson's state. The control law is based on a highly nonlinear computational model of Parkinson's disease (PD) with unknown parameters. The restoration of thalamic relay reliability is formulated as the desired outcome of the adaptive control methodology, and the DBS waveform is the control input. The control input is adjusted in real time according to estimates of unknown parameters as well as the feedback signal. Simulation results show that the proposed adaptive control algorithm succeeds in restoring the relay reliability of the thalamus, and at the same time achieves accurate estimation of unknown parameters. Our findings point to the potential value of adaptive control approach that could be used to regulate DBS waveform in more effective treatment of PD.

Adaptive fuzzy prescribed performance control for MIMO nonlinear systems with unknown control direction and unknown dead-zone inputs.

PubMed

Shi, Wuxi; Luo, Rui; Li, Baoquan

2017-01-01

In this study, an adaptive fuzzy prescribed performance control approach is developed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems with unknown control direction and unknown dead-zone inputs. The properties of symmetric matrix are exploited to design adaptive fuzzy prescribed performance controller, and a Nussbaum-type function is incorporated in the controller to estimate the unknown control direction. This method has two prominent advantages: it does not require the priori knowledge of control direction and only three parameters need to be updated on-line for this MIMO systems. It is proved that all the signals in the resulting closed-loop system are bounded and that the tracking errors converge to a small residual set with the prescribed performance bounds. The effectiveness of the proposed approach is validated by simulation results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lei; Kruk, Sergey; Koshelev, Kirill

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Nonlinear Wavefront Control with All-Dielectric Metasurfaces.

PubMed

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; Kravchenko, Ivan; Luther-Davies, Barry; Kivshar, Yuri

2018-06-13

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront of parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Our nonlinear metasurfaces produce phase gradients over a full 0-2π phase range with a 92% diffraction efficiency.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE PAGES

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; ...

2018-05-11

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

A Higher Harmonic Optimal Controller to Optimise Rotorcraft Aeromechanical Behaviour

NASA Technical Reports Server (NTRS)

Leyland, Jane Anne

1996-01-01

Three methods to optimize rotorcraft aeromechanical behavior for those cases where the rotorcraft plant can be adequately represented by a linear model system matrix were identified and implemented in a stand-alone code. These methods determine the optimal control vector which minimizes the vibration metric subject to constraints at discrete time points, and differ from the commonly used non-optimal constraint penalty methods such as those employed by conventional controllers in that the constraints are handled as actual constraints to an optimization problem rather than as just additional terms in the performance index. The first method is to use a Non-linear Programming algorithm to solve the problem directly. The second method is to solve the full set of non-linear equations which define the necessary conditions for optimality. The third method is to solve each of the possible reduced sets of equations defining the necessary conditions for optimality when the constraints are pre-selected to be either active or inactive, and then to simply select the best solution. The effects of maneuvers and aeroelasticity on the systems matrix are modelled by using a pseudo-random pseudo-row-dependency scheme to define the systems matrix. Cases run to date indicate that the first method of solution is reliable, robust, and easiest to use, and that it was superior to the conventional controllers which were considered.

A recursive approach to the equations of motion for the maneuvering and control of flexible multi-body systems

NASA Technical Reports Server (NTRS)

Kwak, Moon K.; Meirovitch, Leonard

1991-01-01

Interest lies in a mathematical formulation capable of accommodating the problem of maneuvering a space structure consisting of a chain of articulated flexible substructures. Simultaneously, any perturbations from the 'rigid body' maneuvering and any elastic vibration must be suppressed. The equations of motion for flexible bodies undergoing rigid body motions and elastic vibrations can be obtained conveniently by means of Lagrange's equations in terms of quasi-coordinates. The advantage of this approach is that it yields equations in terms of body axes, which are the same axes that are used to express the control forces and torques. The equations of motion are nonlinear hybrid differential quations. The partial differential equations can be discretized (in space) by means of the finite element method or the classical Rayleigh-Ritz method. The result is a set of nonlinear ordinary differential equations of high order. The nonlinearity can be traced to the rigid body motions and the high order to the elastic vibration. Elastic motions tend to be small when compared with rigid body motions.

Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

NASA Astrophysics Data System (ADS)

Manfredi, Sabato

2016-06-01

Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.

Stabilization of business cycles of finance agents using nonlinear optimal control

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics

NASA Technical Reports Server (NTRS)

Ho, K. K.; Moody, G. B.; Peng, C. K.; Mietus, J. E.; Larson, M. G.; Levy, D.; Goldberger, A. L.

1997-01-01

BACKGROUND: Despite much recent interest in quantification of heart rate variability (HRV), the prognostic value of conventional measures of HRV and of newer indices based on nonlinear dynamics is not universally accepted. METHODS AND RESULTS: We have designed algorithms for analyzing ambulatory ECG recordings and measuring HRV without human intervention, using robust methods for obtaining time-domain measures (mean and SD of heart rate), frequency-domain measures (power in the bands of 0.001 to 0.01 Hz [VLF], 0.01 to 0.15 Hz [LF], and 0.15 to 0.5 Hz [HF] and total spectral power [TP] over all three of these bands), and measures based on nonlinear dynamics (approximate entropy [ApEn], a measure of complexity, and detrended fluctuation analysis [DFA], a measure of long-term correlations). The study population consisted of chronic congestive heart failure (CHF) case patients and sex- and age-matched control subjects in the Framingham Heart Study. After exclusion of technically inadequate studies and those with atrial fibrillation, we used these algorithms to study HRV in 2-hour ambulatory ECG recordings of 69 participants (mean age, 71.7+/-8.1 years). By use of separate Cox proportional-hazards models, the conventional measures SD (P<.01), LF (P<.01), VLF (P<.05), and TP (P<.01) and the nonlinear measure DFA (P<.05) were predictors of survival over a mean follow-up period of 1.9 years; other measures, including ApEn (P>.3), were not. In multivariable models, DFA was of borderline predictive significance (P=.06) after adjustment for the diagnosis of CHF and SD. CONCLUSIONS: These results demonstrate that HRV analysis of ambulatory ECG recordings based on fully automated methods can have prognostic value in a population-based study and that nonlinear HRV indices may contribute prognostic value to complement traditional HRV measures.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

Linear Mechanisms and Pressure Fluctuations in Wall Turbulence

NASA Astrophysics Data System (ADS)

Septham, Kamthon; Morrison, Jonathan

2014-11-01

Full-domain, linear feedback control of turbulent channel flow at Reτ <= 400 via vU' at low wavenumbers is an effective method to attenuate turbulent channel flow such that it is relaminarised. The passivity-based control approach is adopted and explained by the conservative characteristics of the nonlinear terms contributing to the Reynolds-Orr equation (Sharma et al .Phys .Fluids 2011). The linear forcing acts on the wall-normal velocity field and thus the pressure field via the linear (rapid) source term of the Poisson equation for pressure fluctuations, 2U'∂v/∂x . The minimum required spanwise wavelength resolution without losing control is constant at λz+ = 125, based on the wall friction velocity at t = 0 . The result shows that the maximum forcing is located at y+ ~ 20 , corresponding to the location of the maximum in the mean-square pressure gradient. The effectiveness of linear control is qualitatively explained by Landahl's theory for timescales, in that the control proceeds via the shear interaction timescale which is much shorter than both the nonlinear and viscous timescales. The response of the rapid (linear) and slow (nonlinear) pressure fluctuations to the linear control is examined and discussed.

A simple attitude control of quadrotor helicopter based on Ziegler-Nichols rules for tuning PD parameters.

PubMed

He, ZeFang; Zhao, Long

2014-01-01

An attitude control strategy based on Ziegler-Nichols rules for tuning PD (proportional-derivative) parameters of quadrotor helicopters is presented to solve the problem that quadrotor tends to be instable. This problem is caused by the narrow definition domain of attitude angles of quadrotor helicopters. The proposed controller is nonlinear and consists of a linear part and a nonlinear part. The linear part is a PD controller with PD parameters tuned by Ziegler-Nichols rules and acts on the quadrotor decoupled linear system after feedback linearization; the nonlinear part is a feedback linearization item which converts a nonlinear system into a linear system. It can be seen from the simulation results that the attitude controller proposed in this paper is highly robust, and its control effect is better than the other two nonlinear controllers. The nonlinear parts of the other two nonlinear controllers are the same as the attitude controller proposed in this paper. The linear part involves a PID (proportional-integral-derivative) controller with the PID controller parameters tuned by Ziegler-Nichols rules and a PD controller with the PD controller parameters tuned by GA (genetic algorithms). Moreover, this attitude controller is simple and easy to implement.

Integrating viscoelastic mass spring dampers into position-based dynamics to simulate soft tissue deformation in real time

PubMed Central

Lu, Yuhua; Liu, Qian

2018-01-01

We propose a novel method to simulate soft tissue deformation for virtual surgery applications. The method considers the mechanical properties of soft tissue, such as its viscoelasticity, nonlinearity and incompressibility; its speed, stability and accuracy also meet the requirements for a surgery simulator. Modifying the traditional equation for mass spring dampers (MSD) introduces nonlinearity and viscoelasticity into the calculation of elastic force. Then, the elastic force is used in the constraint projection step for naturally reducing constraint potential. The node position is enforced by the combined spring force and constraint conservative force through Newton's second law. We conduct a comparison study of conventional MSD and position-based dynamics for our new integrating method. Our approach enables stable, fast and large step simulation by freely controlling visual effects based on nonlinearity, viscoelasticity and incompressibility. We implement a laparoscopic cholecystectomy simulator to demonstrate the practicality of our method, in which liver and gallbladder deformation can be simulated in real time. Our method is an appropriate choice for the development of real-time virtual surgery applications. PMID:29515870

Integrating viscoelastic mass spring dampers into position-based dynamics to simulate soft tissue deformation in real time.

PubMed

Xu, Lang; Lu, Yuhua; Liu, Qian

2018-02-01

We propose a novel method to simulate soft tissue deformation for virtual surgery applications. The method considers the mechanical properties of soft tissue, such as its viscoelasticity, nonlinearity and incompressibility; its speed, stability and accuracy also meet the requirements for a surgery simulator. Modifying the traditional equation for mass spring dampers (MSD) introduces nonlinearity and viscoelasticity into the calculation of elastic force. Then, the elastic force is used in the constraint projection step for naturally reducing constraint potential. The node position is enforced by the combined spring force and constraint conservative force through Newton's second law. We conduct a comparison study of conventional MSD and position-based dynamics for our new integrating method. Our approach enables stable, fast and large step simulation by freely controlling visual effects based on nonlinearity, viscoelasticity and incompressibility. We implement a laparoscopic cholecystectomy simulator to demonstrate the practicality of our method, in which liver and gallbladder deformation can be simulated in real time. Our method is an appropriate choice for the development of real-time virtual surgery applications.

Non-linear aeroelastic prediction for aircraft applications

NASA Astrophysics Data System (ADS)

de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.

2007-05-01

Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. To evaluate the methodologies on real aircraft problems. To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research in this domain. This is set within the context of a generic industrial process and the requirements of UK and US aeroelastic qualification. A range of test cases, from simple small DOF cases to full aircraft, have been used to evaluate and validate the non-linear methods developed and to make comparison with the linear methods in everyday use. These have focused mainly on aerodynamic non-linearity, although some results for structural non-linearity are also presented. The challenges associated with time domain (coupled computational fluid dynamics-computational structural model (CFD-CSM)) methods have been addressed through the development of grid movement, fluid-structure coupling, and control surface movement technologies. Conclusions regarding the accuracy and computational cost of these are presented. The computational cost of time-domain methods, despite substantial improvements in efficiency, remains high. However, significant advances have been made in reduced order methods, that allow non-linear behaviour to be modelled, but at a cost comparable with that of the regular linear methods. Of particular note is a method based on Hopf bifurcation that has reached an appropriate maturity for deployment on real aircraft configurations, though only limited results are presented herein. Results are also presented for dynamically linearised CFD approaches that hold out the possibility of non-linear results at a fraction of the cost of time coupled CFD-CSM methods. Local linearisation approaches (higher order harmonic balance and continuation method) are also presented; these have the advantage that no prior assumption of the nature of the aeroelastic instability is required, but currently these methods are limited to low DOF problems and it is thought that these will not reach a level of maturity appropriate to real aircraft problems for some years to come. Nevertheless, guidance on the most likely approaches has been derived and this forms the basis for ongoing research. It is important to recognise that the aeroelastic design and qualification requires a variety of methods applicable at different stages of the process. The methods reported herein are mapped to the process, so that their applicability and complementarity may be understood. Overall, the programme has provided a suite of methods that allow realistic consideration of non-linearity in the aeroelastic design and qualification of aircraft. Deployment of these methods is underway in the industrial environment, but full realisation of the benefit of these approaches will require appropriate engagement with the standards community so that safety standards may take proper account of the inclusion of non-linearity.

Nonlinear predictive control for adaptive adjustments of deep brain stimulation parameters in basal ganglia-thalamic network.

PubMed

Su, Fei; Wang, Jiang; Niu, Shuangxia; Li, Huiyan; Deng, Bin; Liu, Chen; Wei, Xile

2018-02-01

The efficacy of deep brain stimulation (DBS) for Parkinson's disease (PD) depends in part on the post-operative programming of stimulation parameters. Closed-loop stimulation is one method to realize the frequent adjustment of stimulation parameters. This paper introduced the nonlinear predictive control method into the online adjustment of DBS amplitude and frequency. This approach was tested in a computational model of basal ganglia-thalamic network. The autoregressive Volterra model was used to identify the process model based on physiological data. Simulation results illustrated the efficiency of closed-loop stimulation methods (amplitude adjustment and frequency adjustment) in improving the relay reliability of thalamic neurons compared with the PD state. Besides, compared with the 130Hz constant DBS the closed-loop stimulation methods can significantly reduce the energy consumption. Through the analysis of inter-spike-intervals (ISIs) distribution of basal ganglia neurons, the evoked network activity by the closed-loop frequency adjustment stimulation was closer to the normal state. Copyright © 2017 Elsevier Ltd. All rights reserved.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond.

PubMed

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-05-26

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 10(20) N m(-3). This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

PubMed Central

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-01-01

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m−3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics. PMID:27225287

Application of dynamic recurrent neural networks in nonlinear system identification

NASA Astrophysics Data System (ADS)

Du, Yun; Wu, Xueli; Sun, Huiqin; Zhang, Suying; Tian, Qiang

2006-11-01

An adaptive identification method of simple dynamic recurrent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteristics of system can reflect the dynamic characteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNN, and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topological structure in usual dynamic recurrent neural network.

Non-destructive evaluation method employing dielectric electrostatic ultrasonic transducers

NASA Technical Reports Server (NTRS)

Yost, William T. (Inventor); Cantrell, Jr., John H. (Inventor)

2003-01-01

An acoustic nonlinearity parameter (.beta.) measurement method and system for Non-Destructive Evaluation (NDE) of materials and structural members novelly employs a loosely mounted dielectric electrostatic ultrasonic transducer (DEUT) to receive and convert ultrasonic energy into an electrical signal which can be analyzed to determine the .beta. of the test material. The dielectric material is ferroelectric with a high dielectric constant .di-elect cons.. A computer-controlled measurement system coupled to the DEUT contains an excitation signal generator section and a measurement and analysis section. As a result, the DEUT measures the absolute particle displacement amplitudes in test material, leading to derivation of the nonlinearity parameter (.beta.) without the costly, low field reliability methods of the prior art.

Automatic guidance control of an articulated all-wheel-steered vehicle

NASA Astrophysics Data System (ADS)

Kim, Young Chol; Yun, Kyong-Han; Min, Kyung-Deuk

2014-04-01

This paper presents automatic guidance control of a single-articulated all-wheel-steered vehicle being developed by the Korea Railroad Research Institute. The vehicle has an independent drive motor on each wheel except for the front axle. The guidance controller is designed so that the vehicle follows the given reference path within permissible lateral deviations. We use a three-input/three-output linearised model derived from the nonlinear dynamic model of the vehicle. For the purpose of simplifying the controller and making it tunable, we consider a decentralised control configuration. We first design a second-order decoupling compensator for the two-input/two-output system that is strongly coupled and then design a first-order controller for each decoupled feedback loop by using the characteristic ratio assignment method. The simulation results for the nonlinear dynamic model indicate that the proposed control configuration successfully achieves the design objectives.

Nonlinear integral sliding mode control design of photovoltaic pumping system: Real time implementation.

PubMed

Chihi, Asma; Ben Azza, Hechmi; Jemli, Mohamed; Sellami, Anis

2017-09-01

The aim of this paper is to provide high performance control of pumping system. The proposed method is designed by an indirect field oriented control based on Sliding Mode (SM) technique. The first contribution of this work is to design modified switching surfaces which presented by adding an integral action to the considered controlled variables. Then, in order to prevent the chattering phenomenon, modified nonlinear component is developed. The SM concept and a Lyapunov function are combined to compute the Sliding Mode Control (SMC) gains. Besides, the motor performance is validated by numeric simulations and real time implementation using a dSpace system with DS1104 controller board. Also, to show the effectiveness of the proposed approach, the obtained results are compared with other techniques such as conventional PI, Proportional Sliding Mode (PSM) and backstepping controls. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Direct heuristic dynamic programming for damping oscillations in a large power system.

PubMed

Lu, Chao; Si, Jennie; Xie, Xiaorong

2008-08-01

This paper applies a neural-network-based approximate dynamic programming method, namely, the direct heuristic dynamic programming (direct HDP), to a large power system stability control problem. The direct HDP is a learning- and approximation-based approach to addressing nonlinear coordinated control under uncertainty. One of the major design parameters, the controller learning objective function, is formulated to directly account for network-wide low-frequency oscillation with the presence of nonlinearity, uncertainty, and coupling effect among system components. Results include a novel learning control structure based on the direct HDP with applications to two power system problems. The first case involves static var compensator supplementary damping control, which is used to provide a comprehensive evaluation of the learning control performance. The second case aims at addressing a difficult complex system challenge by providing a new solution to a large interconnected power network oscillation damping control problem that frequently occurs in the China Southern Power Grid.

New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

NASA Astrophysics Data System (ADS)

Rahman, Md. Saifur; Lee, Yiu-Yin

2017-10-01

In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

NASA Astrophysics Data System (ADS)

Ghorbanidehno, Hojat; Kokkinaki, Amalia; Kitanidis, Peter K.; Darve, Eric

2017-12-01

Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of "noisy" observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

Stability and Control CFD Investigations of a Generic 53 Degree Swept UCAV Configuration

NASA Technical Reports Server (NTRS)

Frink, Neal T.

2014-01-01

NATO STO Task Group AVT-201 on "Extended Assessment of Reliable Stability & Control Prediction Methods for NATO Air Vehicles" is studying various computational approaches to predict stability and control parameters for aircraft undergoing non-linear flight conditions. This paper contributes an assessment through correlations with wind tunnel data for the state of aerodynamic predictive capability of time-accurate RANS methodology on the group's focus configuration, a 53deg swept and twisted lambda wing UCAV, undergoing a variety of roll, pitch, and yaw motions. The vehicle aerodynamics is dominated by the complex non-linear physics of round leading-edge vortex flow separation. Correlations with experimental data are made for static longitudinal/lateral sweeps, and at varying frequencies of prescribed roll/pitch/yaw sinusoidal motion for the vehicle operating with and without control surfaces. The data and the derived understanding should prove useful to the AVT-201 team and other researchers who are developing techniques for augmenting flight simulation models from low-speed CFD predictions of aircraft traversing non-linear regions of a flight envelope.

Maneuver simulations of flexible spacecraft by solving TPBVP

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Li, Feiyue

1991-01-01

The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.

Robust LS-SVM-based adaptive constrained control for a class of uncertain nonlinear systems with time-varying predefined performance

NASA Astrophysics Data System (ADS)

Luo, Jianjun; Wei, Caisheng; Dai, Honghua; Yuan, Jianping

2018-03-01

This paper focuses on robust adaptive control for a class of uncertain nonlinear systems subject to input saturation and external disturbance with guaranteed predefined tracking performance. To reduce the limitations of classical predefined performance control method in the presence of unknown initial tracking errors, a novel predefined performance function with time-varying design parameters is first proposed. Then, aiming at reducing the complexity of nonlinear approximations, only two least-square-support-vector-machine-based (LS-SVM-based) approximators with two design parameters are required through norm form transformation of the original system. Further, a novel LS-SVM-based adaptive constrained control scheme is developed under the time-vary predefined performance using backstepping technique. Wherein, to avoid the tedious analysis and repeated differentiations of virtual control laws in the backstepping technique, a simple and robust finite-time-convergent differentiator is devised to only extract its first-order derivative at each step in the presence of external disturbance. In this sense, the inherent demerit of backstepping technique-;explosion of terms; brought by the recursive virtual controller design is conquered. Moreover, an auxiliary system is designed to compensate the control saturation. Finally, three groups of numerical simulations are employed to validate the effectiveness of the newly developed differentiator and the proposed adaptive constrained control scheme.

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T-S fuzzy approach

NASA Astrophysics Data System (ADS)

Hu, Xiaoxiang; Wu, Ligang; Hu, Changhua; Wang, Zhaoqiang; Gao, Huijun

2014-08-01

By utilising Takagi-Sugeno (T-S) fuzzy set approach, this paper addresses the robust H∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics' enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T-S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T-S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

Reduced order modeling and active flow control of an inlet duct

NASA Astrophysics Data System (ADS)

Ge, Xiaoqing

Many aerodynamic applications require the modeling of compressible flows in or around a body, e.g., the design of aircraft, inlet or exhaust duct, wind turbines, or tall buildings. Traditional methods use wind tunnel experiments and computational fluid dynamics (CFD) to investigate the spatial and temporal distribution of the flows. Although they provide a great deal of insight into the essential characteristics of the flow field, they are not suitable for control analysis and design due to the high physical/computational cost. Many model reduction methods have been studied to reduce the complexity of the flow model. There are two main approaches: linearization based input/output modeling and proper orthogonal decomposition (POD) based model reduction. The former captures mostly the local behavior near a steady state, which is suitable to model laminar flow dynamics. The latter obtains a reduced order model by projecting the governing equation onto an "optimal" subspace and is able to model complex nonlinear flow phenomena. In this research we investigate various model reduction approaches and compare them in flow modeling and control design. We propose an integrated model-based control methodology and apply it to the reduced order modeling and active flow control of compressible flows within a very aggressive (length to exit diameter ratio, L/D, of 1.5) inlet duct and its upstream contraction section. The approach systematically applies reduced order modeling, estimator design, sensor placement and control design to improve the aerodynamic performance. The main contribution of this work is the development of a hybrid model reduction approach that attempts to combine the best features of input/output model identification and POD method. We first identify a linear input/output model by using a subspace algorithm. We next project the difference between CFD response and the identified model response onto a set of POD basis. This trajectory is fit to a nonlinear dynamical model to augment the linear input/output model. Thus, the full system is decomposed into a dominant linear subsystem and a low order nonlinear subsystem. The hybrid model is then used for control design and compared with other modeling methods in CFD simulations. Numerical results indicate that the hybrid model accurately predicts the nonlinear behavior of the flow for a 2D diffuser contraction section model. It also performs best in terms of feedback control design and learning control. Since some outputs of interest (e.g., the AIP pressure recovery) are not observable during normal operations, static and dynamic estimators are designed to recreate the information from available sensor measurements. The latter also provides a state estimation for feedback controller. Based on the reduced order models and estimators, different controllers are designed to improve the aerodynamic performance of the contraction section and inlet duct. The integrated control methodology is evaluated with CFD simulations. Numerical results demonstrate the feasibility and efficacy of the active flow control based on reduced order models. Our reduced order models not only generate a good approximation of the nonlinear flow dynamics over a wide input range, but also help to design controllers that significantly improve the flow response. The tools developed for model reduction, estimator and control design can also be applied to wind tunnel experiment.

Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems

NASA Astrophysics Data System (ADS)

Lenka, Bichitra Kumar; Banerjee, Soumitro

2018-03-01

We discuss the asymptotic stability of autonomous linear and nonlinear fractional order systems where the state equations contain same or different fractional orders which lie between 0 and 2. First, we use the Laplace transform method to derive some sufficient conditions which ensure asymptotic stability of linear fractional order systems. Then by using the obtained results and linearization technique, a stability theorem is presented for autonomous nonlinear fractional order system. Finally, we design a control strategy for stabilization of autonomous nonlinear fractional order systems, and apply the results to the chaotic fractional order Lorenz system in order to verify its effectiveness.

An Adaptive B-Spline Neural Network and Its Application in Terminal Sliding Mode Control for a Mobile Satcom Antenna Inertially Stabilized Platform.

PubMed

Zhang, Xiaolei; Zhao, Yan; Guo, Kai; Li, Gaoliang; Deng, Nianmao

2017-04-28

The mobile satcom antenna (MSA) enables a moving vehicle to communicate with a geostationary Earth orbit satellite. To realize continuous communication, the MSA should be aligned with the satellite in both sight and polarization all the time. Because of coupling effects, unknown disturbances, sensor noises and unmodeled dynamics existing in the system, the control system should have a strong adaptability. The significant features of terminal sliding mode control method are robustness and finite time convergence, but the robustness is related to the large switching control gain which is determined by uncertain issues and can lead to chattering phenomena. Neural networks can reduce the chattering and approximate nonlinear issues. In this work, a novel B-spline curve-based B-spline neural network (BSNN) is developed. The improved BSNN has the capability of shape changing and self-adaption. In addition, the output of the proposed BSNN is applied to approximate the nonlinear function in the system. The results of simulations and experiments are also compared with those of PID method, non-singularity fast terminal sliding mode (NFTSM) control and radial basis function (RBF) neural network-based NFTSM. It is shown that the proposed method has the best performance, with reliable control precision.

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

Neural-Network-Based Adaptive Decentralized Fault-Tolerant Control for a Class of Interconnected Nonlinear Systems.

PubMed

Li, Xiao-Jian; Yang, Guang-Hong

2018-01-01

This paper is concerned with the adaptive decentralized fault-tolerant tracking control problem for a class of uncertain interconnected nonlinear systems with unknown strong interconnections. An algebraic graph theory result is introduced to address the considered interconnections. In addition, to achieve the desirable tracking performance, a neural-network-based robust adaptive decentralized fault-tolerant control (FTC) scheme is given to compensate the actuator faults and system uncertainties. Furthermore, via the Lyapunov analysis method, it is proven that all the signals of the resulting closed-loop system are semiglobally bounded, and the tracking errors of each subsystem exponentially converge to a compact set, whose radius is adjustable by choosing different controller design parameters. Finally, the effectiveness and advantages of the proposed FTC approach are illustrated with two simulated examples.

A recurrent neural-network-based sensor and actuator fault detection and isolation for nonlinear systems with application to the satellite's attitude control subsystem.

PubMed

Talebi, H A; Khorasani, K; Tafazoli, S

2009-01-01

This paper presents a robust fault detection and isolation (FDI) scheme for a general class of nonlinear systems using a neural-network-based observer strategy. Both actuator and sensor faults are considered. The nonlinear system considered is subject to both state and sensor uncertainties and disturbances. Two recurrent neural networks are employed to identify general unknown actuator and sensor faults, respectively. The neural network weights are updated according to a modified backpropagation scheme. Unlike many previous methods developed in the literature, our proposed FDI scheme does not rely on availability of full state measurements. The stability of the overall FDI scheme in presence of unknown sensor and actuator faults as well as plant and sensor noise and uncertainties is shown by using the Lyapunov's direct method. The stability analysis developed requires no restrictive assumptions on the system and/or the FDI algorithm. Magnetorquer-type actuators and magnetometer-type sensors that are commonly employed in the attitude control subsystem (ACS) of low-Earth orbit (LEO) satellites for attitude determination and control are considered in our case studies. The effectiveness and capabilities of our proposed fault diagnosis strategy are demonstrated and validated through extensive simulation studies.

Non-linear effects of soda taxes on consumption and weight outcomes.

PubMed

Fletcher, Jason M; Frisvold, David E; Tefft, Nathan

2015-05-01

The potential health impacts of imposing large taxes on soda to improve population health have been of interest for over a decade. As estimates of the effects of existing soda taxes with low rates suggest little health improvements, recent proposals suggest that large taxes may be effective in reducing weight because of non-linear consumption responses or threshold effects. This paper tests this hypothesis in two ways. First, we estimate non-linear effects of taxes using the range of current rates. Second, we leverage the sudden, relatively large soda tax increase in two states during the early 1990s combined with new synthetic control methods useful for comparative case studies. Our findings suggest virtually no evidence of non-linear or threshold effects. Copyright © 2014 John Wiley & Sons, Ltd.

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

NASA Technical Reports Server (NTRS)

Molusis, J. A.; Mookerjee, P.; Bar-Shalom, Y.

1983-01-01

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Self-calibrating models for dynamic monitoring and diagnosis

NASA Technical Reports Server (NTRS)

Kuipers, Benjamin

1996-01-01

A method for automatically building qualitative and semi-quantitative models of dynamic systems, and using them for monitoring and fault diagnosis, is developed and demonstrated. The qualitative approach and semi-quantitative method are applied to monitoring observation streams, and to design of non-linear control systems.

Adaptive GSA-based optimal tuning of PI controlled servo systems with reduced process parametric sensitivity, robust stability and controller robustness.

PubMed

Precup, Radu-Emil; David, Radu-Codrut; Petriu, Emil M; Radac, Mircea-Bogdan; Preitl, Stefan

2014-11-01

This paper suggests a new generation of optimal PI controllers for a class of servo systems characterized by saturation and dead zone static nonlinearities and second-order models with an integral component. The objective functions are expressed as the integral of time multiplied by absolute error plus the weighted sum of the integrals of output sensitivity functions of the state sensitivity models with respect to two process parametric variations. The PI controller tuning conditions applied to a simplified linear process model involve a single design parameter specific to the extended symmetrical optimum (ESO) method which offers the desired tradeoff to several control system performance indices. An original back-calculation and tracking anti-windup scheme is proposed in order to prevent the integrator wind-up and to compensate for the dead zone nonlinearity of the process. The minimization of the objective functions is carried out in the framework of optimization problems with inequality constraints which guarantee the robust stability with respect to the process parametric variations and the controller robustness. An adaptive gravitational search algorithm (GSA) solves the optimization problems focused on the optimal tuning of the design parameter specific to the ESO method and of the anti-windup tracking gain. A tuning method for PI controllers is proposed as an efficient approach to the design of resilient control systems. The tuning method and the PI controllers are experimentally validated by the adaptive GSA-based tuning of PI controllers for the angular position control of a laboratory servo system.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hohimer, J.P.

The use of laser-based analytical methods in nuclear-fuel processing plants is considered. The species and locations for accountability, process control, and effluent control measurements in the Coprocessing, Thorex, and reference Purex fuel processing operations are identified and the conventional analytical methods used for these measurements are summarized. The laser analytical methods based upon Raman, absorption, fluorescence, and nonlinear spectroscopy are reviewed and evaluated for their use in fuel processing plants. After a comparison of the capabilities of the laser-based and conventional analytical methods, the promising areas of application of the laser-based methods in fuel processing plants are identified.

Adaptive cruise control with stop&go function using the state-dependent nonlinear model predictive control approach.

PubMed

Shakouri, Payman; Ordys, Andrzej; Askari, Mohamad R

2012-09-01

In the design of adaptive cruise control (ACC) system two separate control loops - an outer loop to maintain the safe distance from the vehicle traveling in front and an inner loop to control the brake pedal and throttle opening position - are commonly used. In this paper a different approach is proposed in which a single control loop is utilized. The objective of the distance tracking is incorporated into the single nonlinear model predictive control (NMPC) by extending the original linear time invariant (LTI) models obtained by linearizing the nonlinear dynamic model of the vehicle. This is achieved by introducing the additional states corresponding to the relative distance between leading and following vehicles, and also the velocity of the leading vehicle. Control of the brake and throttle position is implemented by taking the state-dependent approach. The model demonstrates to be more effective in tracking the speed and distance by eliminating the necessity of switching between the two controllers. It also offers smooth variation in brake and throttle controlling signal which subsequently results in a more uniform acceleration of the vehicle. The results of proposed method are compared with other ACC systems using two separate control loops. Furthermore, an ACC simulation results using a stop&go scenario are shown, demonstrating a better fulfillment of the design requirements. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

A Simple Attitude Control of Quadrotor Helicopter Based on Ziegler-Nichols Rules for Tuning PD Parameters

PubMed Central

He, ZeFang

2014-01-01

An attitude control strategy based on Ziegler-Nichols rules for tuning PD (proportional-derivative) parameters of quadrotor helicopters is presented to solve the problem that quadrotor tends to be instable. This problem is caused by the narrow definition domain of attitude angles of quadrotor helicopters. The proposed controller is nonlinear and consists of a linear part and a nonlinear part. The linear part is a PD controller with PD parameters tuned by Ziegler-Nichols rules and acts on the quadrotor decoupled linear system after feedback linearization; the nonlinear part is a feedback linearization item which converts a nonlinear system into a linear system. It can be seen from the simulation results that the attitude controller proposed in this paper is highly robust, and its control effect is better than the other two nonlinear controllers. The nonlinear parts of the other two nonlinear controllers are the same as the attitude controller proposed in this paper. The linear part involves a PID (proportional-integral-derivative) controller with the PID controller parameters tuned by Ziegler-Nichols rules and a PD controller with the PD controller parameters tuned by GA (genetic algorithms). Moreover, this attitude controller is simple and easy to implement. PMID:25614879

A Novel Weighted Kernel PCA-Based Method for Optimization and Uncertainty Quantification

NASA Astrophysics Data System (ADS)

Thimmisetty, C.; Talbot, C.; Chen, X.; Tong, C. H.

2016-12-01

It has been demonstrated that machine learning methods can be successfully applied to uncertainty quantification for geophysical systems through the use of the adjoint method coupled with kernel PCA-based optimization. In addition, it has been shown through weighted linear PCA how optimization with respect to both observation weights and feature space control variables can accelerate convergence of such methods. Linear machine learning methods, however, are inherently limited in their ability to represent features of non-Gaussian stochastic random fields, as they are based on only the first two statistical moments of the original data. Nonlinear spatial relationships and multipoint statistics leading to the tortuosity characteristic of channelized media, for example, are captured only to a limited extent by linear PCA. With the aim of coupling the kernel-based and weighted methods discussed, we present a novel mathematical formulation of kernel PCA, Weighted Kernel Principal Component Analysis (WKPCA), that both captures nonlinear relationships and incorporates the attribution of significance levels to different realizations of the stochastic random field of interest. We also demonstrate how new instantiations retaining defining characteristics of the random field can be generated using Bayesian methods. In particular, we present a novel WKPCA-based optimization method that minimizes a given objective function with respect to both feature space random variables and observation weights through which optimal snapshot significance levels and optimal features are learned. We showcase how WKPCA can be applied to nonlinear optimal control problems involving channelized media, and in particular demonstrate an application of the method to learning the spatial distribution of material parameter values in the context of linear elasticity, and discuss further extensions of the method to stochastic inversion.

Implementation of Nonlinear Control Laws for an Optical Delay Line

NASA Technical Reports Server (NTRS)

Hench, John J.; Lurie, Boris; Grogan, Robert; Johnson, Richard

2000-01-01

This paper discusses the implementation of a globally stable nonlinear controller algorithm for the Real-Time Interferometer Control System Testbed (RICST) brassboard optical delay line (ODL) developed for the Interferometry Technology Program at the Jet Propulsion Laboratory. The control methodology essentially employs loop shaping to implement linear control laws. while utilizing nonlinear elements as means of ameliorating the effects of actuator saturation in its coarse, main, and vernier stages. The linear controllers were implemented as high-order digital filters and were designed using Bode integral techniques to determine the loop shape. The nonlinear techniques encompass the areas of exact linearization, anti-windup control, nonlinear rate limiting and modal control. Details of the design procedure are given as well as data from the actual mechanism.

Deterministic Reconfigurable Control Design for the X-33 Vehicle

NASA Technical Reports Server (NTRS)

Wagner, Elaine A.; Burken, John J.; Hanson, Curtis E.; Wohletz, Jerry M.

1998-01-01

In the event of a control surface failure, the purpose of a reconfigurable control system is to redistribute the control effort among the remaining working surfaces such that satisfactory stability and performance are retained. Four reconfigurable control design methods were investigated for the X-33 vehicle: Redistributed Pseudo-Inverse, General Constrained Optimization, Automated Failure Dependent Gain Schedule, and an Off-line Nonlinear General Constrained Optimization. The Off-line Nonlinear General Constrained Optimization approach was chosen for implementation on the X-33. Two example failures are shown, a right outboard elevon jam at 25 deg. at a Mach 3 entry condition, and a left rudder jam at 30 degrees. Note however, that reconfigurable control laws have been designed for the entire flight envelope. Comparisons between responses with the nominal controller and reconfigurable controllers show the benefits of reconfiguration. Single jam aerosurface failures were considered, and failure detection and identification is considered accomplished in the actuator controller. The X-33 flight control system will incorporate reconfigurable flight control in the baseline system.

Reconfigurable Control Design for the Full X-33 Flight Envelope

NASA Technical Reports Server (NTRS)

Cotting, M. Christopher; Burken, John J.

2001-01-01

A reconfigurable control law for the full X-33 flight envelope has been designed to accommodate a failed control surface and redistribute the control effort among the remaining working surfaces to retain satisfactory stability and performance. An offline nonlinear constrained optimization approach has been used for the X-33 reconfigurable control design method. Using a nonlinear, six-degree-of-freedom simulation, three example failures are evaluated: ascent with a left body flap jammed at maximum deflection; entry with a right inboard elevon jammed at maximum deflection; and landing with a left rudder jammed at maximum deflection. Failure detection and identification are accomplished in the actuator controller. Failure response comparisons between the nominal control mixer and the reconfigurable control subsystem (mixer) show the benefits of reconfiguration. Single aerosurface jamming failures are considered. The cases evaluated are representative of the study conducted to prove the adequate and safe performance of the reconfigurable control mixer throughout the full flight envelope. The X-33 flight control system incorporates reconfigurable flight control in the existing baseline system.

Towards Validation of an Adaptive Flight Control Simulation Using Statistical Emulation

NASA Technical Reports Server (NTRS)

He, Yuning; Lee, Herbert K. H.; Davies, Misty D.

2012-01-01

Traditional validation of flight control systems is based primarily upon empirical testing. Empirical testing is sufficient for simple systems in which a.) the behavior is approximately linear and b.) humans are in-the-loop and responsible for off-nominal flight regimes. A different possible concept of operation is to use adaptive flight control systems with online learning neural networks (OLNNs) in combination with a human pilot for off-nominal flight behavior (such as when a plane has been damaged). Validating these systems is difficult because the controller is changing during the flight in a nonlinear way, and because the pilot and the control system have the potential to co-adapt in adverse ways traditional empirical methods are unlikely to provide any guarantees in this case. Additionally, the time it takes to find unsafe regions within the flight envelope using empirical testing means that the time between adaptive controller design iterations is large. This paper describes a new concept for validating adaptive control systems using methods based on Bayesian statistics. This validation framework allows the analyst to build nonlinear models with modal behavior, and to have an uncertainty estimate for the difference between the behaviors of the model and system under test.

Distributed neural network control for adaptive synchronization of uncertain dynamical multiagent systems.

PubMed

Peng, Zhouhua; Wang, Dan; Zhang, Hongwei; Sun, Gang

2014-08-01

This paper addresses the leader-follower synchronization problem of uncertain dynamical multiagent systems with nonlinear dynamics. Distributed adaptive synchronization controllers are proposed based on the state information of neighboring agents. The control design is developed for both undirected and directed communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case where a neighborhood observer is proposed based on relative output information of neighboring agents. Then, distributed observer-based synchronization controllers are derived and a parameter-dependent Riccati inequality is employed to prove the stability. This design has a favorable decouple property between the observer and the controller designs for nonlinear multiagent systems. For both cases, the developed controllers guarantee that the state of each agent synchronizes to that of the leader with bounded residual errors. Two illustrative examples validate the efficacy of the proposed methods.

Feedback linearizing control of a MIMO power system

NASA Astrophysics Data System (ADS)

Ilyes, Laszlo

Prior research has demonstrated that either the mechanical or electrical subsystem of a synchronous electric generator may be controlled using single-input single-output (SISO) nonlinear feedback linearization. This research suggests a new approach which applies nonlinear feedback linearization to a multi-input multi-output (MIMO) model of the synchronous electric generator connected to an infinite bus load model. In this way, the electrical and mechanical subsystems may be linearized and simultaneously decoupled through the introduction of a pair of auxiliary inputs. This allows well known, linear, SISO control methods to be effectively applied to the resulting systems. The derivation of the feedback linearizing control law is presented in detail, including a discussion on the use of symbolic math processing as a development tool. The linearizing and decoupling properties of the control law are validated through simulation. And finally, the robustness of the control law is demonstrated.

Controller design for a class of nonlinear MIMO coupled system using multiple models and second level adaptation.

PubMed

Pandey, Vinay Kumar; Kar, Indrani; Mahanta, Chitralekha

2017-07-01

In this paper, an adaptive control method using multiple models with second level adaptation is proposed for a class of nonlinear multi-input multi-output (MIMO) coupled systems. Multiple estimation models are used to tune the unknown parameters at the first level. The second level adaptation provides a single parameter vector for the controller. A feedback linearization technique is used to design a state feedback control. The efficacy of the designed controller is validated by conducting real time experiment on a laboratory setup of twin rotor MIMO system (TRMS). The TRMS setup is discussed in detail and the experiments were performed for regulation and tracking problem for pitch and yaw control using different reference signals. An Extended Kalman Filter (EKF) has been used to observe the unavailable states of the TRMS. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Application of fuzzy adaptive control to a MIMO nonlinear time-delay pump-valve system.

PubMed

Lai, Zhounian; Wu, Peng; Wu, Dazhuan

2015-07-01

In this paper, a control strategy to balance the reliability against efficiency is introduced to overcome the common off-design operation problem in pump-valve systems. The pump-valve system is a nonlinear multi-input-multi-output (MIMO) system with time delays which cannot be accurately measured but can be approximately modeled using Bernoulli Principle. A fuzzy adaptive controller is applied to approximate system parameters and achieve the control of delay-free model since the system model is inaccurate and the direct feedback linearization method cannot be applied. An extended Smith predictor is introduced to compensate time delays of the system using the inaccurate system model. The experiment is carried out to verify the effectiveness of the control strategy whose results show that the control performance is well achieved. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Piezoelectric Power Requirements for Active Vibration Control

NASA Technical Reports Server (NTRS)

Brennan, Matthew C.; McGowan, Anna-Maria Rivas

1997-01-01

This paper presents a method for predicting the power consumption of piezoelectric actuators utilized for active vibration control. Analytical developments and experimental tests show that the maximum power required to control a structure using surface-bonded piezoelectric actuators is independent of the dynamics between the piezoelectric actuator and the host structure. The results demonstrate that for a perfectly-controlled system, the power consumption is a function of the quantity and type of piezoelectric actuators and the voltage and frequency of the control law output signal. Furthermore, as control effectiveness decreases, the power consumption of the piezoelectric actuators decreases. In addition, experimental results revealed a non-linear behavior in the material properties of piezoelectric actuators. The material non- linearity displayed a significant increase in capacitance with an increase in excitation voltage. Tests show that if the non-linearity of the capacitance was accounted for, a conservative estimate of the power can easily be determined.

Flatness-based control and Kalman filtering for a continuous-time macroeconomic model

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Busawon, K.; Binns, R.

2017-11-01

The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

PubMed

Si, Wenjie; Dong, Xunde; Yang, Feifei

2018-03-01

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

Model Based Predictive Control of Multivariable Hammerstein Processes with Fuzzy Logic Hypercube Interpolated Models

PubMed Central

Coelho, Antonio Augusto Rodrigues

2016-01-01

This paper introduces the Fuzzy Logic Hypercube Interpolator (FLHI) and demonstrates applications in control of multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) processes with Hammerstein nonlinearities. FLHI consists of a Takagi-Sugeno fuzzy inference system where membership functions act as kernel functions of an interpolator. Conjunction of membership functions in an unitary hypercube space enables multivariable interpolation of N-dimensions. Membership functions act as interpolation kernels, such that choice of membership functions determines interpolation characteristics, allowing FLHI to behave as a nearest-neighbor, linear, cubic, spline or Lanczos interpolator, to name a few. The proposed interpolator is presented as a solution to the modeling problem of static nonlinearities since it is capable of modeling both a function and its inverse function. Three study cases from literature are presented, a single-input single-output (SISO) system, a MISO and a MIMO system. Good results are obtained regarding performance metrics such as set-point tracking, control variation and robustness. Results demonstrate applicability of the proposed method in modeling Hammerstein nonlinearities and their inverse functions for implementation of an output compensator with Model Based Predictive Control (MBPC), in particular Dynamic Matrix Control (DMC). PMID:27657723

Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.

PubMed

Kiumarsi, Bahare; Lewis, Frank L

2015-01-01

This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.

Anti-sway control of tethered satellite systems using attitude control of the main satellite

NASA Astrophysics Data System (ADS)

Yousefian, Peyman; Salarieh, Hassan

2015-06-01

In this study a new method is introduced to suppress libration of a tethered satellite system (TSS). It benefits from coupling between satellites and tether libration dynamics. The control concept uses the main satellite attitude maneuvers to suppress librational motion of the tether, and the main satellite's actuators for attitude control are used as the only actuation in the system. The study considers planar motion of a two body TSS system in a circular orbit and it is assumed that the tether's motion will not change it. Governing dynamic equations of motion are derived using the extended Lagrange method. Controllability of the system around the equilibrium state is studied and a linear LQG controller is designed to regulate libration of the system. Tether tension and satellite attitude are assumed as only measurable outputs of the system. The Extended Kalman Filter (EKF) is used to estimate states of the system to be used as feedback to the controller. The designed controller and observer are implemented to the nonlinear plant and simulations demonstrate that the controller lead to reduction of the tether libration propoerly. By the way, because the controller is linear, it is applicable only at low amplitudes in the vicinity of equilibrium point. To reach global stability, a nonlinear controller is demanded.

A Case Study on the Application of a Structured Experimental Method for Optimal Parameter Design of a Complex Control System

NASA Technical Reports Server (NTRS)

Torres-Pomales, Wilfredo

2015-01-01

This report documents a case study on the application of Reliability Engineering techniques to achieve an optimal balance between performance and robustness by tuning the functional parameters of a complex non-linear control system. For complex systems with intricate and non-linear patterns of interaction between system components, analytical derivation of a mathematical model of system performance and robustness in terms of functional parameters may not be feasible or cost-effective. The demonstrated approach is simple, structured, effective, repeatable, and cost and time efficient. This general approach is suitable for a wide range of systems.

State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

PubMed

Korayem, M H; Nekoo, S R

2015-07-01

This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Propulsion system performance resulting from an integrated flight/propulsion control design

NASA Technical Reports Server (NTRS)

Mattern, Duane; Garg, Sanjay

1992-01-01

Propulsion-system-specific results are presented from the application of the integrated methodology for propulsion and airframe control (IMPAC) design approach to integrated flight/propulsion control design for a 'short takeoff and vertical landing' (STOVL) aircraft in transition flight. The IMPAC method is briefly discussed and the propulsion system specifications for the integrated control design are examined. The structure of a linear engine controller that results from partitioning a linear centralized controller is discussed. The details of a nonlinear propulsion control system are presented, including a scheme to protect the engine operational limits: the fan surge margin and the acceleration/deceleration schedule that limits the fuel flow. Also, a simple but effective multivariable integrator windup protection scheme is examined. Nonlinear closed-loop simulation results are presented for two typical pilot commands for transition flight: acceleration while maintaining flightpath angle and a change in flightpath angle while maintaining airspeed. The simulation nonlinearities include the airframe/engine coupling, the actuator and sensor dynamics and limits, the protection scheme for the engine operational limits, and the integrator windup protection. Satisfactory performance of the total airframe plus engine system for transition flight, as defined by the specifications, was maintained during the limit operation of the closed-loop engine subsystem.

Thermal, size and surface effects on the nonlinear pull-in of small-scale piezoelectric actuators

NASA Astrophysics Data System (ADS)

SoltanRezaee, Masoud; Ghazavi, Mohammad-Reza

2017-09-01

Electrostatically actuated miniature wires/tubes have many operational applications in the high-tech industries. In this research, the nonlinear pull-in instability of piezoelectric thermal small-scale switches subjected to Coulomb and dissipative forces is analyzed using strain gradient and modified couple stress theories. The discretized governing equation is solved numerically by means of the step-by-step linearization method. The correctness of the formulated model and solution procedure is validated through comparison with experimental and several theoretical results. Herein, the length-scale, surface energy, van der Waals attraction and nonlinear curvature are considered in the present comprehensive model and the thermo-electro-mechanical behavior of cantilever piezo-beams are discussed in detail. It is found that the piezoelectric actuation can be used as a design parameter to control the pull-in phenomenon. The obtained results are applicable in stability analysis, practical design and control of actuated miniature intelligent devices.

Traffic Predictive Control: Case Study and Evaluation

DOT National Transportation Integrated Search

2017-06-26

This project developed a quantile regression method for predicting future traffic flow at a signalized intersection by combining both historical and real-time data. The algorithm exploits nonlinear correlations in historical measurements and efficien...

Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses

NASA Astrophysics Data System (ADS)

Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin

2016-08-01

This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.

A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics.

PubMed

Zeng, Cheng; Liang, Shan; Xiang, Shuwen

2017-05-01

Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Optimal filtering and Bayesian detection for friction-based diagnostics in machines.

PubMed

Ray, L R; Townsend, J R; Ramasubramanian, A

2001-01-01

Non-model-based diagnostic methods typically rely on measured signals that must be empirically related to process behavior or incipient faults. The difficulty in interpreting a signal that is indirectly related to the fundamental process behavior is significant. This paper presents an integrated non-model and model-based approach to detecting when process behavior varies from a proposed model. The method, which is based on nonlinear filtering combined with maximum likelihood hypothesis testing, is applicable to dynamic systems whose constitutive model is well known, and whose process inputs are poorly known. Here, the method is applied to friction estimation and diagnosis during motion control in a rotating machine. A nonlinear observer estimates friction torque in a machine from shaft angular position measurements and the known input voltage to the motor. The resulting friction torque estimate can be analyzed directly for statistical abnormalities, or it can be directly compared to friction torque outputs of an applicable friction process model in order to diagnose faults or model variations. Nonlinear estimation of friction torque provides a variable on which to apply diagnostic methods that is directly related to model variations or faults. The method is evaluated experimentally by its ability to detect normal load variations in a closed-loop controlled motor driven inertia with bearing friction and an artificially-induced external line contact. Results show an ability to detect statistically significant changes in friction characteristics induced by normal load variations over a wide range of underlying friction behaviors.

Nonlinear adaptive control based on fuzzy sliding mode technique and fuzzy-based compensator.

PubMed

Nguyen, Sy Dzung; Vo, Hoang Duy; Seo, Tae-Il

2017-09-01

It is difficult to efficiently control nonlinear systems in the presence of uncertainty and disturbance (UAD). One of the main reasons derives from the negative impact of the unknown features of UAD as well as the response delay of the control system on the accuracy rate in the real time of the control signal. In order to deal with this, we propose a new controller named CO-FSMC for a class of nonlinear control systems subjected to UAD, which is constituted of a fuzzy sliding mode controller (FSMC) and a fuzzy-based compensator (CO). Firstly, the FSMC and CO are designed independently, and then an adaptive fuzzy structure is discovered to combine them. Solutions for avoiding the singular cases of the fuzzy-based function approximation and reducing the calculating cost are proposed. Based on the solutions, fuzzy sliding mode technique, lumped disturbance observer and Lyapunov stability analysis, a closed-loop adaptive control law is formulated. Simulations along with a real application based on a semi-active train-car suspension are performed to fully evaluate the method. The obtained results reflected that vibration of the chassis mass is insensitive to UAD. Compared with the other fuzzy sliding mode control strategies, the CO-FSMC can provide the best control ability to reduce unwanted vibrations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Linear and nonlinear schemes applied to pitch control of wind turbines.

PubMed

Geng, Hua; Yang, Geng

2014-01-01

Linear controllers have been employed in industrial applications for many years, but sometimes they are noneffective on the system with nonlinear characteristics. This paper discusses the structure, performance, implementation cost, advantages, and disadvantages of different linear and nonlinear schemes applied to the pitch control of the wind energy conversion systems (WECSs). The linear controller has the simplest structure and is easily understood by the engineers and thus is widely accepted by the industry. In contrast, nonlinear schemes are more complicated, but they can provide better performance. Although nonlinear algorithms can be implemented in a powerful digital processor nowadays, they need time to be accepted by the industry and their reliability needs to be verified in the commercial products. More information about the system nonlinear feature is helpful to simplify the controller design. However, nonlinear schemes independent of the system model are more robust to the uncertainties or deviations of the system parameters.

A semi-active H∞ control strategy with application to the vibration suppression of nonlinear high-rise building under earthquake excitations.

PubMed

Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong

2016-01-01

Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibration. In this strategy, a modified Kalman-Bucy observer which is suitable for the proposed semi-active strategy is developed to obtain the state vector from the measured semi-active control force and acceleration feedback, taking into account of the effects of nonlinearity, disturbance and uncertainty of controlled system parameters by the observed nonlinear accelerations. Then, the proposed semi-active H∞ control strategy is applied to the ASCE 20-story benchmark building when subjected to earthquake excitation and compared with the other control approaches by some control criteria. It is indicated that the proposed semi-active H∞ control strategy provides much better control performances by comparison with the semi-active MPC and Clipped-LQG control approaches, and can reduce nonlinear seismic response and minimize the damage in the buildings. Besides, it enhances the reliability of the control performance when compared with the active control strategy. Thus, the proposed semi-active H∞ control strategy is suitable for suppressing the nonlinear vibration of high-rise buildings.

A Study on Application of Fuzzy Adaptive Unscented Kalman Filter to Nonlinear Turbojet Engine Control

NASA Astrophysics Data System (ADS)

Han, Dongju

2018-05-01

Safe and efficient flight powered by an aircraft turbojet engine relies on the performance of the engine controller preventing compressor surge with robustness from noises or disturbances. This paper proposes the effective nonlinear controller associated with the nonlinear filter for the real turbojet engine with highly nonlinear dynamics. For the feasible controller study the nonlinearity of the engine dynamics was investigated by comparing the step responses from the linearized model with the original nonlinear dynamics. The fuzzy-based PID control logic is introduced to control the engine efficiently and FAUKF is applied for robustness from noises. The simulation results prove the effectiveness of FAUKF applied to the proposed controller such that the control performances are superior over the conventional controller and the filer performance using FAUKF indicates the satisfactory results such as clearing the defects by reducing the distortions without compressor surge, whereas the conventional UKF is not fully effective as occurring some distortions with compressor surge due to a process noise.

Dynamics and control of quadcopter using linear model predictive control approach

NASA Astrophysics Data System (ADS)

Islam, M.; Okasha, M.; Idres, M. M.

2017-12-01

This paper investigates the dynamics and control of a quadcopter using the Model Predictive Control (MPC) approach. The dynamic model is of high fidelity and nonlinear, with six degrees of freedom that include disturbances and model uncertainties. The control approach is developed based on MPC to track different reference trajectories ranging from simple ones such as circular to complex helical trajectories. In this control technique, a linearized model is derived and the receding horizon method is applied to generate the optimal control sequence. Although MPC is computer expensive, it is highly effective to deal with the different types of nonlinearities and constraints such as actuators’ saturation and model uncertainties. The MPC parameters (control and prediction horizons) are selected by trial-and-error approach. Several simulation scenarios are performed to examine and evaluate the performance of the proposed control approach using MATLAB and Simulink environment. Simulation results show that this control approach is highly effective to track a given reference trajectory.

Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

NASA Astrophysics Data System (ADS)

Yang, Tao; Cao, Qingjie

2018-03-01

This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.