Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Feedback linearization based control of a variable air volume air conditioning system for cooling applications.

PubMed

Thosar, Archana; Patra, Amit; Bhattacharyya, Souvik

2008-07-01

Design of a nonlinear control system for a Variable Air Volume Air Conditioning (VAVAC) plant through feedback linearization is presented in this article. VAVAC systems attempt to reduce building energy consumption while maintaining the primary role of air conditioning. The temperature of the space is maintained at a constant level by establishing a balance between the cooling load generated in the space and the air supply delivered to meet the load. The dynamic model of a VAVAC plant is derived and formulated as a MIMO bilinear system. Feedback linearization is applied for decoupling and linearization of the nonlinear model. Simulation results for a laboratory scale plant are presented to demonstrate the potential of keeping comfort and maintaining energy optimal performance by this methodology. Results obtained with a conventional PI controller and a feedback linearizing controller are compared and the superiority of the proposed approach is clearly established.

Supporting second grade lower secondary school students’ understanding of linear equation system in two variables using ethnomathematics

NASA Astrophysics Data System (ADS)

Nursyahidah, F.; Saputro, B. A.; Rubowo, M. R.

2018-03-01

The aim of this research is to know the students’ understanding of linear equation system in two variables using Ethnomathematics and to acquire learning trajectory of linear equation system in two variables for the second grade of lower secondary school students. This research used methodology of design research that consists of three phases, there are preliminary design, teaching experiment, and retrospective analysis. Subject of this study is 28 second grade students of Sekolah Menengah Pertama (SMP) 37 Semarang. The result of this research shows that the students’ understanding in linear equation system in two variables can be stimulated by using Ethnomathematics in selling buying tradition in Peterongan traditional market in Central Java as a context. All of strategies and model that was applied by students and also their result discussion shows how construction and contribution of students can help them to understand concept of linear equation system in two variables. All the activities that were done by students produce learning trajectory to gain the goal of learning. Each steps of learning trajectory of students have an important role in understanding the concept from informal to the formal level. Learning trajectory using Ethnomathematics that is produced consist of watching video of selling buying activity in Peterongan traditional market to construct linear equation in two variables, determine the solution of linear equation in two variables, construct model of linear equation system in two variables from contextual problem, and solving a contextual problem related to linear equation system in two variables.

Integrability and correspondence of classical and quantum non-linear three-mode systems

NASA Astrophysics Data System (ADS)

Odzijewicz, A.; Wawreniuk, E.

2018-04-01

The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the quantum system are constructed. We find the explicit formulas for the reproducing measure for these states. Examples of some applications of the obtained results in non-linear quantum optics are presented.

Linearized aerodynamic and control law models of the X-29A airplane and comparison with flight data

NASA Technical Reports Server (NTRS)

Bosworth, John T.

1992-01-01

Flight control system design and analysis for aircraft rely on mathematical models of the vehicle dynamics. In addition to a six degree of freedom nonlinear simulation, the X-29A flight controls group developed a set of programs that calculate linear perturbation models throughout the X-29A flight envelope. The models include the aerodynamics as well as flight control system dynamics and were used for stability, controllability, and handling qualities analysis. These linear models were compared to flight test results to help provide a safe flight envelope expansion. A description is given of the linear models at three flight conditions and two flight control system modes. The models are presented with a level of detail that would allow the reader to reproduce the linear results if desired. Comparison between the response of the linear model and flight measured responses are presented to demonstrate the strengths and weaknesses of the linear models' ability to predict flight dynamics.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

Relevance of Linear Stability Results to Enhanced Oil Recovery

NASA Astrophysics Data System (ADS)

Ding, Xueru; Daripa, Prabir

2012-11-01

How relevant can the results based on linear stability theory for any problem for that matter be to full scale simulation results? Put it differently, is the optimal design of a system based on linear stability results is optimal or even near optimal for the complex nonlinear system with certain objectives of interest in mind? We will address these issues in the context of enhanced oil recovery by chemical flooding. This will be based on an ongoing work. Supported by Qatar National Research Fund (a member of the Qatar Foundation).

Chosen interval methods for solving linear interval systems with special type of matrix

NASA Astrophysics Data System (ADS)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

A linear quadratic regulator approach to the stabilization of uncertain linear systems

NASA Technical Reports Server (NTRS)

Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.

1990-01-01

This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.

Switched periodic systems in discrete time: stability and input-output norms

NASA Astrophysics Data System (ADS)

Bolzern, Paolo; Colaneri, Patrizio

2013-07-01

This paper deals with the analysis of stability and the characterisation of input-output norms for discrete-time periodic switched linear systems. Such systems consist of a network of time-periodic linear subsystems sharing the same state vector and an exogenous switching signal that triggers the jumps between the subsystems. The overall system exhibits a complex dynamic behaviour due to the interplay between the time periodicity of the subsystem parameters and the switching signal. Both arbitrary switching signals and signals satisfying a dwell-time constraint are considered. Linear matrix inequality conditions for stability and guaranteed H2 and H∞ performances are provided. The results heavily rely on the merge of the theory of linear periodic systems and recent developments on switched linear time-invariant systems.

Fast correction approach for wavefront sensorless adaptive optics based on a linear phase diversity technique.

PubMed

Yue, Dan; Nie, Haitao; Li, Ye; Ying, Changsheng

2018-03-01

Wavefront sensorless (WFSless) adaptive optics (AO) systems have been widely studied in recent years. To reach optimum results, such systems require an efficient correction method. This paper presents a fast wavefront correction approach for a WFSless AO system mainly based on the linear phase diversity (PD) technique. The fast closed-loop control algorithm is set up based on the linear relationship between the drive voltage of the deformable mirror (DM) and the far-field images of the system, which is obtained through the linear PD algorithm combined with the influence function of the DM. A large number of phase screens under different turbulence strengths are simulated to test the performance of the proposed method. The numerical simulation results show that the method has fast convergence rate and strong correction ability, a few correction times can achieve good correction results, and can effectively improve the imaging quality of the system while needing fewer measurements of CCD data.

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.

A robust approach to measuring the detective quantum efficiency of radiographic detectors in a clinical setting

NASA Astrophysics Data System (ADS)

McDonald, Michael C.; Kim, H. K.; Henry, J. R.; Cunningham, I. A.

2012-03-01

The detective quantum efficiency (DQE) is widely accepted as a primary measure of x-ray detector performance in the scientific community. A standard method for measuring the DQE, based on IEC 62220-1, requires the system to have a linear response meaning that the detector output signals are proportional to the incident x-ray exposure. However, many systems have a non-linear response due to characteristics of the detector, or post processing of the detector signals, that cannot be disabled and may involve unknown algorithms considered proprietary by the manufacturer. For these reasons, the DQE has not been considered as a practical candidate for routine quality assurance testing in a clinical setting. In this article we described a method that can be used to measure the DQE of both linear and non-linear systems that employ only linear image processing algorithms. The method was validated on a Cesium Iodide based flat panel system that simultaneously stores a raw (linear) and processed (non-linear) image for each exposure. It was found that the resulting DQE was equivalent to a conventional standards-compliant DQE with measurement precision, and the gray-scale inversion and linear edge enhancement did not affect the DQE result. While not IEC 62220-1 compliant, it may be adequate for QA programs.

Stability analysis of a time-periodic 2-dof MEMS structure

NASA Astrophysics Data System (ADS)

Kniffka, Till Jochen; Welte, Johannes; Ecker, Horst

2012-11-01

Microelectromechanical systems (MEMS) are becoming important for all kinds of industrial applications. Among them are filters in communication devices, due to the growing demand for efficient and accurate filtering of signals. In recent developments single degree of freedom (1-dof) oscillators, that are operated at a parametric resonances, are employed for such tasks. Typically vibration damping is low in such MEM systems. While parametric excitation (PE) is used so far to take advantage of a parametric resonance, this contribution suggests to also exploit parametric anti-resonances in order to improve the damping behavior of such systems. Modeling aspects of a 2-dof MEM system and first results of the analysis of the non-linear and the linearized system are the focus of this paper. In principle the investigated system is an oscillating mechanical system with two degrees of freedom x = [x1x2]T that can be described by Mx+Cx+K1x+K3(x2)x+Fes(x,V(t)) = 0. The system is inherently non-linear because of the cubic mechanical stiffness K3 of the structure, but also because of electrostatic forces (1+cos(ωt))Fes(x) that act on the system. Electrostatic forces are generated by comb drives and are proportional to the applied time-periodic voltage V(t). These drives also provide the means to introduce time-periodic coefficients, i.e. parametric excitation (1+cos(ωt)) with frequency ω. For a realistic MEM system the coefficients of the non-linear set of differential equations need to be scaled for efficient numerical treatment. The final mathematical model is a set of four non-linear time-periodic homogeneous differential equations of first order. Numerical results are obtained from two different methods. The linearized time-periodic (LTP) system is studied by calculating the Monodromy matrix of the system. The eigenvalues of this matrix decide on the stability of the LTP-system. To study the unabridged non-linear system, the bifurcation software ManLab is employed. Continuation analysis including stability evaluations are executed and show the frequency ranges for which the 2-dof system becomes unstable due to parametric resonances. Moreover, the existence of frequency intervals are shown where enhanced damping for the system is observed for this MEMS. The results from the stability studies are confirmed by simulation results.

Space station structures development

NASA Technical Reports Server (NTRS)

Teller, V. B.

1986-01-01

A study of three interrelated tasks focusing on deployable Space Station truss structures is discussed. Task 1, the development of an alternate deployment system for linear truss, resulted in the preliminary design of an in-space reloadable linear motor deployer. Task 2, advanced composites deployable truss development, resulted in the testing and evaluation of composite materials for struts used in a deployable linear truss. Task 3, assembly of structures in space/erectable structures, resulted in the preliminary design of Space Station pressurized module support structures. An independent, redundant support system was developed for the common United States modules.

Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems

NASA Astrophysics Data System (ADS)

Wang, Xue-Zhong; Huang, Ting-Zhu; Fu, Ying-Ding

2007-09-01

In this paper, we present some comparison theorems on preconditioned iterative method for solving Z-matrices linear systems, Comparison results show that the rate of convergence of the Gauss-Seidel-type method is faster than the rate of convergence of the SOR-type iterative method.

Feedback linearization of singularly perturbed systems based on canonical similarity transformations

NASA Astrophysics Data System (ADS)

Kabanov, A. A.

2018-05-01

This paper discusses the problem of feedback linearization of a singularly perturbed system in a state-dependent coefficient form. The result is based on the introduction of a canonical similarity transformation. The transformation matrix is constructed from separate blocks for fast and slow part of an original singularly perturbed system. The transformed singular perturbed system has a linear canonical form that significantly simplifies a control design problem. Proposed similarity transformation allows accomplishing linearization of the system without considering the virtual output (as it is needed for normal form method), a technique of a transition from phase coordinates of the transformed system to state variables of the original system is simpler. The application of the proposed approach is illustrated through example.

Experimental analysis of bidirectional reflectance distribution function cross section conversion term in direction cosine space.

PubMed

Butler, Samuel D; Nauyoks, Stephen E; Marciniak, Michael A

2015-06-01

Of the many classes of bidirectional reflectance distribution function (BRDF) models, two popular classes of models are the microfacet model and the linear systems diffraction model. The microfacet model has the benefit of speed and simplicity, as it uses geometric optics approximations, while linear systems theory uses a diffraction approach to compute the BRDF, at the expense of greater computational complexity. In this Letter, nongrazing BRDF measurements of rough and polished surface-reflecting materials at multiple incident angles are scaled by the microfacet cross section conversion term, but in the linear systems direction cosine space, resulting in great alignment of BRDF data at various incident angles in this space. This results in a predictive BRDF model for surface-reflecting materials at nongrazing angles, while avoiding some of the computational complexities in the linear systems diffraction model.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

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.

Applied Time Domain Stability Margin Assessment for Nonlinear Time-Varying Systems

NASA Technical Reports Server (NTRS)

Kiefer, J. M.; Johnson, M. D.; Wall, J. H.; Dominguez, A.

2016-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation. This technique was implemented by using the Stability Aerospace Vehicle Analysis Tool (SAVANT) computer simulation to evaluate the stability of the SLS system with the Adaptive Augmenting Control (AAC) active and inactive along its ascent trajectory. The gains for which the vehicle maintains apparent time-domain stability defines the gain margins, and the time delay similarly defines the phase margin. This method of extracting the control stability margins from the time-domain simulation is relatively straightforward and the resultant margins can be compared to the linearized system results. The sections herein describe the techniques employed to extract the time-domain margins, compare the results between these nonlinear and the linear methods, and provide explanations for observed discrepancies. The SLS ascent trajectory was simulated with SAVANT and the classical linear stability margins were evaluated at one second intervals. The linear analysis was performed with the AAC algorithm disabled to attain baseline stability margins. At each time point, the system was linearized about the current operating point using Simulink's built-in solver. Each linearized system in time was evaluated for its rigid-body gain margin (high frequency gain margin), rigid-body phase margin, and aero gain margin (low frequency gain margin) for each control axis. Using the stability margins derived from the baseline linearization approach, the time domain derived stability margins were determined by executing time domain simulations in which axis-specific incremental gain and phase adjustments were made to the nominal system about the expected neutral stability point at specific flight times. The baseline stability margin time histories were used to shift the system gain to various values around the zero margin point such that a precise amount of expected gain margin was maintained throughout flight. When assessing the gain margins, the gain was applied starting at the time point under consideration, thereafter following the variation in the margin found in the linear analysis. When assessing the rigid-body phase margin, a constant time delay was applied to the system starting at the time point under consideration. If the baseline stability margins were correctly determined via the linear analysis, the time domain simulation results should contain unstable behavior at certain gain and phase values. Examples will be shown from repeated simulations with variable added gain and phase lag. Faithfulness of margins calculated from the linear analysis to the nonlinear system will be demonstrated.

ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2005-01-01

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one-, two- and three-space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obtained for solutions with discontinuities. We also present preliminary results for two-dimensional non-linear systems.

Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis

PubMed Central

Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel

2013-01-01

This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007

Comment on "Synchronization of chaotic systems with delay using intermittent linear state feedback" [Chaos 18, 033122 (2008)].

PubMed

Zhang, Yinping; Wang, Qing-Guo

2008-12-01

In the referenced paper, there is technical carelessness in the third lemma and in the main result. Hence, it is a possible failure when the result is used to design the intermittent linear state feedback controller for exponential synchronization of two chaotic delayed systems.

Controller Synthesis for Periodically Forced Chaotic Systems

NASA Astrophysics Data System (ADS)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

A methodology for design of a linear referencing system for surface transportation

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

Vonderohe, A.; Hepworth, T.

1997-06-01

The transportation community has recently placed significant emphasis on development of data models, procedural standards, and policies for management of linearly-referenced data. There is an Intelligent Transportation Systems initiative underway to create a spatial datum for location referencing in one, two, and three dimensions. Most recently, a call was made for development of a unified linear reference system to support public, private, and military surface transportation needs. A methodology for design of the linear referencing system was developed from geodetic engineering principles and techniques used for designing geodetic control networks. The method is founded upon the law of propagation ofmore » random error and the statistical analysis of systems of redundant measurements, used to produce best estimates for unknown parameters. A complete mathematical development is provided. Example adjustments of linear distance measurement systems are included. The classical orders of design are discussed with regard to the linear referencing system. A simple design example is provided. A linear referencing system designed and analyzed with this method will not only be assured of meeting the accuracy requirements of users, it will have the potential for supporting delivery of error estimates along with the results of spatial analytical queries. Modeling considerations, alternative measurement methods, implementation strategies, maintenance issues, and further research needs are discussed. Recommendations are made for further advancement of the unified linear referencing system concept.« less

Image Processing Research

DTIC Science & Technology

1975-09-30

systems a linear model results in an object f being mappad into an image _ by a point spread function matrix H. Thus with noise j +Hf +n (1) The simplest... linear models for imaging systems are given by space invariant point spread functions (SIPSF) in which case H is block circulant. If the linear model is...Ij,...,k-IM1 is a set of two dimensional indices each distinct and prior to k. Modeling Procedare: To derive the linear predictor (block LP of figure

Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Ishihara, Abraham K.; Krishnakumar, Kalmanje Srinlvas; Bakhtiari-Nejad, Maryam

2009-01-01

This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

Linear dependence between the wavefront gradient and the masked intensity for the point source with a CCD sensor

NASA Astrophysics Data System (ADS)

Yang, Huizhen; Ma, Liang; Wang, Bin

2018-01-01

In contrast to the conventional adaptive optics (AO) system, the wavefront sensorless (WFSless) AO system doesn't need a WFS to measure the wavefront aberrations. It is simpler than the conventional AO in system architecture and can be applied to the complex conditions. The model-based WFSless system has a great potential in real-time correction applications because of its fast convergence. The control algorithm of the model-based WFSless system is based on an important theory result that is the linear relation between the Mean-Square Gradient (MSG) magnitude of the wavefront aberration and the second moment of the masked intensity distribution in the focal plane (also called as Masked Detector Signal-MDS). The linear dependence between MSG and MDS for the point source imaging with a CCD sensor will be discussed from theory and simulation in this paper. The theory relationship between MSG and MDS is given based on our previous work. To verify the linear relation for the point source, we set up an imaging model under atmospheric turbulence. Additionally, the value of MDS will be deviate from that of theory because of the noise of detector and further the deviation will affect the correction effect. The theory results under noise will be obtained through theoretical derivation and then the linear relation between MDS and MDS under noise will be discussed through the imaging model. Results show the linear relation between MDS and MDS under noise is also maintained well, which provides a theoretical support to applications of the model-based WFSless system.

Accuracy of active chirp linearization for broadband frequency modulated continuous wave ladar.

PubMed

Barber, Zeb W; Babbitt, Wm Randall; Kaylor, Brant; Reibel, Randy R; Roos, Peter A

2010-01-10

As the bandwidth and linearity of frequency modulated continuous wave chirp ladar increase, the resulting range resolution, precisions, and accuracy are improved correspondingly. An analysis of a very broadband (several THz) and linear (<1 ppm) chirped ladar system based on active chirp linearization is presented. Residual chirp nonlinearity and material dispersion are analyzed as to their effect on the dynamic range, precision, and accuracy of the system. Measurement precision and accuracy approaching the part per billion level is predicted.

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

1997-01-01

The NASA Lewis Research Center is developing analytical methods and software tools to create a bridge between the controls and computational fluid dynamics (CFD) disciplines. Traditionally, control design engineers have used coarse nonlinear simulations to generate information for the design of new propulsion system controls. However, such traditional methods are not adequate for modeling the propulsion systems of complex, high-speed vehicles like the High Speed Civil Transport. To properly model the relevant flow physics of high-speed propulsion systems, one must use simulations based on CFD methods. Such CFD simulations have become useful tools for engineers that are designing propulsion system components. The analysis techniques and software being developed as part of this effort are an attempt to evolve CFD into a useful tool for control design as well. One major aspect of this research is the generation of linear models from steady-state CFD results. CFD simulations, often used during the design of high-speed inlets, yield high resolution operating point data. Under a NASA grant, the University of Akron has developed analytical techniques and software tools that use these data to generate linear models for control design. The resulting linear models have the same number of states as the original CFD simulation, so they are still very large and computationally cumbersome. Model reduction techniques have been successfully applied to reduce these large linear models by several orders of magnitude without significantly changing the dynamic response. The result is an accurate, easy to use, low-order linear model that takes less time to generate than those generated by traditional means. The development of methods for generating low-order linear models from steady-state CFD is most complete at the one-dimensional level, where software is available to generate models with different kinds of input and output variables. One-dimensional methods have been extended somewhat so that linear models can also be generated from two- and three-dimensional steady-state results. Standard techniques are adequate for reducing the order of one-dimensional CFD-based linear models. However, reduction of linear models based on two- and three-dimensional CFD results is complicated by very sparse, ill-conditioned matrices. Some novel approaches are being investigated to solve this problem.

Research in Applied Mathematics Related to Mathematical System Theory.

DTIC Science & Technology

1977-06-01

This report deals with research results obtained in the field of mathematical system theory . Special emphasis was given to the following areas: (1...Linear system theory over a field: parametrization of multi-input, multi-output systems and the geometric structure of classes of systems of...constant dimension. (2) Linear systems over a ring: development of the theory for very general classes of rings. (3) Nonlinear system theory : basic

Numerical Technology for Large-Scale Computational Electromagnetics

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

Sharpe, R; Champagne, N; White, D

The key bottleneck of implicit computational electromagnetics tools for large complex geometries is the solution of the resulting linear system of equations. The goal of this effort was to research and develop critical numerical technology that alleviates this bottleneck for large-scale computational electromagnetics (CEM). The mathematical operators and numerical formulations used in this arena of CEM yield linear equations that are complex valued, unstructured, and indefinite. Also, simultaneously applying multiple mathematical modeling formulations to different portions of a complex problem (hybrid formulations) results in a mixed structure linear system, further increasing the computational difficulty. Typically, these hybrid linear systems aremore » solved using a direct solution method, which was acceptable for Cray-class machines but does not scale adequately for ASCI-class machines. Additionally, LLNL's previously existing linear solvers were not well suited for the linear systems that are created by hybrid implicit CEM codes. Hence, a new approach was required to make effective use of ASCI-class computing platforms and to enable the next generation design capabilities. Multiple approaches were investigated, including the latest sparse-direct methods developed by our ASCI collaborators. In addition, approaches that combine domain decomposition (or matrix partitioning) with general-purpose iterative methods and special purpose pre-conditioners were investigated. Special-purpose pre-conditioners that take advantage of the structure of the matrix were adapted and developed based on intimate knowledge of the matrix properties. Finally, new operator formulations were developed that radically improve the conditioning of the resulting linear systems thus greatly reducing solution time. The goal was to enable the solution of CEM problems that are 10 to 100 times larger than our previous capability.« less

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

New Galerkin operational matrices for solving Lane-Emden type equations

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.; Doha, E. H.; Saad, A. S.; Bassuony, M. A.

2016-04-01

Lane-Emden type equations model many phenomena in mathematical physics and astrophysics, such as thermal explosions. This paper is concerned with introducing third and fourth kind Chebyshev-Galerkin operational matrices in order to solve such problems. The principal idea behind the suggested algorithms is based on converting the linear or nonlinear Lane-Emden problem, through the application of suitable spectral methods, into a system of linear or nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of the proposed algorithm in the linear case is that the resulting linear systems are specially structured, and this of course reduces the computational effort required to solve such systems. As an application, we consider the solar model polytrope with n=3 to show that the suggested solutions in this paper are in good agreement with the numerical results.

A Method for Generating Reduced-Order Linear Models of Multidimensional Supersonic Inlets

NASA Technical Reports Server (NTRS)

Chicatelli, Amy; Hartley, Tom T.

1998-01-01

Simulation of high speed propulsion systems may be divided into two categories, nonlinear and linear. The nonlinear simulations are usually based on multidimensional computational fluid dynamics (CFD) methodologies and tend to provide high resolution results that show the fine detail of the flow. Consequently, these simulations are large, numerically intensive, and run much slower than real-time. ne linear simulations are usually based on large lumping techniques that are linearized about a steady-state operating condition. These simplistic models often run at or near real-time but do not always capture the detailed dynamics of the plant. Under a grant sponsored by the NASA Lewis Research Center, Cleveland, Ohio, a new method has been developed that can be used to generate improved linear models for control design from multidimensional steady-state CFD results. This CFD-based linear modeling technique provides a small perturbation model that can be used for control applications and real-time simulations. It is important to note the utility of the modeling procedure; all that is needed to obtain a linear model of the propulsion system is the geometry and steady-state operating conditions from a multidimensional CFD simulation or experiment. This research represents a beginning step in establishing a bridge between the controls discipline and the CFD discipline so that the control engineer is able to effectively use multidimensional CFD results in control system design and analysis.

Variable-energy drift-tube linear accelerator

DOEpatents

Swenson, Donald A.; Boyd, Jr., Thomas J.; Potter, James M.; Stovall, James E.

1984-01-01

A linear accelerator system includes a plurality of post-coupled drift-tubes wherein each post coupler is bistably positionable to either of two positions which result in different field distributions. With binary control over a plurality of post couplers, a significant accumlative effect in the resulting field distribution is achieved yielding a variable-energy drift-tube linear accelerator.

Variable-energy drift-tube linear accelerator

DOEpatents

Swenson, D.A.; Boyd, T.J. Jr.; Potter, J.M.; Stovall, J.E.

A linear accelerator system includes a plurality of post-coupled drift-tubes wherein each post coupler is bistably positionable to either of two positions which result in different field distributions. With binary control over a plurality of post couplers, a significant accumlative effect in the resulting field distribution is achieved yielding a variable-energy drift-tube linear accelerator.

Structural and lithologic study of northern California Coast Range and Sacramento Valley, California

NASA Technical Reports Server (NTRS)

Rich, E. I. (Principal Investigator); Steele, W. C.

1973-01-01

The author has identified the following significant results. Photgeologic examination of repetitive multispectral ERTS-1 imagery of Northern California has disclosed several systems of linear features which may be important for the interpretation of the structural history of California. They are separated from an orthogonal system of linears in the Klamath Mts. by a set of discontinuous southeast-trending linear features (the Mendocino system) which is traceable from the Pacific Coast, at Cape Mendocino, into the eastern foothills of the Sierra Nevada. Within the Sierra Nevada, the Mendocino system separates the north-trending Sierran system from a set of linears characteristic of the Modoc Plateau. With minor exception, little overlap exists among the systems which suggests a decipherable chronology and evolutionary history for the region. The San Andres system of linears appears to truncate or co-exist with most of the other systems in the northern Coast Ranges. The Mendocino system truncates the Klamath, Sierran, and Modoc systems. The Sierran system may represent fundamental and long-persisting pre-late Paleozoic zones of crustal weakness which have been reactivated from time to time. The Mendocino system was possibly developed in early Mesozoic and is important to the structural framework of Northern California.

Linear relations in microbial reaction systems: a general overview of their origin, form, and use.

PubMed

Noorman, H J; Heijnen, J J; Ch A M Luyben, K

1991-09-01

In microbial reaction systems, there are a number of linear relations among net conversion rates. These can be very useful in the analysis of experimental data. This article provides a general approach for the formation and application of the linear relations. Two type of system descriptions, one considering the biomass as a black box and the other based on metabolic pathways, are encountered. These are defined in a linear vector and matrix algebra framework. A correct a priori description can be obtained by three useful tests: the independency, consistency, and observability tests. The independency are different. The black box approach provides only conservations relations. They are derived from element, electrical charge, energy, and Gibbs energy balances. The metabolic approach provides, in addition to the conservation relations, metabolic and reaction relations. These result from component, energy, and Gibbs energy balances. Thus it is more attractive to use the metabolic description than the black box approach. A number of different types of linear relations given in the literature are reviewed. They are classified according to the different categories that result from the black box or the metabolic system description. Validation of hypotheses related to metabolic pathways can be supported by experimental validation of the linear metabolic relations. However, definite proof from biochemical evidence remains indispensable.

Frequency domain system identification of helicopter rotor dynamics incorporating models with time periodic coefficients

NASA Astrophysics Data System (ADS)

Hwang, Sunghwan

1997-08-01

One of the most prominent features of helicopter rotor dynamics in forward flight is the periodic coefficients in the equations of motion introduced by the rotor rotation. The frequency response characteristics of such a linear time periodic system exhibits sideband behavior, which is not the case for linear time invariant systems. Therefore, a frequency domain identification methodology for linear systems with time periodic coefficients was developed, because the linear time invariant theory cannot account for sideband behavior. The modulated complex Fourier series was introduced to eliminate the smearing effect of Fourier series expansions of exponentially modulated periodic signals. A system identification theory was then developed using modulated complex Fourier series expansion. Correlation and spectral density functions were derived using the modulated complex Fourier series expansion for linear time periodic systems. Expressions of the identified harmonic transfer function were then formulated using the spectral density functions both with and without additive noise processes at input and/or output. A procedure was developed to identify parameters of a model to match the frequency response characteristics between measured and estimated harmonic transfer functions by minimizing an objective function defined in terms of the trace of the squared frequency response error matrix. Feasibility was demonstrated by the identification of the harmonic transfer function and parameters for helicopter rigid blade flapping dynamics in forward flight. This technique is envisioned to satisfy the needs of system identification in the rotating frame, especially in the context of individual blade control. The technique was applied to the coupled flap-lag-inflow dynamics of a rigid blade excited by an active pitch link. The linear time periodic technique results were compared with the linear time invariant technique results. Also, the effect of noise processes and initial parameter guess on the identification procedure were investigated. To study the effect of elastic modes, a rigid blade with a trailing edge flap excited by a smart actuator was selected and system parameters were successfully identified, but with some expense of computational storage and time. Conclusively, the linear time periodic technique substantially improved the identified parameter accuracy compared to the linear time invariant technique. Also, the linear time periodic technique was robust to noises and initial guess of parameters. However, an elastic mode of higher frequency relative to the system pumping frequency tends to increase the computer storage requirement and computing time.

Focal points and principal solutions of linear Hamiltonian systems revisited

NASA Astrophysics Data System (ADS)

Šepitka, Peter; Šimon Hilscher, Roman

2018-05-01

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

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.

Linear frequency tuning in an LC-resonant system using a C-V response controllable MEMS varactor

NASA Astrophysics Data System (ADS)

Han, Chang-Hoon; Yoon, Yong-Hoon; Ko, Seung-Deok; Seo, Min-Ho; Yoon, Jun-Bo

2017-12-01

This paper proposes a device level solution to achieve linear frequency tuning with respect to a tuning voltage ( V tune ) sweep in an inductor ( L)-capacitor ( C) resonant system. Since the linearity of the resonant frequency vs. tuning voltage ( f- V) relationship in an LC-resonant system is closely related to the C- V response characteristic of the varactor, we propose a C- V response tunable varactor to realize the linear frequency tuning. The proposed varactor was fabricated using microelectromechanical system (MEMS) surface micromachining. The fabricated MEMS varactor has the ability to dynamically change the C- V response characteristic according to a curve control voltage ( V curve- control ). When V curve- control was increased from zero to 9 V, the C- V response curve was changed from a linear to a concave form (i.e., the capacitance decreased quickly in the low tuning voltage region and slowly in the high tuning voltage region). This change in the C- V response characteristic resulted in a change in the f- V relationship, and we successfully demonstrated almost perfectly linear frequency tuning in the LC-resonant system, with a linearity factor of 99.95%.

Statistical methods for launch vehicle guidance, navigation, and control (GN&C) system design and analysis

NASA Astrophysics Data System (ADS)

Rose, Michael Benjamin

A novel trajectory and attitude control and navigation analysis tool for powered ascent is developed. The tool is capable of rapid trade-space analysis and is designed to ultimately reduce turnaround time for launch vehicle design, mission planning, and redesign work. It is streamlined to quickly determine trajectory and attitude control dispersions, propellant dispersions, orbit insertion dispersions, and navigation errors and their sensitivities to sensor errors, actuator execution uncertainties, and random disturbances. The tool is developed by applying both Monte Carlo and linear covariance analysis techniques to a closed-loop, launch vehicle guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight GN&C software models of a closed-loop, six-degree-of-freedom (6-DOF), Monte Carlo simulation are formulated and developed. The nominal reference trajectory (NRT) for the proposed lunar ascent trajectory is defined and generated. The Monte Carlo truth models and GN&C algorithms are linearized about the NRT, the linear covariance equations are formulated, and the linear covariance simulation is developed. The performance of the launch vehicle GN&C system is evaluated using both Monte Carlo and linear covariance techniques and their trajectory and attitude control dispersion, propellant dispersion, orbit insertion dispersion, and navigation error results are validated and compared. Statistical results from linear covariance analysis are generally within 10% of Monte Carlo results, and in most cases the differences are less than 5%. This is an excellent result given the many complex nonlinearities that are embedded in the ascent GN&C problem. Moreover, the real value of this tool lies in its speed, where the linear covariance simulation is 1036.62 times faster than the Monte Carlo simulation. Although the application and results presented are for a lunar, single-stage-to-orbit (SSTO), ascent vehicle, the tools, techniques, and mathematical formulations that are discussed are applicable to ascent on Earth or other planets as well as other rocket-powered systems such as sounding rockets and ballistic missiles.

Correction for spatial averaging in laser speckle contrast analysis

PubMed Central

Thompson, Oliver; Andrews, Michael; Hirst, Evan

2011-01-01

Practical laser speckle contrast analysis systems face a problem of spatial averaging of speckles, due to the pixel size in the cameras used. Existing practice is to use a system factor in speckle contrast analysis to account for spatial averaging. The linearity of the system factor correction has not previously been confirmed. The problem of spatial averaging is illustrated using computer simulation of time-integrated dynamic speckle, and the linearity of the correction confirmed using both computer simulation and experimental results. The valid linear correction allows various useful compromises in the system design. PMID:21483623

Multivariable control of the Space Shuttle Remote Manipulator System using linearization by state feedback

NASA Technical Reports Server (NTRS)

Gettman, Chang-Ching L.; Adams, Neil; Bedrossian, Nazareth; Valavani, Lena

1993-01-01

This paper demonstrates an approach to nonlinear control system design that uses linearization by state feedback to allow faster maneuvering of payloads by the Shuttle Remote Manipulator System (SRMS). A nonlinear feedback law is defined to cancel the nonlinear plant dynamics so that a linear controller can be designed for the SRMS. First a nonlinear design model was generated via SIMULINK. This design model included nonlinear arm dynamics derived from the Lagrangian approach, linearized servo model, and linearized gearbox model. The current SRMS position hold controller was implemented on this system. Next, a trajectory was defined using a rigid body kinematics SRMS tool, KRMS. The maneuver was simulated. Finally, higher bandwidth controllers were developed. Results of the new controllers were compared with the existing SRMS automatic control modes for the Space Station Freedom Mission Build 4 Payload extended on the SRMS.

On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series

NASA Astrophysics Data System (ADS)

Gottwald, Georg A.; Wormell, J. P.; Wouters, Jeroen

2016-09-01

Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model of the observations, based on results for central limit theorems for deterministic dynamical systems, and used to detect linear response breakdown. We apply the method to discrete maps which do not obey linear response and show that the successful detection of breakdown depends on the length of the time series, the magnitude of the perturbation and on the choice of the observable. We find that in order to reliably reject the assumption of linear response for typical observables sufficiently large data sets are needed. Even for simple systems such as the logistic map, one needs of the order of 106 observations to reliably detect the breakdown with a confidence level of 95 %; if less observations are available one may be falsely led to conclude that linear response theory is valid. The amount of data required is larger the smaller the applied perturbation. For judiciously chosen observables the necessary amount of data can be drastically reduced, but requires detailed a priori knowledge about the invariant measure which is typically not available for complex dynamical systems. Furthermore we explore the use of the fluctuation-dissipation theorem (FDT) in cases with limited data length or coarse-graining of observations. The FDT, if applied naively to a system without linear response, is shown to be very sensitive to the details of the sampling method, resulting in erroneous predictions of the response.

The linear regulator problem for parabolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1983-01-01

An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.

Parametrically excited non-linear multidegree-of-freedom systems with repeated natural frequencies

NASA Astrophysics Data System (ADS)

Tezak, E. G.; Nayfeh, A. H.; Mook, D. T.

1982-12-01

A method for analyzing multidegree-of-freedom systems having a repeated natural frequency subjected to a parametric excitation is presented. Attention is given to the ordering of the various terms (linear and non-linear) in the governing equations. The analysis is based on the method of multiple scales. As a numerical example involving a parametric resonance, panel flutter is discussed in detail in order to illustrate the type of results one can expect to obtain with this analysis. Some of the analytical results are verified by a numerical integration of the governing equations.

Measurement system analysis of viscometers used for drilling mud characterization

NASA Astrophysics Data System (ADS)

Mat-Shayuti, M. S.; Adzhar, S. N.

2017-07-01

Viscometers in the Faculty of Chemical Engineering, University Teknologi MARA, are subject to heavy utilization from the members of the faculty. Due to doubts surrounding their result integrity and maintenance management, Measurement System Analysis was executed. 5 samples of drilling muds with varied barite content from 5 - 25 weight% were prepared and their rheological properties determined in 3 trials by 3 operators using the viscometers. Gage Linearity and Bias Study were performed using Minitab software and the result shows high biases in the range of 19.2% to 38.7%, with non-linear trend along the span of measurements. Gage Repeatability & Reproducibility (Nested) analysis later produces Percent Repeatability & Reproducibility more than 7.7% and Percent Tolerance above 30%. Lastly, good and marginal Distinct Categories output are seen among the results. Despite acceptable performance of the measurement system in Distinct Categories, the poor results in accuracy, linearity, and Percent Repeatability & Reproducibility render the gage generally not capable. Improvement to the measurement system is imminent.

Colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots

NASA Astrophysics Data System (ADS)

Průša, Vít; Řehoř, Martin; Tůma, Karel

2017-02-01

The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systems.

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

Plasmonic modes in nanowire dimers: A study based on the hydrodynamic Drude model including nonlocal and nonlinear effects

NASA Astrophysics Data System (ADS)

Moeferdt, Matthias; Kiel, Thomas; Sproll, Tobias; Intravaia, Francesco; Busch, Kurt

2018-02-01

A combined analytical and numerical study of the modes in two distinct plasmonic nanowire systems is presented. The computations are based on a discontinuous Galerkin time-domain approach, and a fully nonlinear and nonlocal hydrodynamic Drude model for the metal is utilized. In the linear regime, these computations demonstrate the strong influence of nonlocality on the field distributions as well as on the scattering and absorption spectra. Based on these results, second-harmonic-generation efficiencies are computed over a frequency range that covers all relevant modes of the linear spectra. In order to interpret the physical mechanisms that lead to corresponding field distributions, the associated linear quasielectrostatic problem is solved analytically via conformal transformation techniques. This provides an intuitive classification of the linear excitations of the systems that is then applied to the full Maxwell case. Based on this classification, group theory facilitates the determination of the selection rules for the efficient excitation of modes in both the linear and nonlinear regimes. This leads to significantly enhanced second-harmonic generation via judiciously exploiting the system symmetries. These results regarding the mode structure and second-harmonic generation are of direct relevance to other nanoantenna systems.

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2011-01-01

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

MUSTA fluxes for systems of conservation laws

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2006-08-01

This paper is about numerical fluxes for hyperbolic systems and we first present a numerical flux, called GFORCE, that is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first-order upwind method. Then we incorporate GFORCE in the framework of the MUSTA approach [E.F. Toro, Multi-Stage Predictor-Corrector Fluxes for Hyperbolic Equations. Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003], resulting in a version that we call GMUSTA. For non-linear systems this gives results that are comparable to those of the Godunov method in conjunction with the exact Riemann solver or complete approximate Riemann solvers, noting however that in our approach, the solution of the Riemann problem in the conventional sense is avoided. Both the GFORCE and GMUSTA fluxes are extended to multi-dimensional non-linear systems in a straightforward unsplit manner, resulting in linearly stable schemes that have the same stability regions as the straightforward multi-dimensional extension of Godunov's method. The methods are applicable to general meshes. The schemes of this paper share with the family of centred methods the common properties of being simple and applicable to a large class of hyperbolic systems, but the schemes of this paper are distinctly more accurate. Finally, we proceed to the practical implementation of our numerical fluxes in the framework of high-order finite volume WENO methods for multi-dimensional non-linear hyperbolic systems. Numerical results are presented for the Euler equations and for the equations of magnetohydrodynamics.

Mechanical System Reliability and Cost Integration Using a Sequential Linear Approximation Method

NASA Technical Reports Server (NTRS)

Kowal, Michael T.

1997-01-01

The development of new products is dependent on product designs that incorporate high levels of reliability along with a design that meets predetermined levels of system cost. Additional constraints on the product include explicit and implicit performance requirements. Existing reliability and cost prediction methods result in no direct linkage between variables affecting these two dominant product attributes. A methodology to integrate reliability and cost estimates using a sequential linear approximation method is proposed. The sequential linear approximation method utilizes probability of failure sensitivities determined from probabilistic reliability methods as well a manufacturing cost sensitivities. The application of the sequential linear approximation method to a mechanical system is demonstrated.

The relative degree enhancement problem for MIMO nonlinear systems

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

Schoenwald, D.A.; Oezguener, Ue.

1995-07-01

The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for amore » completely decentralized feedback linearization result for at least one input-output channel.« less

Consensus Algorithms for Networks of Systems with Second- and Higher-Order Dynamics

NASA Astrophysics Data System (ADS)

Fruhnert, Michael

This thesis considers homogeneous networks of linear systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilizable. We show that, in continuous-time, consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. For networks of continuous-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback. For networks of discrete-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Schur. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. We show that consensus can always be achieved for marginally stable systems and discretized systems. Simple conditions for consensus achieving controllers are obtained when the Laplacian eigenvalues are all real. For networks of continuous-time time-variant higher-order systems, we show that uniform consensus can always be achieved if systems are quadratically stabilizable. In this case, we provide a simple condition to obtain a linear feedback control. For networks of discrete-time higher-order systems, we show that constant gains can be chosen such that consensus is achieved for a variety of network topologies. First, we develop simple results for networks of time-invariant systems and networks of time-variant systems that are given in controllable canonical form. Second, we formulate the problem in terms of Linear Matrix Inequalities (LMIs). The condition found simplifies the design process and avoids the parallel solution of multiple LMIs. The result yields a modified Algebraic Riccati Equation (ARE) for which we present an equivalent LMI condition.

From linear mechanics to nonlinear mechanics

NASA Technical Reports Server (NTRS)

Loeb, Julian

1955-01-01

Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

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.

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

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

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

Anomaly General Circulation Models.

NASA Astrophysics Data System (ADS)

Navarra, Antonio

The feasibility of the anomaly model is assessed using barotropic and baroclinic models. In the barotropic case, both a stationary and a time-dependent model has been formulated and constructed, whereas only the stationary, linear case is considered in the baroclinic case. Results from the barotropic model indicate that a relation between the stationary solution and the time-averaged non-linear solution exists. The stationary linear baroclinic solution can therefore be considered with some confidence. The linear baroclinic anomaly model poses a formidable mathematical problem because it is necessary to solve a gigantic linear system to obtain the solution. A new method to find solution of large linear system, based on a projection on the Krylov subspace is shown to be successful when applied to the linearized baroclinic anomaly model. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted to obtain the solution. With an appropriate setting of the damping parameters, the iterative Krylov method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows the treatment of the important problem of linear waves in the atmosphere. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These problem leads to large unsymmetrical linear systems of order 10000 and more which can now be successfully tackled by the Krylov method. The (R7) linear anomaly model is used to investigate extensively the linear response to equatorial and mid-latitude prescribed heating. The results indicate that the solution is deeply affected by the presence of the stationary waves in the basic state. The instability of the asymmetric flows, first pointed out by Simmons et al. (1983), is active also in the baroclinic case. However, the presence of baroclinic processes modifies the dominant response. The most sensitive areas are identified; they correspond to north Japan, the Pole and Greenland regions. A limited set of higher resolution (R15) experiments indicate that this situation is still present and enhanced at higher resolution. The linear anomaly model is also applied to a realistic case. (Abstract shortened with permission of author.).

Linear dynamic coupling in geared rotor systems

NASA Technical Reports Server (NTRS)

David, J. W.; Mitchell, L. D.

1986-01-01

The effects of high frequency oscillations caused by the gear mesh, on components of a geared system that can be modeled as rigid discs are analyzed using linear dynamic coupling terms. The coupled, nonlinear equations of motion for a disc attached to a rotating shaft are presented. The results of a trial problem analysis show that the inclusion of the linear dynamic coupling terms can produce significant changes in the predicted response of geared rotor systems, and that the produced sideband responses are greater than the unbalanced response. The method is useful in designing gear drives for heavy-lift helicopters, industrial speed reducers, naval propulsion systems, and heavy off-road equipment.

The Elementary Operations of Human Vision Are Not Reducible to Template-Matching

PubMed Central

Neri, Peter

2015-01-01

It is generally acknowledged that biological vision presents nonlinear characteristics, yet linear filtering accounts of visual processing are ubiquitous. The template-matching operation implemented by the linear-nonlinear cascade (linear filter followed by static nonlinearity) is the most widely adopted computational tool in systems neuroscience. This simple model achieves remarkable explanatory power while retaining analytical tractability, potentially extending its reach to a wide range of systems and levels in sensory processing. The extent of its applicability to human behaviour, however, remains unclear. Because sensory stimuli possess multiple attributes (e.g. position, orientation, size), the issue of applicability may be asked by considering each attribute one at a time in relation to a family of linear-nonlinear models, or by considering all attributes collectively in relation to a specified implementation of the linear-nonlinear cascade. We demonstrate that human visual processing can operate under conditions that are indistinguishable from linear-nonlinear transduction with respect to substantially different stimulus attributes of a uniquely specified target signal with associated behavioural task. However, no specific implementation of a linear-nonlinear cascade is able to account for the entire collection of results across attributes; a satisfactory account at this level requires the introduction of a small gain-control circuit, resulting in a model that no longer belongs to the linear-nonlinear family. Our results inform and constrain efforts at obtaining and interpreting comprehensive characterizations of the human sensory process by demonstrating its inescapably nonlinear nature, even under conditions that have been painstakingly fine-tuned to facilitate template-matching behaviour and to produce results that, at some level of inspection, do conform to linear filtering predictions. They also suggest that compliance with linear transduction may be the targeted outcome of carefully crafted nonlinear circuits, rather than default behaviour exhibited by basic components. PMID:26556758

On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

PubMed

Tunç, Cemil; Tunç, Osman

2016-01-01

In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

Artificial Intelligence Methodologies in Flight Related Differential Game, Control and Optimization Problems

DTIC Science & Technology

1993-01-31

28 Controllability and Observability ............................. .32 ’ Separation of Learning and Control ... ... 37 Linearization via... Linearization via Transformation of Coordinates and Nonlinear Fedlback . .1 Main Result ......... .............................. 13 Discussion...9 2.1 Basic Structure of a NLM........................ .󈧟 2.2 General Structure of NNLM .......................... .28 2.3 Linear System

Analysis of separation test for automatic brake adjuster based on linear radon transformation

NASA Astrophysics Data System (ADS)

Luo, Zai; Jiang, Wensong; Guo, Bin; Fan, Weijun; Lu, Yi

2015-01-01

The linear Radon transformation is applied to extract inflection points for online test system under the noise conditions. The linear Radon transformation has a strong ability of anti-noise and anti-interference by fitting the online test curve in several parts, which makes it easy to handle consecutive inflection points. We applied the linear Radon transformation to the separation test system to solve the separating clearance of automatic brake adjuster. The experimental results show that the feature point extraction error of the gradient maximum optimal method is approximately equal to ±0.100, while the feature point extraction error of linear Radon transformation method can reach to ±0.010, which has a lower error than the former one. In addition, the linear Radon transformation is robust.

Polarization-dependent plasmonic photocurrents in two-dimensional electron systems

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

Popov, V. V., E-mail: popov-slava@yahoo.co.uk; Saratov State University, Saratov 410012; Saratov Scientific Center of the Russian Academy of Sciences, Saratov 410028

2016-06-27

Plasmonic polarization dependent photocurrents in a homogeneous two-dimensional electron system are studied. Those effects are completely different from the photon drag and electronic photogalvanic effects as well as from the plasmonic ratchet effect in a density modulated two-dimensional electron system. Linear and helicity-dependent contributions to the photocurrent are found. The linear contribution can be interpreted as caused by the longitudinal and transverse plasmon drag effect. The helicity-dependent contribution originates from the non-linear electron convection and changes its sign with reversing the plasmonic field helicity. It is shown that the helicity-dependent component of the photocurrent can exceed the linear one bymore » several orders of magnitude in high-mobility two-dimensional electron systems. The results open possibilities for all-electronic detection of the radiation polarization states by exciting the plasmonic photocurrents in two-dimensional electron systems.« less

Modal interaction in linear dynamic systems near degenerate modes

NASA Technical Reports Server (NTRS)

Afolabi, D.

1991-01-01

In various problems in structural dynamics, the eigenvalues of a linear system depend on a characteristic parameter of the system. Under certain conditions, two eigenvalues of the system approach each other as the characteristic parameter is varied, leading to modal interaction. In a system with conservative coupling, the two eigenvalues eventually repel each other, leading to the curve veering effect. In a system with nonconservative coupling, the eigenvalues continue to attract each other, eventually colliding, leading to eigenvalue degeneracy. Modal interaction is studied in linear systems with conservative and nonconservative coupling using singularity theory, sometimes known as catastrophe theory. The main result is this: eigenvalue degeneracy is a cause of instability; in systems with conservative coupling, it induces only geometric instability, whereas in systems with nonconservative coupling, eigenvalue degeneracy induces both geometric and elastic instability. Illustrative examples of mechanical systems are given.

Solving rational matrix equations in the state space with applications to computer-aided control-system design

NASA Technical Reports Server (NTRS)

Packard, A. K.; Sastry, S. S.

1986-01-01

A method of solving a class of linear matrix equations over various rings is proposed, using results from linear geometric control theory. An algorithm, successfully implemented, is presented, along with non-trivial numerical examples. Applications of the method to the algebraic control system design methodology are discussed.

Study on sampling of continuous linear system based on generalized Fourier transform

NASA Astrophysics Data System (ADS)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Optimal second order sliding mode control for linear uncertain systems.

PubMed

Das, Madhulika; Mahanta, Chitralekha

2014-11-01

In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Analysis and simulation of a magnetic bearing suspension system for a laboratory model annular momentum control device

NASA Technical Reports Server (NTRS)

Groom, N. J.; Woolley, C. T.; Joshi, S. M.

1981-01-01

A linear analysis and the results of a nonlinear simulation of a magnetic bearing suspension system which uses permanent magnet flux biasing are presented. The magnetic bearing suspension is part of a 4068 N-m-s (3000 lb-ft-sec) laboratory model annular momentum control device (AMCD). The simulation includes rigid body rim dynamics, linear and nonlinear axial actuators, linear radial actuators, axial and radial rim warp, and power supply and power driver current limits.

The Development of a Dual-Warhead Impact System for Dynamic Linearity Measurement of a High-g Micro-Electro-Mechanical-Systems (MEMS) Accelerometer

PubMed Central

Shi, Yunbo; Yang, Zhicai; Ma, Zongmin; Cao, Huiliang; Kou, Zhiwei; Zhi, Dan; Chen, Yanxiang; Feng, Hengzhen; Liu, Jun

2016-01-01

Despite its extreme significance, dynamic linearity measurement for high-g accelerometers has not been discussed experimentally in previous research. In this study, we developed a novel method using a dual-warhead Hopkinson bar to measure the dynamic linearity of a high-g acceleration sensor with a laser interference impact experiment. First, we theoretically determined that dynamic linearity is a performance indicator that can be used to assess the quality merits of high-g accelerometers and is the basis of the frequency response. We also found that the dynamic linearity of the dual-warhead Hopkinson bar without an accelerometer is 2.5% experimentally. Further, we verify that dynamic linearity of the accelerometer is 3.88% after calibrating the Hopkinson bar with the accelerometer. The results confirm the reliability and feasibility of measuring dynamic linearity for high-g accelerometers using this method. PMID:27338383

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.

Report on the status of linear drive coolers for the Department of Defense Standard Advanced Dewar Assembly (SADA)

NASA Astrophysics Data System (ADS)

Salazar, William

2003-01-01

The Standard Advanced Dewar Assembly (SADA) is the critical module in the Department of Defense (DoD) standardization effort of scanning second-generation thermal imaging systems. DoD has established a family of SADA's to address requirements for high performance (SADA I), mid-to-high performance (SADA II), and compact class (SADA III) systems. SADA's consist of the Infrared Focal Plane Array (IRFPA), Dewar, Command and Control Electronics (C&CE), and the cryogenic cooler. SADA's are used in weapons systems such as Comanche and Apache helicopters, the M1 Abrams Tank, the M2 Bradley Fighting Vehicle, the Line of Sight Antitank (LOSAT) system, the Improved Target Acquisition System (ITAS), and Javelin's Command Launch Unit (CLU). DOD has defined a family of tactical linear drive coolers in support of the family of SADA's. The Stirling linear drive cryo-coolers are utilized to cool the SADA's Infrared Focal Plane Arrays (IRFPAs) to their operating cryogenic temperatures. These linear drive coolers are required to meet strict cool-down time requirements along with lower vibration output, lower audible noise, and higher reliability than currently fielded rotary coolers. This paper will (1) outline the characteristics of each cooler, (2) present the status and results of qualification tests, and (3) present the status and test results of efforts to increase linear drive cooler reliability.

1-kW monolithic narrow linewidth linear-polarized fiber laser at 1030 nm

NASA Astrophysics Data System (ADS)

Xu, Yang; Fang, Qiang; Cui, Xuelong; Hou, Bowen; Fu, Shijie; Xie, Zhaoxin; Shi, Wei

2018-02-01

We demonstrate an all-fiberized, linear-polarized, narrow spectral linewidth laser system with kilowatts-level output power at 1030 nm in master oscillator-power amplifier (MOPA) configuration. The laser system consists of a linear-polarized, narrow linewidth ( 28 GHz) fiber laser oscillator and two stages of linear-polarized fiber amplifiers. A 925 W linear-polarized fiber laser with a polarization extinction ratio (PER) of 15.2 dB and a spectral width of 60 GHz at the central wavelength of 1030.1 nm is achieved. Owing to the setting of the appropriate parameters for the laser, no indication of Stimulate Brillouin Scattering (SBS) is observed in the system. Moreover, thanks to the excellent quantum efficiency of the laser and the thightly coiling of the active fiber in the main amplifier, the mode instability (MI) is successfully avoided. As a result, the near diffraction-limited beam quality (M2<1.3) is achieved.

Unfolded equations for current interactions of 4d massless fields as a free system in mixed dimensions

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

Gelfond, O. A., E-mail: gel@lpi.ru; Vasiliev, M. A., E-mail: vasiliev@lpi.ru

2015-03-15

Interactions of massless fields of all spins in four dimensions with currents of any spin are shown to result from a solution of the linear problem that describes a gluing between a rank-one (massless) system and a rank-two (current) system in the unfolded dynamics approach. Since the rank-two system is dual to a free rank-one higher-dimensional system that effectively describes conformal fields in six space-time dimensions, the constructed system can be interpreted as describing a mixture between linear conformal fields in four and six dimensions. An interpretation of the obtained results in the spirit of the AdS/CFT correspondence is discussed.

Nonlinear wave chaos: statistics of second harmonic fields.

PubMed

Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M

2017-10-01

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

Physics and control of wall turbulence for drag reduction.

PubMed

Kim, John

2011-04-13

Turbulence physics responsible for high skin-friction drag in turbulent boundary layers is first reviewed. A self-sustaining process of near-wall turbulence structures is then discussed from the perspective of controlling this process for the purpose of skin-friction drag reduction. After recognizing that key parts of this self-sustaining process are linear, a linear systems approach to boundary-layer control is discussed. It is shown that singular-value decomposition analysis of the linear system allows us to examine different approaches to boundary-layer control without carrying out the expensive nonlinear simulations. Results from the linear analysis are consistent with those observed in full nonlinear simulations, thus demonstrating the validity of the linear analysis. Finally, fundamental performance limit expected of optimal control input is discussed.

Model-based adaptive sliding mode control of the subcritical boiler-turbine system with uncertainties.

PubMed

Tian, Zhen; Yuan, Jingqi; Xu, Liang; Zhang, Xiang; Wang, Jingcheng

2018-05-25

As higher requirements are proposed for the load regulation and efficiency enhancement, the control performance of boiler-turbine systems has become much more important. In this paper, a novel robust control approach is proposed to improve the coordinated control performance for subcritical boiler-turbine units. To capture the key features of the boiler-turbine system, a nonlinear control-oriented model is established and validated with the history operation data of a 300 MW unit. To achieve system linearization and decoupling, an adaptive feedback linearization strategy is proposed, which could asymptotically eliminate the linearization error caused by the model uncertainties. Based on the linearized boiler-turbine system, a second-order sliding mode controller is designed with the super-twisting algorithm. Moreover, the closed-loop system is proved robustly stable with respect to uncertainties and disturbances. Simulation results are presented to illustrate the effectiveness of the proposed control scheme, which achieves excellent tracking performance, strong robustness and chattering reduction. Copyright © 2018. Published by Elsevier Ltd.

The Matrix Pencil and its Applications to Speech Processing

DTIC Science & Technology

2007-03-01

Elementary Linear Algebra ” 8th edition, pp. 278, 2000 John Wiley & Sons, Inc., New York [37] Wai C. Chu, “Speech Coding Algorithms”, New Jeresy: John...Ben; Daniel, James W.; “Applied Linear Algebra ”, pp. 342-345, 1988 Prentice Hall, Englewood Cliffs, NJ [35] Haykin, Simon “Applied Linear Adaptive...ABSTRACT Matrix Pencils facilitate the study of differential equations resulting from oscillating systems. Certain problems in linear ordinary

Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Powers, Robert K.

1987-01-01

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.

Development of a Linear Stirling System Model with Varying Heat Inputs

NASA Technical Reports Server (NTRS)

Regan, Timothy F.; Lewandowski, Edward J.

2007-01-01

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC's nonlinear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Assessment of disk MHD generators for a base load powerplant

NASA Technical Reports Server (NTRS)

Chubb, D. L.; Retallick, F. D.; Lu, C. L.; Stella, M.; Teare, J. D.; Loubsky, W. J.; Louis, J. F.; Misra, B.

1981-01-01

Results from a study of the disk MHD generator are presented. Both open and closed cycle disk systems were investigated. Costing of the open cycle disk components (nozzle, channel, diffuser, radiant boiler, magnet and power management) was done. However, no detailed costing was done for the closed cycle systems. Preliminary plant design for the open cycle systems was also completed. Based on the system study results, an economic assessment of the open cycle systems is presented. Costs of the open cycle disk conponents are less than comparable linear generator components. Also, costs of electricity for the open cycle disk systems are competitive with comparable linear systems. Advantages of the disk design simplicity are considered. Improvements in the channel availability or a reduction in the channel lifetime requirement are possible as a result of the disk design.

A harmonic linear dynamical system for prominent ECG feature extraction.

PubMed

Thi, Ngoc Anh Nguyen; Yang, Hyung-Jeong; Kim, SunHee; Do, Luu Ngoc

2014-01-01

Unsupervised mining of electrocardiography (ECG) time series is a crucial task in biomedical applications. To have efficiency of the clustering results, the prominent features extracted from preprocessing analysis on multiple ECG time series need to be investigated. In this paper, a Harmonic Linear Dynamical System is applied to discover vital prominent features via mining the evolving hidden dynamics and correlations in ECG time series. The discovery of the comprehensible and interpretable features of the proposed feature extraction methodology effectively represents the accuracy and the reliability of clustering results. Particularly, the empirical evaluation results of the proposed method demonstrate the improved performance of clustering compared to the previous main stream feature extraction approaches for ECG time series clustering tasks. Furthermore, the experimental results on real-world datasets show scalability with linear computation time to the duration of the time series.

A Comparison of Multivariable Control Design Techniques for a Turbofan Engine Control

NASA Technical Reports Server (NTRS)

Garg, Sanjay; Watts, Stephen R.

1995-01-01

This paper compares two previously published design procedures for two different multivariable control design techniques for application to a linear engine model of a jet engine. The two multivariable control design techniques compared were the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) and the H-Infinity synthesis. The two control design techniques were used with specific previously published design procedures to synthesize controls which would provide equivalent closed loop frequency response for the primary control loops while assuring adequate loop decoupling. The resulting controllers were then reduced in order to minimize the programming and data storage requirements for a typical implementation. The reduced order linear controllers designed by each method were combined with the linear model of an advanced turbofan engine and the system performance was evaluated for the continuous linear system. Included in the performance analysis are the resulting frequency and transient responses as well as actuator usage and rate capability for each design method. The controls were also analyzed for robustness with respect to structured uncertainties in the unmodeled system dynamics. The two controls were then compared for performance capability and hardware implementation issues.

Controlling Flexible Manipulators, an Experimental Investigation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Hastings, Gordon Greene

1986-01-01

Lightweight, slender manipulators offer faster response and/or greater workspace range for the same size actuators than tradional manipulators. Lightweight construction of manipulator links results in increased structural flexibility. The increase flexibility must be considered in the design of control systems to properly account for the dynamic flexible vibrations and static deflections. Real time control of the flexible manipulator vibrations are experimentally investigated. Models intended for real-time control of distributed parameter system such as flexible manipulators rely on model approximation schemes. An linear model based on the application of Lagrangian dynamics to a rigid body mode and a series of separable flexible modes is examined with respect to model order requirements, and modal candidate selection. Balanced realizations are applied to the linear flexible model to obtain an estimate of appropriate order for a selected model. Describing the flexible deflections as a linear combination of modes results in measurements of beam state, which yield information about several modes. To realize the potential of linear systems theory, knowledge of each state must be available. State estimation is also accomplished by implementation of a Kalman Filter. State feedback control laws are implemented based upon linear quadratic regulator design.

Allan deviation computations of a linear frequency synthesizer system using frequency domain techniques

NASA Technical Reports Server (NTRS)

Wu, Andy

1995-01-01

Allan Deviation computations of linear frequency synthesizer systems have been reported previously using real-time simulations. Even though it takes less time compared with the actual measurement, it is still very time consuming to compute the Allan Deviation for long sample times with the desired confidence level. Also noises, such as flicker phase noise and flicker frequency noise, can not be simulated precisely. The use of frequency domain techniques can overcome these drawbacks. In this paper the system error model of a fictitious linear frequency synthesizer is developed and its performance using a Cesium (Cs) atomic frequency standard (AFS) as a reference is evaluated using frequency domain techniques. For a linear timing system, the power spectral density at the system output can be computed with known system transfer functions and known power spectral densities from the input noise sources. The resulting power spectral density can then be used to compute the Allan Variance at the system output. Sensitivities of the Allan Variance at the system output to each of its independent input noises are obtained, and they are valuable for design trade-off and trouble-shooting.

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

Frequency-modulated laser ranging sensor with closed-loop control

NASA Astrophysics Data System (ADS)

Müller, Fabian M.; Böttger, Gunnar; Janeczka, Christian; Arndt-Staufenbiel, Norbert; Schröder, Henning; Schneider-Ramelow, Martin

2018-02-01

Advances in autonomous driving and robotics are creating high demand for inexpensive and mass-producible distance sensors. A laser ranging system (Lidar), based on the frequency-modulated continuous-wave (FMCW) method is built in this work. The benefits of an FMCW Lidar system are the low-cost components and the performance in comparison to conventional time-of-flight Lidar systems. The basic system consists of a DFB laser diode (λ= 1308 nm) and an asymmetric fiber-coupled Mach-Zehnder interferometer with a fixed delay line in one arm. Linear tuning of the laser optical frequency via injection current modulation creates a beat signal at the interferometer output. The frequency of the beat signal is proportional to the optical path difference in the interferometer. Since the laser frequency-to-current response is non-linear, a closed-loop feed-back system is designed to improve the tuning linearity, and consequently the measurement resolution. For fast active control, an embedded system with FPGA is used, resulting in a nearly linear frequency tuning, realizing a narrow peak in the Fourier spectrum of the beat signal. For free-space measurements, a setup with two distinct interferometers is built. The fully fiber-coupled Mach-Zehnder reference interferometer is part of the feed-back loop system, while the other - a Michelson interferometer - has a free-space arm with collimator lens and reflective target. A resolution of 2:0 mm for a 560 mm distance is achieved. The results for varying target distances show high consistency and a linear relation to the measured beat-frequency.

Step responses of a torsional system with multiple clearances: Study of vibro-impact phenomenon using experimental and computational methods

NASA Astrophysics Data System (ADS)

Oruganti, Pradeep Sharma; Krak, Michael D.; Singh, Rajendra

2018-01-01

Recently Krak and Singh (2017) proposed a scientific experiment that examined vibro-impacts in a torsional system under a step down excitation and provided preliminary measurements and limited non-linear model studies. A major goal of this article is to extend the prior work with a focus on the examination of vibro-impact phenomena observed under step responses in a torsional system with one, two or three controlled clearances. First, new measurements are made at several locations with a higher sampling frequency. Measured angular accelerations are examined in both time and time-frequency domains. Minimal order non-linear models of the experiment are successfully constructed, using piecewise linear stiffness and Coulomb friction elements; eight cases of the generic system are examined though only three are experimentally studied. Measured and predicted responses for single and dual clearance configurations exhibit double sided impacts and time varying periods suggest softening trends under the step down torque. Non-linear models are experimentally validated by comparing results with new measurements and with those previously reported. Several metrics are utilized to quantify and compare the measured and predicted responses (including peak to peak accelerations). Eigensolutions and step responses of the corresponding linearized models are utilized to better understand the nature of the non-linear dynamic system. Finally, the effect of step amplitude on the non-linear responses is examined for several configurations, and hardening trends are observed in the torsional system with three clearances.

Fixed interval smoothing with discrete measurements.

NASA Technical Reports Server (NTRS)

Bierman, G. J.

1972-01-01

Smoothing equations for a linear continuous dynamic system with linear discrete measurements, derived from the discrete results of Rauch, Tung, and Striebel (1965), (R-T-S), are used to extend, through recursive updating, the previously published results of Bryson and Frazier (1963), (B-F), and yield a modified Bryson and Frazier, (M-B-F), algorithm. A comparison of the (M-B-F) and (R-T-S) algorithms leads to the conclusion that the former is to be preferred because it entails less computation, less storage, and less instability. It is felt that the presented (M-B-F) smoothing algorithm is a practical mechanization and should be of value in smoothing discretely observed dynamic linear systems.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

NASA Astrophysics Data System (ADS)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Study of Piezoelectric Vibration Energy Harvester with non-linear conditioning circuit using an integrated model

NASA Astrophysics Data System (ADS)

Manzoor, Ali; Rafique, Sajid; Usman Iftikhar, Muhammad; Mahmood Ul Hassan, Khalid; Nasir, Ali

2017-08-01

Piezoelectric vibration energy harvester (PVEH) consists of a cantilever bimorph with piezoelectric layers pasted on its top and bottom, which can harvest power from vibrations and feed to low power wireless sensor nodes through some power conditioning circuit. In this paper, a non-linear conditioning circuit, consisting of a full-bridge rectifier followed by a buck-boost converter, is employed to investigate the issues of electrical side of the energy harvesting system. An integrated mathematical model of complete electromechanical system has been developed. Previously, researchers have studied PVEH with sophisticated piezo-beam models but employed simplistic linear circuits, such as resistor, as electrical load. In contrast, other researchers have worked on more complex non-linear circuits but with over-simplified piezo-beam models. Such models neglect different aspects of the system which result from complex interactions of its electrical and mechanical subsystems. In this work, authors have integrated the distributed parameter-based model of piezo-beam presented in literature with a real world non-linear electrical load. Then, the developed integrated model is employed to analyse the stability of complete energy harvesting system. This work provides a more realistic and useful electromechanical model having realistic non-linear electrical load unlike the simplistic linear circuit elements employed by many researchers.

Structural Aspects of System Identification

NASA Technical Reports Server (NTRS)

Glover, Keith

1973-01-01

The problem of identifying linear dynamical systems is studied by considering structural and deterministic properties of linear systems that have an impact on stochastic identification algorithms. In particular considered is parametrization of linear systems so that there is a unique solution and all systems in appropriate class can be represented. It is assumed that a parametrization of system matrices has been established from a priori knowledge of the system, and the question is considered of when the unknown parameters of this system can be identified from input/output observations. It is assumed that the transfer function can be asymptotically identified, and the conditions are derived for the local, global and partial identifiability of the parametrization. Then it is shown that, with the right formulation, identifiability in the presence of feedback can be treated in the same way. Similarly the identifiability of parametrizations of systems driven by unobserved white noise is considered using the results from the theory of spectral factorization.

Robustness Analysis of Integrated LPV-FDI Filters and LTI-FTC System for a Transport Aircraft

NASA Technical Reports Server (NTRS)

Khong, Thuan H.; Shin, Jong-Yeob

2007-01-01

This paper proposes an analysis framework for robustness analysis of a nonlinear dynamics system that can be represented by a polynomial linear parameter varying (PLPV) system with constant bounded uncertainty. The proposed analysis framework contains three key tools: 1) a function substitution method which can convert a nonlinear system in polynomial form into a PLPV system, 2) a matrix-based linear fractional transformation (LFT) modeling approach, which can convert a PLPV system into an LFT system with the delta block that includes key uncertainty and scheduling parameters, 3) micro-analysis, which is a well known robust analysis tool for linear systems. The proposed analysis framework is applied to evaluating the performance of the LPV-fault detection and isolation (FDI) filters of the closed-loop system of a transport aircraft in the presence of unmodeled actuator dynamics and sensor gain uncertainty. The robustness analysis results are compared with nonlinear time simulations.

Rheological techniques for determining degradation of polylactic acid in bioresorbable medical polymer systems

NASA Astrophysics Data System (ADS)

Choong, Gabriel Y. H.; Parsons, Andrew J.; Grant, David M.; De Focatiis, Davide S. A.

2015-05-01

A method developed in the 1980s for the conversion of linear rheological data to molar mass distribution is revisited in the context of degradable polymers. The method is first applied using linear rheology for a linear polystyrene, for which all conversion parameters are known. A proof of principle is then carried out on four polycarbonate grades. Finally, preliminary results are shown on degradable polylactides. The application of this method to degrading polymer systems, and to systems containing nanofillers, is also discussed. This work forms part of a wider study of bioresorbable nanocomposites using polylactides, novel hydroxyapatite nanoparticles and tailored dispersants for medical applications.

On a new iterative method for solving linear systems and comparison results

NASA Astrophysics Data System (ADS)

Jing, Yan-Fei; Huang, Ting-Zhu

2008-10-01

In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

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

Jesus, Isaías Pereira de, E-mail: isaias@ufpi.edu.br

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Iterative color-multiplexed, electro-optical processor.

PubMed

Psaltis, D; Casasent, D; Carlotto, M

1979-11-01

A noncoherent optical vector-matrix multiplier using a linear LED source array and a linear P-I-N photodiode detector array has been combined with a 1-D adder in a feedback loop. The resultant iterative optical processor and its use in solving simultaneous linear equations are described. Operation on complex data is provided by a novel color-multiplexing system.

Effect of non-linearity in predicting doppler waveforms through a novel model

PubMed Central

Gayasen, Aman; Dua, Sunil Kumar; Sengupta, Amit; Nagchoudhuri, D

2003-01-01

Background In pregnancy, the uteroplacental vascular system develops de novo locally in utero and a systemic haemodynamic & bio-rheological alteration accompany it. Any abnormality in the non-linear vascular system is believed to trigger the onset of serious morbid conditions like pre-eclampsia and/or intrauterine growth restriction (IUGR). Exact Aetiopathogenesis is unknown. Advancement in the field of non-invasive doppler image analysis and simulation incorporating non-linearities may unfold the complexities associated with the inaccessible uteroplacental vessels. Earlier modeling approaches approximate it as a linear system. Method We proposed a novel electrical model for the uteroplacental system that uses MOSFETs as non-linear elements in place of traditional linear transmission line (TL) model. The model to simulate doppler FVW's was designed by including the inputs from our non-linear mathematical model. While using the MOSFETs as voltage-controlled switches, a fair degree of controlled-non-linearity has been introduced in the model. Comparative analysis was done between the simulated data and the actual doppler FVW's waveforms. Results & Discussion Normal pregnancy has been successfully modeled and the doppler output waveforms are simulated for different gestation time using the model. It is observed that the dicrotic notch disappears and the S/D ratio decreases as the pregnancy matures. Both these results are established clinical facts. Effects of blood density, viscosity and the arterial wall elasticity on the blood flow velocity profile were also studied. Spectral analysis on the output of the model (blood flow velocity) indicated that the Total Harmonic Distortion (THD) falls during the mid-gestation. Conclusion Total harmonic distortion (THD) is found to be informative in determining the Feto-maternal health. Effects of the blood density, the viscosity and the elasticity changes on the blood FVW are simulated. Future works are expected to concentrate mainly on improving the load with respect to varying non-linear parameters in the model. Heart rate variability, which accounts for the vascular tone, should also be included. We also expect the model to initiate extensive clinical or experimental studies in the near future. PMID:14561227

Biomechanically based simulation of brain deformations for intraoperative image correction: coupling of elastic and fluid models

NASA Astrophysics Data System (ADS)

Hagemann, Alexander; Rohr, Karl; Stiehl, H. Siegfried

2000-06-01

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.

Discrete Applied Mathematics

DTIC Science & Technology

1993-05-31

program. In paper [28], we give a brief and elementary proof of a result of Hoffman [1952) about approximate solutions to systems, of linear inequalities...UCLA, Vestvood, CA, February 1993. " Linear Problems: Formulation and Solution," International Linear Algebra Society, Pensacola, FL, May 1993. Denise S...thresAold If there is a number h and a linear k-separator w assigning a real number to each vertex so that for any subset S of vertices, the sum of w

Development and Preliminary Testing of a High Precision Long Stroke Slit Change Mechanism for the SPICE Instrument

NASA Technical Reports Server (NTRS)

Paciotti, Gabriel; Humphries, Martin; Rottmeier, Fabrice; Blecha, Luc

2014-01-01

In the frame of ESA's Solar Orbiter scientific mission, Almatech has been selected to design, develop and test the Slit Change Mechanism of the SPICE (SPectral Imaging of the Coronal Environment) instrument. In order to guaranty optical cleanliness level while fulfilling stringent positioning accuracies and repeatability requirements for slit positioning in the optical path of the instrument, a linear guiding system based on a double flexible blade arrangement has been selected. The four different slits to be used for the SPICE instrument resulted in a total stroke of 16.5 mm in this linear slit changer arrangement. The combination of long stroke and high precision positioning requirements has been identified as the main design challenge to be validated through breadboard models testing. This paper presents the development of SPICE's Slit Change Mechanism (SCM) and the two-step validation tests successfully performed on breadboard models of its flexible blade support system. The validation test results have demonstrated the full adequacy of the flexible blade guiding system implemented in SPICE's Slit Change Mechanism in a stand-alone configuration. Further breadboard test results, studying the influence of the compliant connection to the SCM linear actuator on an enhanced flexible guiding system design have shown significant enhancements in the positioning accuracy and repeatability of the selected flexible guiding system. Preliminary evaluation of the linear actuator design, including a detailed tolerance analyses, has shown the suitability of this satellite roller screw based mechanism for the actuation of the tested flexible guiding system and compliant connection. The presented development and preliminary testing of the high-precision long-stroke Slit Change Mechanism for the SPICE Instrument are considered fully successful such that future tests considering the full Slit Change Mechanism can be performed, with the gained confidence, directly on a Qualification Model. The selected linear Slit Change Mechanism design concept, consisting of a flexible guiding system driven by a hermetically sealed linear drive mechanism, is considered validated for the specific application of the SPICE instrument, with great potential for other special applications where contamination and high precision positioning are dominant design drivers.

Controllable excitation of higher-order rogue waves in nonautonomous systems with both varying linear and harmonic external potentials

NASA Astrophysics Data System (ADS)

Jia, Heping; Yang, Rongcao; Tian, Jinping; Zhang, Wenmei

2018-05-01

The nonautonomous nonlinear Schrödinger (NLS) equation with both varying linear and harmonic external potentials is investigated and the semirational rogue wave (RW) solution is presented by similarity transformation. Based on the solution, the interactions between Peregrine soliton and breathers, and the controllability of the semirational RWs in periodic distribution and exponential decreasing nonautonomous systems with both linear and harmonic potentials are studied. It is found that the harmonic potential only influences the constraint condition of the semirational solution, the linear potential is related to the trajectory of the semirational RWs, while dispersion and nonlinearity determine the excitation position of the higher-order RWs. The higher-order RWs can be partly, completely and biperiodically excited in periodic distribution system and the diverse excited patterns can be generated for different parameter relations in exponential decreasing system. The results reveal that the excitation of the higher-order RWs can be controlled in the nonautonomous system by choosing dispersion, nonlinearity and external potentials.

Applicability of linearized-theory attached-flow methods to design and analysis of flap systems at low speeds for thin swept wings with sharp leading edges

NASA Technical Reports Server (NTRS)

Carlson, Harry W.; Darden, Christine M.

1987-01-01

Low-speed experimental force and data on a series of thin swept wings with sharp leading edges and leading and trailing-edge flaps are compared with predictions made using a linearized-theory method which includes estimates of vortex forces. These comparisons were made to assess the effectiveness of linearized-theory methods for use in the design and analysis of flap systems in subsonic flow. Results demonstrate that linearized-theory, attached-flow methods (with approximate representation of vortex forces) can form the basis of a rational system for flap design and analysis. Even attached-flow methods that do not take vortex forces into account can be used for the selection of optimized flap-system geometry, but design-point performance levels tend to be underestimated unless vortex forces are included. Illustrative examples of the use of these methods in the design of efficient low-speed flap systems are included.

Experimental and Theoretical Results in Output Trajectory Redesign for Flexible Structures

NASA Technical Reports Server (NTRS)

Dewey, J. S.; Leang, K.; Devasia, S.

1998-01-01

In this paper we study the optimal redesign of output trajectories for linear invertible systems. This is particularly important for tracking control of flexible structures because the input-state trajectores, that achieve tracking of the required output may cause excessive vibrations in the structure. We pose and solve this problem, in the context of linear systems, as the minimization of a quadratic cost function. The theory is developed and applied to the output tracking of a flexible structure and experimental results are presented.

Development of a Linear Stirling Model with Varying Heat Inputs

NASA Technical Reports Server (NTRS)

Regan, Timothy F.; Lewandowski, Edward J.

2007-01-01

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC s non-linear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Mixed H2/Hinfinity output-feedback control of second-order neutral systems with time-varying state and input delays.

PubMed

Karimi, Hamid Reza; Gao, Huijun

2008-07-01

A mixed H2/Hinfinity output-feedback control design methodology is presented in this paper for second-order neutral linear systems with time-varying state and input delays. Delay-dependent sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities (LMIs). A controller, which guarantees asymptotic stability and a mixed H2/Hinfinity performance for the closed-loop system of the second-order neutral linear system, is then developed directly instead of coupling the model to a first-order neutral system. A Lyapunov-Krasovskii method underlies the LMI-based mixed H2/Hinfinity output-feedback control design using some free weighting matrices. The simulation results illustrate the effectiveness of the proposed methodology.

Application of a local linearization technique for the solution of a system of stiff differential equations associated with the simulation of a magnetic bearing assembly

NASA Technical Reports Server (NTRS)

Kibler, K. S.; Mcdaniel, G. A.

1981-01-01

A digital local linearization technique was used to solve a system of stiff differential equations which simulate a magnetic bearing assembly. The results prove the technique to be accurate, stable, and efficient when compared to a general purpose variable order Adams method with a stiff option.

Applications of nonlinear systems theory to control design

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.

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.

Experimental study of refrigeration performance based on linear Fresnel solar thermal photovoltaic system

NASA Astrophysics Data System (ADS)

Song, Jinghui; Yuan, Hui; Xia, Yunfeng; Kan, Weimin; Deng, Xiaowen; Liu, Shi; Liang, Wanlong; Deng, Jianhua

2018-03-01

This paper introduces the working principle and system constitution of the linear Fresnel solar lithium bromide absorption refrigeration cycle, and elaborates several typical structures of absorption refrigeration cycle, including single-effect, two-stage cycle and double-effect lithium bromide absorption refrigeration cycle A 1.n effect absorption chiller system based on the best parameters was introduced and applied to a linear Fresnel solar absorption chiller system. Through the field refrigerator performance test, the results show: Based on this heat cycle design and processing 1.n lithium bromide absorption refrigeration power up to 35.2KW, It can meet the theoretical expectations and has good flexibility and reliability, provides guidance for the use of solar thermal energy.

A 2D systems approach to iterative learning control for discrete linear processes with zero Markov parameters

NASA Astrophysics Data System (ADS)

Hladowski, Lukasz; Galkowski, Krzysztof; Cai, Zhonglun; Rogers, Eric; Freeman, Chris T.; Lewin, Paul L.

2011-07-01

In this article a new approach to iterative learning control for the practically relevant case of deterministic discrete linear plants with uniform rank greater than unity is developed. The analysis is undertaken in a 2D systems setting that, by using a strong form of stability for linear repetitive processes, allows simultaneous consideration of both trial-to-trial error convergence and along the trial performance, resulting in design algorithms that can be computed using linear matrix inequalities (LMIs). Finally, the control laws are experimentally verified on a gantry robot that replicates a pick and place operation commonly found in a number of applications to which iterative learning control is applicable.

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

NASA Astrophysics Data System (ADS)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

Linear and nonlinear response in sheared soft spheres

NASA Astrophysics Data System (ADS)

Tighe, Brian

2013-11-01

Packings of soft spheres provide an idealized model of foams, emulsions, and grains, while also serving as the canonical example of a system undergoing a jamming transition. Packings' mechanical response has now been studied exhaustively in the context of ``strict linear response,'' i.e. by linearizing about a stable static packing and solving the resulting equations of motion. Both because the system is close to a critical point and because the soft sphere pair potential is non-analytic at the point of contact, it is reasonable to ask under what circumstances strict linear response provides a good approximation to the actual response. We simulate sheared soft sphere packings close to jamming and identify two distinct strain scales: (i) the scale on which strict linear response fails, coinciding with a topological change in the packing's contact network; and (ii) the scale on which linear superposition of the averaged stress-strain curve breaks down. This latter scale provides a ``weak linear response'' criterion and is likely to be more experimentally relevant.

Computational process to study the wave propagation In a non-linear medium by quasi- linearization

NASA Astrophysics Data System (ADS)

Sharath Babu, K.; Venkata Brammam, J.; Baby Rani, CH

2018-03-01

Two objects having distinct velocities come into contact an impact can occur. The impact study i.e., in the displacement of the objects after the impact, the impact force is function of time‘t’ which is behaves similar to compression force. The impact tenure is very short so impulses must be generated subsequently high stresses are generated. In this work we are examined the wave propagation inside the object after collision and measured the object non-linear behavior in the one-dimensional case. Wave transmission is studied by means of material acoustic parameter value. The objective of this paper is to present a computational study of propagating pulsation and harmonic waves in nonlinear media using quasi-linearization and subsequently utilized the central difference scheme. This study gives focus on longitudinal, one- dimensional wave propagation. In the finite difference scheme Non-linear system is reduced to a linear system by applying quasi-linearization method. The computed results exhibit good agreement on par with the selected non-liner wave propagation.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

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

Garrett, C. Kristopher; Hauck, Cory D.

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

A holistic approach to movement education in sport and fitness: a systems based model.

PubMed

Polsgrove, Myles Jay

2012-01-01

The typical model used by movement professionals to enhance performance relies on the notion that a linear increase in load results in steady and progressive gains, whereby, the greater the effort, the greater the gains in performance. Traditional approaches to movement progression typically rely on the proper sequencing of extrinsically based activities to facilitate the individual in reaching performance objectives. However, physical rehabilitation or physical performance rarely progresses in such a linear fashion; instead they tend to evolve non-linearly and rather unpredictably. A dynamic system can be described as an entity that self-organizes into increasingly complex forms. Applying this view to the human body, practitioners could facilitate non-linear performance gains through a systems based programming approach. Utilizing a dynamic systems view, the Holistic Approach to Movement Education (HADME) is a model designed to optimize performance by accounting for non-linear and self-organizing traits associated with human movement. In this model, gains in performance occur through advancing individual perspectives and through optimizing sub-system performance. This inward shift of the focus of performance creates a sharper self-awareness and may lead to more optimal movements. Copyright © 2011 Elsevier Ltd. All rights reserved.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

DOE PAGES

Garrett, C. Kristopher; Hauck, Cory D.

2018-04-05

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

Dynamic analysis of Free-Piston Stirling Engine/Linear Alternator-load system-experimentally validated

NASA Technical Reports Server (NTRS)

Kankam, M. David; Rauch, Jeffrey S.; Santiago, Walter

1992-01-01

This paper discusses the effects of variations in system parameters on the dynamic behavior of the Free-Piston Stirling Engine/Linear Alternator (FPSE/LA)-load system. The mathematical formulations incorporate both the mechanical and thermodynamic properties of the FPSE, as well as the electrical equations of the connected load. A state-space technique in the frequency domain is applied to the resulting system of equations to facilitate the evaluation of parametric impacts on the system dynamic stability. Also included is a discussion on the system transient stability as affected by sudden changes in some key operating conditions. Some representative results are correlated with experimental data to verify the model and analytic formulation accuracies. Guidelines are given for ranges of the system parameters which will ensure an overall stable operation.

Dynamic analysis of free-piston Stirling engine/linear alternator-load system - Experimentally validated

NASA Technical Reports Server (NTRS)

Kankam, M. D.; Rauch, Jeffrey S.; Santiago, Walter

1992-01-01

This paper discusses the effects of a variations in system parameters on the dynamic behavior of a Free-Piston Stirling Engine/Linear Alternator (FPSE/LA)-load system. The mathematical formulations incorporates both the mechanical and thermodynamic properties of the FPSE, as well as the electrical equations of the connected load. State-space technique in the frequency domain is applied to the resulting system of equations to facilitate the evaluation of parametric impacts on the system dynamic stability. Also included is a discussion on the system transient stability as affected by sudden changes in some key operating conditions. Some representative results are correlated with experimental data to verify the model and analytic formulation accuracies. Guidelines are given for ranges of the system parameters which will ensure an overall stable operation.

SLFP: a stochastic linear fractional programming approach for sustainable waste management.

PubMed

Zhu, H; Huang, G H

2011-12-01

A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk. Copyright © 2011 Elsevier Ltd. All rights reserved.

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.

Deflection angle detecting system for the large-angle and high-linearity fast steering mirror using quadrant detector

NASA Astrophysics Data System (ADS)

Ni, Yingxue; Wu, Jiabin; San, Xiaogang; Gao, Shijie; Ding, Shaohang; Wang, Jing; Wang, Tao

2018-02-01

A deflection angle detecting system (DADS) using a quadrant detector (QD) is developed to achieve the large deflection angle and high linearity for the fast steering mirror (FSM). The mathematical model of the DADS is established by analyzing the principle of position detecting and error characteristics of the QD. Based on this mathematical model, the method of optimizing deflection angle and linearity of FSM is demonstrated, which is proved feasible by simulation and experimental results. Finally, a QD-based FSM is designed and tested. The results show that it achieves 0.72% nonlinearity, ±2.0 deg deflection angle, and 1.11-μrad resolution. Therefore, the application of this method will be beneficial to design the FSM.

Accurate electrostatic and van der Waals pull-in prediction for fully clamped nano/micro-beams using linear universal graphs of pull-in instability

NASA Astrophysics Data System (ADS)

Tahani, Masoud; Askari, Amir R.

2014-09-01

In spite of the fact that pull-in instability of electrically actuated nano/micro-beams has been investigated by many researchers to date, no explicit formula has been presented yet which can predict pull-in voltage based on a geometrically non-linear and distributed parameter model. The objective of present paper is to introduce a simple and accurate formula to predict this value for a fully clamped electrostatically actuated nano/micro-beam. To this end, a non-linear Euler-Bernoulli beam model is employed, which accounts for the axial residual stress, geometric non-linearity of mid-plane stretching, distributed electrostatic force and the van der Waals (vdW) attraction. The non-linear boundary value governing equation of equilibrium is non-dimensionalized and solved iteratively through single-term Galerkin based reduced order model (ROM). The solutions are validated thorough direct comparison with experimental and other existing results reported in previous studies. Pull-in instability under electrical and vdW loads are also investigated using universal graphs. Based on the results of these graphs, non-dimensional pull-in and vdW parameters, which are defined in the text, vary linearly versus the other dimensionless parameters of the problem. Using this fact, some linear equations are presented to predict pull-in voltage, the maximum allowable length, the so-called detachment length, and the minimum allowable gap for a nano/micro-system. These linear equations are also reduced to a couple of universal pull-in formulas for systems with small initial gap. The accuracy of the universal pull-in formulas are also validated by comparing its results with available experimental and some previous geometric linear and closed-form findings published in the literature.

Robust H(∞) positional control of 2-DOF robotic arm driven by electro-hydraulic servo system.

PubMed

Guo, Qing; Yu, Tian; Jiang, Dan

2015-11-01

In this paper an H∞ positional feedback controller is developed to improve the robust performance under structural and parametric uncertainty disturbance in electro-hydraulic servo system (EHSS). The robust control model is described as the linear state-space equation by upper linear fractional transformation. According to the solution of H∞ sub-optimal control problem, the robust controller is designed and simplified to lower order linear model which is easily realized in EHSS. The simulation and experimental results can validate the robustness of this proposed method. The comparison result with PI control shows that the robust controller is suitable for this EHSS under the critical condition where the desired system bandwidth is higher and the external load of the hydraulic actuator is closed to its limited capability. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Bilinear effect in complex systems

NASA Astrophysics Data System (ADS)

Lam, Lui; Bellavia, David C.; Han, Xiao-Pu; Alston Liu, Chih-Hui; Shu, Chang-Qing; Wei, Zhengjin; Zhou, Tao; Zhu, Jichen

2010-09-01

The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear distribution is different from the power law or the stretched exponent distribution, and is called the Bilinear Effect for short. With assumptions mimicking the organization of ancient Chinese regimes, a 3-layer network model is constructed. Numerical results of this model show the bilinear effect, providing a plausible explanation of the historical data. The bilinear effect in two other social systems is presented, indicating that such a piecewise-linear effect is widespread in social systems.

Multi-Maneuver Clohessy-Wiltshire Targeting

NASA Technical Reports Server (NTRS)

Dannemiller, David P.

2011-01-01

Orbital rendezvous involves execution of a sequence of maneuvers by a chaser vehicle to bring the chaser to a desired state relative to a target vehicle while meeting intermediate and final relative constraints. Intermediate and final relative constraints are necessary to meet a multitude of requirements such as to control approach direction, ensure relative position is adequate for operation of space-to-space communication systems and relative sensors, provide fail-safe trajectory features, and provide contingency hold points. The effect of maneuvers on constraints is often coupled, so the maneuvers must be solved for as a set. For example, maneuvers that affect orbital energy change both the chaser's height and downrange position relative to the target vehicle. Rendezvous designers use experience and rules-of-thumb to design a sequence of maneuvers and constraints. A non-iterative method is presented for targeting a rendezvous scenario that includes a sequence of maneuvers and relative constraints. This method is referred to as Multi-Maneuver Clohessy-Wiltshire Targeting (MM_CW_TGT). When a single maneuver is targeted to a single relative position, the classic CW targeting solution is obtained. The MM_CW_TGT method involves manipulation of the CW state transition matrix to form a linear system. As a starting point for forming the algorithm, the effects of a series of impulsive maneuvers on the state are derived. Simple and moderately complex examples are used to demonstrate the pattern of the resulting linear system. The general form of the pattern results in an algorithm for formation of the linear system. The resulting linear system relates the effect of maneuver components and initial conditions on relative constraints specified by the rendezvous designer. Solution of the linear system includes the straight-forward inverse of a square matrix. Inversion of the square matrix is assured if the designer poses a controllable scenario - a scenario where the the constraints can be met by the sequence of maneuvers. Matrices in the linear system are dependent on selection of maneuvers and constraints by the designer, but the matrices are independent of the chaser's initial conditions. For scenarios where the sequence of maneuvers and constraints are fixed, the linear system can be formed and the square matrix inverted prior to real-time operations. Example solutions are presented for several rendezvous scenarios to illustrate the utility of the method. The MM_CW_TGT method has been used during the preliminary design of rendezvous scenarios and is expected to be useful for iterative methods in the generation of an initial guess and corrections.

Sex differences in the fetal heart rate variability indices of twins.

PubMed

Tendais, Iva; Figueiredo, Bárbara; Gonçalves, Hernâni; Bernardes, João; Ayres-de-Campos, Diogo; Montenegro, Nuno

2015-03-01

To evaluate the differences in linear and complex heart rate dynamics in twin pairs according to fetal sex combination [male-female (MF), male-male (MM), and female-female (FF)]. Fourteen twin pairs (6 MF, 3 MM, and 5 FF) were monitored between 31 and 36.4 weeks of gestation. Twenty-six fetal heart rate (FHR) recordings of both twins were simultaneously acquired and analyzed with a system for computerized analysis of cardiotocograms. Linear and nonlinear FHR indices were calculated. Overall, MM twins presented higher intrapair average in linear indices than the other pairs, whereas FF twins showed higher sympathetic-vagal balance. MF twins exhibited higher intrapair average in entropy indices and MM twins presented lower entropy values than FF twins considering the (automatically selected) threshold rLu. MM twin pairs showed higher intrapair differences in linear heart rate indices than MF and FF twins, whereas FF twins exhibited lower intrapair differences in entropy indices. The results of this exploratory study suggest that twins have sex-specific differences in linear and nonlinear indices of FHR. MM twins expressed signs of a more active autonomic nervous system and MF twins showed the most active complexity control system. These results suggest that fetal sex combination should be taken into consideration when performing detailed evaluation of the FHR in twins.

On improving linear solver performance: a block variant of GMRES

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

Baker, A H; Dennis, J M; Jessup, E R

2004-05-10

The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors.more » Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.« less

Conditions for Stabilizability of Linear Switched Systems

NASA Astrophysics Data System (ADS)

Minh, Vu Trieu

2011-06-01

This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence.

Quasi-optical reflective polarimeter for wide millimeter-wave band

NASA Astrophysics Data System (ADS)

Shinnaga, Hiroko; Tsuboi, Masato; Kasuga, Takashi

1998-11-01

We constructed a new reflective-type polarimeter system at 35 - 250 GHz for the 45 m telescope at Nobeyama Radio Observatory (NRO). Using the system, we can measure both linear polarization and circular polarization for our needs. The new system has two key points. First is that we can tune the center frequency of the polarimeter in the available frequency range, second is that insertion loss is low (0.15 plus or minus 0.03 dB at 86 GHz). These characteristics extended achievable scientific aims. In this paper, we present the design and the performance of the system. Using the system, we measured linear polarizations of some astronomical objects at 86 GHz, with SiO (nu) equals 0,1 and 2 at J equals 2 - 1 and 29SiO (nu) equals 0 J equals 2 - 1 simultaneously. As a result, the observation revealed SiO (nu) equals 0 J equals 2 - 1 of VY Canis Majoris is highly linearly polarized, the degree of linear polarization is up to 64%, in spite of SiO J equals 2 - 1 (nu) equals 1 is not highly linearly polarized. The highly linearly polarized feature is a strong evidence that 28SiO J equals 2 - 1 transition at the ground vibrational state originate through maser action. This is the first detection of the cosmic maser emission of SiO (nu) equals 0 J equals 2 - 1 transition.

Time-delay control of a magnetic levitated linear positioning system

NASA Technical Reports Server (NTRS)

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

1994-01-01

In this paper, a high accuracy linear positioning system with a linear force actuator and magnetic levitation is proposed. By locating a permanently magnetized rod inside a current-carrying solenoid, the axial force is achieved by the boundary effect of magnet poles and utilized to power the linear motion, while the force for levitation is governed by Ampere's Law supplied with the same solenoid. With the levitation in a radial direction, there is hardly any friction between the rod and the solenoid. The high speed motion can hence be achieved. Besides, the axial force acting on the rod is a smooth function of rod position, so the system can provide nanometer resolution linear positioning to the molecule size. Since the force-position relation is highly nonlinear, and the mathematical model is derived according to some assumptions, such as the equivalent solenoid of the permanently magnetized rod, so there exists unknown dynamics in practical application. Thus 'robustness' is an important issue in controller design. Meanwhile the load effect reacts directly on the servo system without transmission elements, so the capability of 'disturbance rejection; is also required. With the above consideration, a time-delay control scheme is chosen and applied. By comparing the input-output relation and the mathematical model, the time-delay controller calculates an estimation of unmodeled dynamics and disturbances and then composes the desired compensation into the system. Effectiveness of the linear positioning system and control scheme are illustrated with simulation results.

SCI Identification (SCIDNT) program user's guide. [maximum likelihood method for linear rotorcraft models

NASA Technical Reports Server (NTRS)

1979-01-01

The computer program Linear SCIDNT which evaluates rotorcraft stability and control coefficients from flight or wind tunnel test data is described. It implements the maximum likelihood method to maximize the likelihood function of the parameters based on measured input/output time histories. Linear SCIDNT may be applied to systems modeled by linear constant-coefficient differential equations. This restriction in scope allows the application of several analytical results which simplify the computation and improve its efficiency over the general nonlinear case.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

NASA Astrophysics Data System (ADS)

Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-02-01

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude.

PubMed

McDowell, J J; Wood, H M

1984-03-01

Eight human subjects pressed a lever on a range of variable-interval schedules for 0.25 cent to 35.0 cent per reinforcement. Herrnstein's hyperbola described seven of the eight subjects' response-rate data well. For all subjects, the y-asymptote of the hyperbola increased with increasing reinforcer magnitude and its reciprocal was a linear function of the reciprocal of reinforcer magnitude. These results confirm predictions made by linear system theory; they contradict formal properties of Herrnstein's account and of six other mathematical accounts of single-alternative responding.

Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude

PubMed Central

McDowell, J. J; Wood, Helena M.

1984-01-01

Eight human subjects pressed a lever on a range of variable-interval schedules for 0.25¢ to 35.0¢ per reinforcement. Herrnstein's hyperbola described seven of the eight subjects' response-rate data well. For all subjects, the y-asymptote of the hyperbola increased with increasing reinforcer magnitude and its reciprocal was a linear function of the reciprocal of reinforcer magnitude. These results confirm predictions made by linear system theory; they contradict formal properties of Herrnstein's account and of six other mathematical accounts of single-alternative responding. PMID:16812366

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

The numerical solution of linear multi-term fractional differential equations: systems of equations

NASA Astrophysics Data System (ADS)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

NASA Astrophysics Data System (ADS)

Zhang, Langwen; Xie, Wei; Wang, Jingcheng

2017-11-01

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min-max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

Impact of Cross-Axis Structural Dynamics on Validation of Linear Models for Space Launch System

NASA Technical Reports Server (NTRS)

Pei, Jing; Derry, Stephen D.; Zhou Zhiqiang; Newsom, Jerry R.

2014-01-01

A feasibility study was performed to examine the advisability of incorporating a set of Programmed Test Inputs (PTIs) during the Space Launch System (SLS) vehicle flight. The intent of these inputs is to provide validation to the preflight models for control system stability margins, aerodynamics, and structural dynamics. During October 2009, Ares I-X program was successful in carrying out a series of PTI maneuvers which provided a significant amount of valuable data for post-flight analysis. The resulting data comparisons showed excellent agreement with the preflight linear models across the frequency spectrum of interest. However unlike Ares I-X, the structural dynamics associated with the SLS boost phase configuration are far more complex and highly coupled in all three axes. This presents a challenge when implementing this similar system identification technique to SLS. Preliminary simulation results show noticeable mismatches between PTI validation and analytical linear models in the frequency range of the structural dynamics. An alternate approach was examined which demonstrates the potential for better overall characterization of the system frequency response as well as robustness of the control design.

A Linear Programming Approach to Routing Control in Networks of Constrained Nonlinear Positive Systems with Concave Flow Rates

NASA Technical Reports Server (NTRS)

Arneson, Heather M.; Dousse, Nicholas; Langbort, Cedric

2014-01-01

We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

DOE PAGES

Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.; ...

2016-11-07

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

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

Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

Input-output characterization of an ultrasonic testing system by digital signal analysis

NASA Technical Reports Server (NTRS)

Karaguelle, H.; Lee, S. S.; Williams, J., Jr.

1984-01-01

The input/output characteristics of an ultrasonic testing system used for stress wave factor measurements were studied. The fundamentals of digital signal processing are summarized. The inputs and outputs are digitized and processed in a microcomputer using digital signal processing techniques. The entire ultrasonic test system, including transducers and all electronic components, is modeled as a discrete-time linear shift-invariant system. Then the impulse response and frequency response of the continuous time ultrasonic test system are estimated by interpolating the defining points in the unit sample response and frequency response of the discrete time system. It is found that the ultrasonic test system behaves as a linear phase bandpass filter. Good results were obtained for rectangular pulse inputs of various amplitudes and durations and for tone burst inputs whose center frequencies are within the passband of the test system and for single cycle inputs of various amplitudes. The input/output limits on the linearity of the system are determined.

HOLLOTRON switch for megawatt lightweight space inverters

NASA Technical Reports Server (NTRS)

Poeschel, R. L.; Goebel, D. M.; Schumacher, R. W.

1991-01-01

The feasibility of satisfying the switching requirements for a megawatt ultralight inverter system using HOLLOTRON switch technology was determined. The existing experimental switch hardware was modified to investigate a coaxial HOLLOTRON switch configuration and the results were compared with those obtained for a modified linear HOLLOTRON configuration. It was concluded that scaling the HOLLOTRON switch to the current and voltage specifications required for a megawatt converter system is indeed feasible using a modified linear configuration. The experimental HOLLOTRON switch operated at parameters comparable to the scaled coaxial HOLLOTRON. However, the linear HOLLOTRON data verified the capability for meeting all the design objectives simultaneously including current density (greater than 2 A/sq cm), voltage (5 kV), switching frequency (20 kHz), switching time (300 ns), and forward voltage drop (less than or equal to 20 V). Scaling relations were determined and a preliminary design was completed for an engineering model linear HOLLOTRON switch to meet the megawatt converter system specifications.

A straightforward characterization of non-modal effects from the evolution of linear dynamical systems

NASA Astrophysics Data System (ADS)

Arratia, Cristobal

2014-11-01

A simple construction will be shown, which reveals a general property satisfied by the evolution in time of a state vector composed by a superposition of orthogonal eigenmodes of a linear dynamical system. This property results from the conservation of the inner product between such state vectors evolving forward and backwards in time, and it can be simply evaluated from the state vector and its first and second time derivatives. This provides an efficient way to characterize, instantaneously along any specific phase-space trajectory of the linear system, the relevance of the non-normality of the linearized Navier-Stokes operator on the energy (or any other norm) gain or decay of small perturbations. Examples of this characterization applied to stationary or time dependent base flows will be shown. CONICYT, Concurso de Apoyo al Retorno de Investigadores del Extranjero, folio 821320055.

Intelligent control of non-linear dynamical system based on the adaptive neurocontroller

NASA Astrophysics Data System (ADS)

Engel, E.; Kovalev, I. V.; Kobezhicov, V.

2015-10-01

This paper presents an adaptive neuro-controller for intelligent control of non-linear dynamical system. The formed as the fuzzy selective neural net the adaptive neuro-controller on the base of system's state, creates the effective control signal under random perturbations. The validity and advantages of the proposed adaptive neuro-controller are demonstrated by numerical simulations. The simulation results show that the proposed controller scheme achieves real-time control speed and the competitive performance, as compared to PID, fuzzy logic controllers.

String Stability of a Linear Formation Flight Control System

NASA Technical Reports Server (NTRS)

Allen, Michael J.; Ryan, Jack; Hanson, Curtis E.; Parle, James F.

2002-01-01

String stability analysis of an autonomous formation flight system was performed using linear and nonlinear simulations. String stability is a measure of how position errors propagate from one vehicle to another in a cascaded system. In the formation flight system considered here, each i(sup th) aircraft uses information from itself and the preceding ((i-1)(sup th)) aircraft to track a commanded relative position. A possible solution for meeting performance requirements with such a system is to allow string instability. This paper explores two results of string instability and outlines analysis techniques for string unstable systems. The three analysis techniques presented here are: linear, nonlinear formation performance, and ride quality. The linear technique was developed from a worst-case scenario and could be applied to the design of a string unstable controller. The nonlinear formation performance and ride quality analysis techniques both use nonlinear formation simulation. Three of the four formation-controller gain-sets analyzed in this paper were limited more by ride quality than by performance. Formations of up to seven aircraft in a cascaded formation could be used in the presence of light gusts with this string unstable system.

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

Modeling the formation of ordered nano-assemblies comprised by dendrimers and linear polyelectrolytes: The role of Coulombic interactions

NASA Astrophysics Data System (ADS)

Eleftheriou, E.; Karatasos, K.

2012-10-01

Models of mixtures of peripherally charged dendrimers with oppositely charged linear polyelectrolytes in the presence of explicit solvent are studied by means of molecular dynamics simulations. Under the influence of varying strength of electrostatic interactions, these systems appear to form dynamically arrested film-like interconnected structures in the polymer-rich phase. Acting like a pseudo-thermodynamic inverse temperature, the increase of the strength of the Coulombic interactions drive the polymeric constituents of the mixture to a gradual dynamic freezing-in. The timescale of the average density fluctuations of the formed complexes initially increases in the weak electrostatic regime reaching a finite limit as the strength of electrostatic interactions grow. Although the models are overall electrically neutral, during this process the dendrimer/linear complexes develop a polar character with an excess charge mainly close to the periphery of the dendrimers. The morphological characteristics of the resulted pattern are found to depend on the size of the polymer chains on account of the distinct conformational features assumed by the complexed linear polyelectrolytes of different length. In addition, the length of the polymer chain appears to affect the dynamics of the counterions, thus affecting the ionic transport properties of the system. It appears, therefore, that the strength of electrostatic interactions together with the length of the linear polyelectrolytes are parameters to which these systems are particularly responsive, offering thus the possibility for a better control of the resulted structure and the electric properties of these soft-colloidal systems.

Statistical Tests of System Linearity Based on the Method of Surrogate Data

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

Hunter, N.; Paez, T.; Red-Horse, J.

When dealing with measured data from dynamic systems we often make the tacit assumption that the data are generated by linear dynamics. While some systematic tests for linearity and determinism are available - for example the coherence fimction, the probability density fimction, and the bispectrum - fi,u-ther tests that quanti$ the existence and the degree of nonlinearity are clearly needed. In this paper we demonstrate a statistical test for the nonlinearity exhibited by a dynamic system excited by Gaussian random noise. We perform the usual division of the input and response time series data into blocks as required by themore » Welch method of spectrum estimation and search for significant relationships between a given input fkequency and response at harmonics of the selected input frequency. We argue that systematic tests based on the recently developed statistical method of surrogate data readily detect significant nonlinear relationships. The paper elucidates the method of surrogate data. Typical results are illustrated for a linear single degree-of-freedom system and for a system with polynomial stiffness nonlinearity.« less

Classical Michaelis-Menten and system theory approach to modeling metabolite formation kinetics.

PubMed

Popović, Jovan

2004-01-01

When single doses of drug are administered and kinetics are linear, techniques, which are based on the compartment approach and the linear system theory approach, in modeling the formation of the metabolite from the parent drug are proposed. Unlike the purpose-specific compartment approach, the methodical, conceptual and computational uniformity in modeling various linear biomedical systems is the dominant characteristic of the linear system approach technology. Saturation of the metabolic reaction results in nonlinear kinetics according to the Michaelis-Menten equation. The two compartment open model with Michaelis-Menten elimination kinetics is theorethicaly basic when single doses of drug are administered. To simulate data or to fit real data using this model, one must resort to numerical integration. A biomathematical model for multiple dosage regimen calculations of nonlinear metabolic systems in steady-state and a working example with phenytoin are presented. High correlation between phenytoin steady-state serum levels calculated from individual Km and Vmax values in the 15 adult epileptic outpatients and the observed levels at the third adjustment of phenytoin daily dose (r=0.961, p<0.01) were found.

An extended GS method for dense linear systems

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

2009-09-01

Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

DTIC Science & Technology

1980-05-01

reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

PubMed

Sanz, Luis; Alonso, Juan Antonio

2017-12-01

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

NASA Technical Reports Server (NTRS)

Gupta, Sandeep

1996-01-01

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.

2000-01-01

Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.

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.

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.

INTERCOMPARISON ON THE MEASUREMENT OF THE QUANTITY PERSONAL DOSE EQUIVALENT HP(10) IN PHOTON FIELDS. LINEARITY DEPENDENCE, LOWER LIMIT OF DETECTION AND UNCERTAINTY IN MEASUREMENT OF DOSIMETRY SYSTEMS OF INDIVIDUAL MONITORING SERVICES IN GABON AND GHANA.

PubMed

Ondo Meye, P; Schandorf, C; Amoako, J K; Manteaw, P O; Amoatey, E A; Adjei, D N

2017-12-01

An inter-comparison study was conducted to assess the capability of dosimetry systems of individual monitoring services (IMSs) in Gabon and Ghana to measure personal dose equivalent Hp(10) in photon fields. The performance indicators assessed were the lower limit of detection, linearity and uncertainty in measurement. Monthly and quarterly recording levels were proposed with corresponding values of 0.08 and 0.025 mSv, and 0.05 and 0.15 mSv for the TLD and OSL systems, respectively. The linearity dependence of the dosimetry systems was performed following the requirement given in the Standard IEC 62387 of the International Electrotechnical Commission (IEC). The results obtained for the two systems were satisfactory. The procedure followed for the uncertainty assessment is the one given in the IEC technical report TR62461. The maximum relative overall uncertainties, in absolute value, expressed in terms of Hp(10), for the TL dosimetry system Harshaw 6600, are 44. 35% for true doses below 0.40 mSv and 36.33% for true doses ≥0.40 mSv. For the OSL dosimetry system microStar, the maximum relative overall uncertainties, in absolute value, are 52.17% for true doses below 0.40 mSv and 37.43% for true doses ≥0.40 mSv. These results are in good agreement with the requirements for accuracy of the International Commission on Radiological protection. When expressing the uncertainties in terms of response, comparison with the IAEA requirements for overall accuracy showed that the uncertainty results were also acceptable. The values of Hp(10) directly measured by the two dosimetry systems showed a significant underestimation for the Harshaw 6600 system, and a slight overestimation for the microStar system. After correction for linearity of the measured doses, the two dosimetry systems gave better and comparable results. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

A theoretical investigation of symmetry-origin unidirectional energy gradient in light-harvesting dendrimers.

PubMed

Koda, Shin-ichi

2016-03-21

We theoretically investigate a possibility that the symmetry of the repetitively branched structure of light-harvesting dendrimers creates the energy gradient descending toward inner generations (layers of pigment molecules) of the dendrimers. In the first half of this paper, we define a model system using the Frenkel exciton Hamiltonian that focuses only on the topology of dendrimers and numerically show that excitation energy tends to gather at inner generations of the model system at a thermal equilibrium state. This indicates that an energy gradient is formed in the model system. In the last half, we attribute this result to the symmetry of the model system and propose two symmetry-origin mechanisms creating the energy gradient. The present analysis and proposition are based on the theory of the linear chain (LC) decomposition [S. Koda, J. Chem. Phys. 142, 204112 (2015)], which equivalently transforms the model system into a set of one-dimensional systems on the basis of the symmetry of dendrimers. In the picture of the LC decomposition, we find that energy gradient is formed both in each linear chain and among linear chains, and these two mechanisms explain the numerical results well.

A theoretical investigation of symmetry-origin unidirectional energy gradient in light-harvesting dendrimers

NASA Astrophysics Data System (ADS)

Koda, Shin-ichi

2016-03-01

We theoretically investigate a possibility that the symmetry of the repetitively branched structure of light-harvesting dendrimers creates the energy gradient descending toward inner generations (layers of pigment molecules) of the dendrimers. In the first half of this paper, we define a model system using the Frenkel exciton Hamiltonian that focuses only on the topology of dendrimers and numerically show that excitation energy tends to gather at inner generations of the model system at a thermal equilibrium state. This indicates that an energy gradient is formed in the model system. In the last half, we attribute this result to the symmetry of the model system and propose two symmetry-origin mechanisms creating the energy gradient. The present analysis and proposition are based on the theory of the linear chain (LC) decomposition [S. Koda, J. Chem. Phys. 142, 204112 (2015)], which equivalently transforms the model system into a set of one-dimensional systems on the basis of the symmetry of dendrimers. In the picture of the LC decomposition, we find that energy gradient is formed both in each linear chain and among linear chains, and these two mechanisms explain the numerical results well.

Asymptotic behavior of modulated Taylor-Couette flows with a crystalline inner cylinder

NASA Technical Reports Server (NTRS)

Braun, R. J.; Mcfadden, G. B.; Murray, B. T.; Coriell, S. R.; Glicksman, M. E.; Selleck, M. E.

1993-01-01

The linear stability of a modulated Taylor-Couette system when the inner cylindrical boundary consists of a crystalline solid-liquid interface is considered. Both experimentally and in numerical calculations it is found that the two-phase system is significantly less stable than the analogous rigid-walled system for materials with moderately large Prandtl numbers. A numerical treatment based on Floquet theory is described, which gives results that are in good agreement with preliminary experimental findings. In addition, this instability is further examined by carrying out a formal asymptotic expansion of the solution in the limit of large Prandtl number. In this limit the Floquet analysis is considerably simplified, and the linear stability of the modulated system can be determined to leading order through a conventional stability analysis, without recourse to Floquet theory. The resulting simplified problem is then studied for both the narrow gap geometry and for the case of a finite gap. It is surprising that the determination of the linear stability of the two-phase system is considerably simpler than that of the rigid-walled system, despite the complications introduced by the presence of the crystal-melt interface.

Miscible gravitational instability of initially stable horizontal interface in a porous medium: Non-monotonic density profiles

NASA Astrophysics Data System (ADS)

Kim, Min Chan

2014-11-01

To simulate a CO2 sequestration process, some researchers employed a water/propylene glycol (PPG) system which shows a non-monotonic density profile. Motivated by this fact, the stability of the diffusion layer of two miscible fluids saturated in a porous medium is analyzed. For a non-monotonic density profile system, linear stability equations are derived in a global domain, and then transformed into a system of ordinary differential equations in an infinite domain. Initial growth rate analysis is conducted without the quasi-steady state approximation (QSSA) and shows that initially the system is unconditionally stable for the least stable disturbance. For the time evolving case, the ordinary differential equations are solved applying the eigen-analysis and numerical shooting scheme with and without the QSSA. To support these theoretical results, direct numerical simulations are conducted using the Fourier spectral method. The results of theoretical linear stability analyses and numerical simulations validate one another. The present linear and nonlinear analyses show that the water/PPG system is more unstable than the CO2/brine one, and the flow characteristics of these two systems are quite different from each other.

Online Detection of Driver Fatigue Using Steering Wheel Angles for Real Driving Conditions.

PubMed

Li, Zuojin; Li, Shengbo Eben; Li, Renjie; Cheng, Bo; Shi, Jinliang

2017-03-02

This paper presents a drowsiness on-line detection system for monitoring driver fatigue level under real driving conditions, based on the data of steering wheel angles (SWA) collected from sensors mounted on the steering lever. The proposed system firstly extracts approximate entropy (ApEn)featuresfromfixedslidingwindowsonreal-timesteeringwheelanglestimeseries. Afterthat, this system linearizes the ApEn features series through an adaptive piecewise linear fitting using a given deviation. Then, the detection system calculates the warping distance between the linear features series of the sample data. Finally, this system uses the warping distance to determine the drowsiness state of the driver according to a designed binary decision classifier. The experimental data were collected from 14.68 h driving under real road conditions, including two fatigue levels: "wake" and "drowsy". The results show that the proposed system is capable of working online with an average 78.01% accuracy, 29.35% false detections of the "awake" state, and 15.15% false detections of the "drowsy" state. The results also confirm that the proposed method based on SWA signal is valuable for applications in preventing traffic accidents caused by driver fatigue.

Online Detection of Driver Fatigue Using Steering Wheel Angles for Real Driving Conditions

PubMed Central

Li, Zuojin; Li, Shengbo Eben; Li, Renjie; Cheng, Bo; Shi, Jinliang

2017-01-01

This paper presents a drowsiness on-line detection system for monitoring driver fatigue level under real driving conditions, based on the data of steering wheel angles (SWA) collected from sensors mounted on the steering lever. The proposed system firstly extracts approximate entropy (ApEn) features from fixed sliding windows on real-time steering wheel angles time series. After that, this system linearizes the ApEn features series through an adaptive piecewise linear fitting using a given deviation. Then, the detection system calculates the warping distance between the linear features series of the sample data. Finally, this system uses the warping distance to determine the drowsiness state of the driver according to a designed binary decision classifier. The experimental data were collected from 14.68 h driving under real road conditions, including two fatigue levels: “wake” and “drowsy”. The results show that the proposed system is capable of working online with an average 78.01% accuracy, 29.35% false detections of the “awake” state, and 15.15% false detections of the “drowsy” state. The results also confirm that the proposed method based on SWA signal is valuable for applications in preventing traffic accidents caused by driver fatigue. PMID:28257094

Improved importance sampling technique for efficient simulation of digital communication systems

NASA Technical Reports Server (NTRS)

Lu, Dingqing; Yao, Kung

1988-01-01

A new, improved importance sampling (IIS) approach to simulation is considered. Some basic concepts of IS are introduced, and detailed evolutions of simulation estimation variances for Monte Carlo (MC) and IS simulations are given. The general results obtained from these evolutions are applied to the specific previously known conventional importance sampling (CIS) technique and the new IIS technique. The derivation for a linear system with no signal random memory is considered in some detail. For the CIS technique, the optimum input scaling parameter is found, while for the IIS technique, the optimum translation parameter is found. The results are generalized to a linear system with memory and signals. Specific numerical and simulation results are given which show the advantages of CIS over MC and IIS over CIS for simulations of digital communications systems.

Convergence Results on Iteration Algorithms to Linear Systems

PubMed Central

Wang, Zhuande; Yang, Chuansheng; Yuan, Yubo

2014-01-01

In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods. PMID:24991640

Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

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

Barnich, Glenn; Troessaert, Cedric

2009-04-15

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

NASA Astrophysics Data System (ADS)

Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

2010-05-01

The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low-Low Satellite-to-Satellite Tracking

Design and performance testing of an ultrasonic linear motor with dual piezoelectric actuators.

PubMed

Smithmaitrie, Pruittikorn; Suybangdum, Panumas; Laoratanakul, Pitak; Muensit, Nantakan

2012-05-01

In this work, design and performance testing of an ultrasonic linear motor with dual piezoelectric actuator patches are studied. The motor system consists of a linear stator, a pre-load weight, and two piezoelectric actuator patches. The piezoelectric actuators are bonded with the linear elastic stator at specific locations. The stator generates propagating waves when the piezoelectric actuators are subjected to harmonic excitations. Vibration characteristics of the linear stator are analyzed and compared with finite element and experimental results. The analytical, finite element, and experimental results show agreement. In the experiments, performance of the ultrasonic linear motor is tested. Relationships between velocity and pre-load weight, velocity and applied voltage, driving force and applied voltage, and velocity and driving force are reported. The design of the dual piezoelectric actuators yields a simpler structure with a smaller number of actuators and lower stator stiffness compared with a conventional design of an ultrasonic linear motor with fully laminated piezoelectric actuators.

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

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.

Systemic oxidative stress associated with the neurological diseases of aging.

PubMed

Serra, Jorge A; Domínguez, Raúl O; Marschoff, Enrique R; Guareschi, Eduardo M; Famulari, Arturo L; Boveris, Alberto

2009-12-01

Markers of oxidative stress were measured in blood samples of 338 subjects (965 observations): Alzheimer's, vascular dementia, diabetes (type II) superimposed to dementias, Parkinson's disease and controls. Patients showed increased thiobarbituric acid reactive substances (+21%; P < 0.05), copper-zinc superoxide dismutase (+64%; P < 0.001) and decreased antioxidant capacity (-28%; P < 0.001); pairs of variables resulted linearly related across groups (P < 0.001). Catalase and glutathione peroxidase, involved in discrimination between diseases, resulted non-significant. When diabetes is superimposed with dementias, changes resulted less marked but significant. Also, superoxide dismutase resulted not linearly correlated with any other variable or age-related (pure Alzheimer's peaks at 70 years, P < 0.001). Systemic oxidative stress was significantly associated (P < 0.001) with all diseases indicating a disbalance in peripheral/adaptive responses to oxidative disorders through different free radical metabolic pathways. While other changes - methionine cycle, insulin correlation - are also associated with dementias, the responses presented here show a simple linear relation between prooxidants and antioxidant defenses.

Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [application to Augmentor Wing Jet STOL Research Aircraft flare control autopilot design

NASA Technical Reports Server (NTRS)

Patel, R. V.; Toda, M.; Sridhar, B.

1977-01-01

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Vestibular coriolis effect differences modeled with three-dimensional linear-angular interactions.

PubMed

Holly, Jan E

2004-01-01

The vestibular coriolis (or "cross-coupling") effect is traditionally explained by cross-coupled angular vectors, which, however, do not explain the differences in perceptual disturbance under different acceleration conditions. For example, during head roll tilt in a rotating chair, the magnitude of perceptual disturbance is affected by a number of factors, including acceleration or deceleration of the chair rotation or a zero-g environment. Therefore, it has been suggested that linear-angular interactions play a role. The present research investigated whether these perceptual differences and others involving linear coriolis accelerations could be explained under one common framework: the laws of motion in three dimensions, which include all linear-angular interactions among all six components of motion (three angular and three linear). The results show that the three-dimensional laws of motion predict the differences in perceptual disturbance. No special properties of the vestibular system or nervous system are required. In addition, simulations were performed with angular, linear, and tilt time constants inserted into the model, giving the same predictions. Three-dimensional graphics were used to highlight the manner in which linear-angular interaction causes perceptual disturbance, and a crucial component is the Stretch Factor, which measures the "unexpected" linear component.

LDRD final report on massively-parallel linear programming : the parPCx system.

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

Parekh, Ojas; Phillips, Cynthia Ann; Boman, Erik Gunnar

2005-02-01

This report summarizes the research and development performed from October 2002 to September 2004 at Sandia National Laboratories under the Laboratory-Directed Research and Development (LDRD) project ''Massively-Parallel Linear Programming''. We developed a linear programming (LP) solver designed to use a large number of processors. LP is the optimization of a linear objective function subject to linear constraints. Companies and universities have expended huge efforts over decades to produce fast, stable serial LP solvers. Previous parallel codes run on shared-memory systems and have little or no distribution of the constraint matrix. We have seen no reports of general LP solver runsmore » on large numbers of processors. Our parallel LP code is based on an efficient serial implementation of Mehrotra's interior-point predictor-corrector algorithm (PCx). The computational core of this algorithm is the assembly and solution of a sparse linear system. We have substantially rewritten the PCx code and based it on Trilinos, the parallel linear algebra library developed at Sandia. Our interior-point method can use either direct or iterative solvers for the linear system. To achieve a good parallel data distribution of the constraint matrix, we use a (pre-release) version of a hypergraph partitioner from the Zoltan partitioning library. We describe the design and implementation of our new LP solver called parPCx and give preliminary computational results. We summarize a number of issues related to efficient parallel solution of LPs with interior-point methods including data distribution, numerical stability, and solving the core linear system using both direct and iterative methods. We describe a number of applications of LP specific to US Department of Energy mission areas and we summarize our efforts to integrate parPCx (and parallel LP solvers in general) into Sandia's massively-parallel integer programming solver PICO (Parallel Interger and Combinatorial Optimizer). We conclude with directions for long-term future algorithmic research and for near-term development that could improve the performance of parPCx.« less

Non-linear dynamic compensation system

NASA Technical Reports Server (NTRS)

Lin, Yu-Hwan (Inventor); Lurie, Boris J. (Inventor)

1992-01-01

A non-linear dynamic compensation subsystem is added in the feedback loop of a high precision optical mirror positioning control system to smoothly alter the control system response bandwidth from a relatively wide response bandwidth optimized for speed of control system response to a bandwidth sufficiently narrow to reduce position errors resulting from the quantization noise inherent in the inductosyn used to measure mirror position. The non-linear dynamic compensation system includes a limiter for limiting the error signal within preselected limits, a compensator for modifying the limiter output to achieve the reduced bandwidth response, and an adder for combining the modified error signal with the difference between the limited and unlimited error signals. The adder output is applied to control system motor so that the system response is optimized for accuracy when the error signal is within the preselected limits, optimized for speed of response when the error signal is substantially beyond the preselected limits and smoothly varied therebetween as the error signal approaches the preselected limits.

Non-linear controls influence functions in an aircraft dynamics simulator

NASA Technical Reports Server (NTRS)

Guerreiro, Nelson M.; Hubbard, James E., Jr.; Motter, Mark A.

2006-01-01

In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft s control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland s continuing study of active wing load control.

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

NASA Technical Reports Server (NTRS)

Folta, David C.; Carpenter, J. Russell

1999-01-01

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Design and testing of a coaxial linear magnetic spring with integral linear motor. [for spacecraft energy storage

NASA Technical Reports Server (NTRS)

Patt, P. J.

1985-01-01

The design of a coaxial linear magnetic spring which incorporates a linear motor to control axial motion and overcome system damping is presented, and the results of static and dynamic tests are reported. The system has nominal stiffness 25,000 N/m and is designed to oscillate a 900-g component over a 4.6-mm stroke in a Stirling-cycle cryogenic refrigerator being developed for long-service (5-10-yr) space applications (Stolfi et al., 1983). Mosaics of 10 radially magnetized high-coercivity SmCO5 segments enclosed in Ti cans are employed, and the device is found to have quality factor 70-100, corresponding to energy-storage efficiency 91-94 percent. Drawings, diagrams, and graphs are provided.

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

NASA Astrophysics Data System (ADS)

Basin, M.; Maldonado, J. J.; Zendejo, O.

2016-07-01

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

The method of perturbation-harmonic balance for analysing nonlinear free vibration of MDOF systems and structures

NASA Astrophysics Data System (ADS)

Tang, Qiangang; Sun, Shixian

1992-03-01

In this paper, the perturbation technique is introduced into the method of harmonic balance. A new method used for analyzing nonlinear free vibration of multidegree-of-freedom systems and structures is obtained. The form of solution is expanded into a series of small parameters and harmonics, so no term will be lost in the solution and the algebraic equations are linear. With the linear transformations, the matrices of the equations become diagonal. As soon as the modes related to linear vibration are found, the solution can be obtained. This method is superior to the method of linearized iteration. The examples show that the method has high accuracy for small-amplitude problems and the results for rather large amplitudes are satisfactory.

A simple-shear rheometer for linear viscoelastic characterization of vocal fold tissues at phonatory frequencies.

PubMed

Chan, Roger W; Rodriguez, Maritza L

2008-08-01

Previous studies reporting the linear viscoelastic shear properties of the human vocal fold cover or mucosa have been based on torsional rheometry, with measurements limited to low audio frequencies, up to around 80 Hz. This paper describes the design and validation of a custom-built, controlled-strain, linear, simple-shear rheometer system capable of direct empirical measurements of viscoelastic shear properties at phonatory frequencies. A tissue specimen was subjected to simple shear between two parallel, rigid acrylic plates, with a linear motor creating a translational sinusoidal displacement of the specimen via the upper plate, and the lower plate transmitting the harmonic shear force resulting from the viscoelastic response of the specimen. The displacement of the specimen was measured by a linear variable differential transformer whereas the shear force was detected by a piezoelectric transducer. The frequency response characteristics of these system components were assessed by vibration experiments with accelerometers. Measurements of the viscoelastic shear moduli (G' and G") of a standard ANSI S2.21 polyurethane material and those of human vocal fold cover specimens were made, along with estimation of the system signal and noise levels. Preliminary results showed that the rheometer can provide valid and reliable rheometric data of vocal fold lamina propria specimens at frequencies of up to around 250 Hz, well into the phonatory range.

Radiation Field Forming for Industrial Electron Accelerators Using Rare-Earth Magnetic Materials

NASA Astrophysics Data System (ADS)

Ermakov, A. N.; Khankin, V. V.; Shvedunov, N. V.; Shvedunov, V. I.; Yurov, D. S.

2016-09-01

The article describes the radiation field forming system for industrial electron accelerators, which would have uniform distribution of linear charge density at the surface of an item being irradiated perpendicular to the direction of its motion. Its main element is non-linear quadrupole lens made with the use of rare-earth magnetic materials. The proposed system has a number of advantages over traditional beam scanning systems that use electromagnets, including easier product irradiation planning, lower instantaneous local dose rate, smaller size, lower cost. Provided are the calculation results for a 10 MeV industrial electron accelerator, as well as measurement results for current distribution in the prototype build based on calculations.

Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

NASA Technical Reports Server (NTRS)

Downie, John D.; Goodman, Joseph W.

1989-01-01

The accuracy requirements of optical processors in adaptive optics systems are determined by estimating the required accuracy in a general optical linear algebra processor (OLAP) that results in a smaller average residual aberration than that achieved with a conventional electronic digital processor with some specific computation speed. Special attention is given to an error analysis of a general OLAP with regard to the residual aberration that is created in an adaptive mirror system by the inaccuracies of the processor, and to the effect of computational speed of an electronic processor on the correction. Results are presented on the ability of an OLAP to compete with a digital processor in various situations.

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

Linear quadratic regulators with eigenvalue placement in a specified region

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar

1988-01-01

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

A Flexible CUDA LU-based Solver for Small, Batched Linear Systems

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

Tumeo, Antonino; Gawande, Nitin A.; Villa, Oreste

This chapter presents the implementation of a batched CUDA solver based on LU factorization for small linear systems. This solver may be used in applications such as reactive flow transport models, which apply the Newton-Raphson technique to linearize and iteratively solve the sets of non linear equations that represent the reactions for ten of thousands to millions of physical locations. The implementation exploits somewhat counterintuitive GPGPU programming techniques: it assigns the solution of a matrix (representing a system) to a single CUDA thread, does not exploit shared memory and employs dynamic memory allocation on the GPUs. These techniques enable ourmore » implementation to simultaneously solve sets of systems with over 100 equations and to employ LU decomposition with complete pivoting, providing the higher numerical accuracy required by certain applications. Other currently available solutions for batched linear solvers are limited by size and only support partial pivoting, although they may result faster in certain conditions. We discuss the code of our implementation and present a comparison with the other implementations, discussing the various tradeoffs in terms of performance and flexibility. This work will enable developers that need batched linear solvers to choose whichever implementation is more appropriate to the features and the requirements of their applications, and even to implement dynamic switching approaches that can choose the best implementation depending on the input data.« less

Quantum Discord for d⊗2 Systems

PubMed Central

Ma, Zhihao; Chen, Zhihua; Fanchini, Felipe Fernandes; Fei, Shao-Ming

2015-01-01

We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for 106 two-qubit random density matrices, we obtain an average deviation of order 10−4. Furthermore, our results give a way to calculate the quantum discord for arbitrary n-qubit GHZ and W states evolving under the action of the amplitude damping noisy channel. PMID:26036771

Model-based frequency response characterization of a digital-image analysis system for epifluorescence microscopy

NASA Technical Reports Server (NTRS)

Hazra, Rajeeb; Viles, Charles L.; Park, Stephen K.; Reichenbach, Stephen E.; Sieracki, Michael E.

1992-01-01

Consideration is given to a model-based method for estimating the spatial frequency response of a digital-imaging system (e.g., a CCD camera) that is modeled as a linear, shift-invariant image acquisition subsystem that is cascaded with a linear, shift-variant sampling subsystem. The method characterizes the 2D frequency response of the image acquisition subsystem to beyond the Nyquist frequency by accounting explicitly for insufficient sampling and the sample-scene phase. Results for simulated systems and a real CCD-based epifluorescence microscopy system are presented to demonstrate the accuracy of the method.

A Block-LU Update for Large-Scale Linear Programming

DTIC Science & Technology

1990-01-01

linear programming problems. Results are given from runs on the Cray Y -MP. 1. Introduction We wish to use the simplex method [Dan63] to solve the...standard linear program, minimize cTx subject to Ax = b 1< x <U, where A is an m by n matrix and c, x, 1, u, and b are of appropriate dimension. The simplex...the identity matrix. The basis is used to solve for the search direction y and the dual variables 7r in the following linear systems: Bky = aq (1.2) and

A High-Order, Time Invariant, Linearized Model for Application to HHCIAFCS Interaction Studies

NASA Technical Reports Server (NTRS)

Cheng, Rendy P.; Tischler, Mark B.; Celi, Roberto

2003-01-01

This paper describes a methodology for the extraction of a linear time invariant model from a nonlinear helicopter model, and followed by an examination of the interactions of the Higher Harmonic Control (HHC) and the Automatic Flight Control System (AFCS). This new method includes an embedded harmonic analyzer inside a linear time invariant model, which allows the periodicity of the helicopter response to be captured. The: coupled high-order model provides the needed level of dynamic fidelity to permit an analysis and optimization of the AFCS and HHC loops. Results of this study indicate that the closed-loop HHC system has little influence on the AFCS or on the vehicle handling qualities, which indicates that the AFCS does not need modification to work with the HHC system. The results also show that the vibration response to maneuvers must be considered during the HHC design process, which leads to much higher required HHC loop crossover frequencies. This research also demonstrates that the transient vibration response during maneuvers can be reduced by optimizing the closed-loop higher harmonic control laws using conventional control system analyses.

Assessment of Health-Cost Externalities of Air Pollution at the National Level using the EVA Model System

NASA Astrophysics Data System (ADS)

Brandt, Jørgen; Silver, Jeremy David; Heile Christensen, Jesper; Skou Andersen, Mikael; Geels, Camilla; Gross, Allan; Buus Hansen, Ayoe; Mantzius Hansen, Kaj; Brandt Hedegaard, Gitte; Ambelas Skjøth, Carsten

2010-05-01

Air pollution has significant negative impacts on human health and well-being, which entail substantial economic consequences. We have developed an integrated model system, EVA (External Valuation of Air pollution), to assess health-related economic externalities of air pollution resulting from specific emission sources/sectors. The EVA system was initially developed to assess externalities from power production, but in this study it is extended to evaluate costs at the national level. The EVA system integrates a regional-scale atmospheric chemistry transport model (DEHM), address-level population data, exposure-response functions and monetary values applicable for Danish/European conditions. Traditionally, systems that assess economic costs of health impacts from air pollution assume linear approximations in the source-receptor relationships. However, atmospheric chemistry is non-linear and therefore the uncertainty involved in the linear assumption can be large. The EVA system has been developed to take into account the non-linear processes by using a comprehensive, state-of-the-art chemical transport model when calculating how specific changes to emissions affect air pollution levels and the subsequent impacts on human health and cost. Furthermore, we present a new "tagging" method, developed to examine how specific emission sources influence air pollution levels without assuming linearity of the non-linear behaviour of atmospheric chemistry. This method is more precise than the traditional approach based on taking the difference between two concentration fields. Using the EVA system, we have estimated the total external costs from the main emission sectors in Denmark, representing the ten major SNAP codes. Finally, we assess the impacts and external costs of emissions from international ship traffic around Denmark, since there is a high volume of ship traffic in the region.

A new adaptive multiple modelling approach for non-linear and non-stationary systems

NASA Astrophysics Data System (ADS)

Chen, Hao; Gong, Yu; Hong, Xia

2016-07-01

This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.

Quantum computation for solving linear systems

NASA Astrophysics Data System (ADS)

Cao, Yudong

Quantum computation is a subject born out of the combination between physics and computer science. It studies how the laws of quantum mechanics can be exploited to perform computations much more efficiently than current computers (termed classical computers as oppose to quantum computers). The thesis starts by introducing ideas from quantum physics and theoretical computer science and based on these ideas, introducing the basic concepts in quantum computing. These introductory discussions are intended for non-specialists to obtain the essential knowledge needed for understanding the new results presented in the subsequent chapters. After introducing the basics of quantum computing, we focus on the recently proposed quantum algorithm for linear systems. The new results include i) special instances of quantum circuits that can be implemented using current experimental resources; ii) detailed quantum algorithms that are suitable for a broader class of linear systems. We show that for some particular problems the quantum algorithm is able to achieve exponential speedup over their classical counterparts.

On the parallel solution of parabolic equations

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Youcef

1989-01-01

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

A free-piston Stirling engine/linear alternator controls and load interaction test facility

NASA Technical Reports Server (NTRS)

Rauch, Jeffrey S.; Kankam, M. David; Santiago, Walter; Madi, Frank J.

1992-01-01

A test facility at LeRC was assembled for evaluating free-piston Stirling engine/linear alternator control options, and interaction with various electrical loads. This facility is based on a 'SPIKE' engine/alternator. The engine/alternator, a multi-purpose load system, a digital computer based load and facility control, and a data acquisition system with both steady-periodic and transient capability are described. Preliminary steady-periodic results are included for several operating modes of a digital AC parasitic load control. Preliminary results on the transient response to switching a resistive AC user load are discussed.

A study of fast ionic conductors by positron annihilation

NASA Astrophysics Data System (ADS)

Wang, Yung-Yu; Yang, Ju-Hua; Pan, Xiao-Liang; Lei, Zhen-Xi

1988-06-01

New fast ionic conductor systems of LiCl-LiF-B2O3 and LiF-B2O3 were studied by using the positron annihilation technique. It was found that the mid-life intensity I2 in positron annihilation has a linear relationship with the material's electrical conductivity log sigma. This result, combined with the measurement result on the linear annihilation parameter, indicated that the voids between microcrystals and network phases provided more transfer paths in the micro-crystalline LiF-LiCl-B2O3 system, which led to improved electrical conductivity in this type of material.

Design of a two-level power system linear state estimator

NASA Astrophysics Data System (ADS)

Yang, Tao

The availability of synchro-phasor data has raised the possibility of a linear state estimator if the inputs are only complex currents and voltages and if there are enough such measurements to meet observability and redundancy requirements. Moreover, the new digital substations can perform some of the computation at the substation itself resulting in a more accurate two-level state estimator. The objective of this research is to develop a two-level linear state estimator processing synchro-phasor data and estimating the states at both the substation level and the control center level. Both the mathematical algorithms that are different from those in the present state estimation procedure and the layered architecture of databases, communications and application programs that are required to support this two-level linear state estimator are described in this dissertation. Besides, as the availability of phasor measurements at substations will increase gradually, this research also describes how the state estimator can be enhanced to handle both the traditional state estimator and the proposed linear state estimator simultaneously. This provides a way to immediately utilize the benefits in those parts of the system where such phasor measurements become available and provides a pathway to transition to the smart grid of the future. The design procedure of the two-level state estimator is applied to two study systems. The first study system is the IEEE-14 bus system. The second one is the 179 bus Western Electricity Coordinating Council (WECC) system. The static database for the substations is constructed from the power flow data of these systems and the real-time measurement database is produced by a power system dynamic simulating tool (TSAT). Time-skew problems that may be caused by communication delays are also considered and simulated. We used the Network Simulator (NS) tool to simulate a simple communication system and analyse its time delay performance. These time delays were too small to affect the results especially since the measurement data is time-stamped and the state estimator for these small systems could be run with subseconf frequency. Keywords: State Estimation, Synchro-Phasor Measurement, Distributed System, Energy Control Center, Substation, Time-skew

Commissioning results of CERN HIE-ISOLDE and INFN ALPI cryogenic control systems

NASA Astrophysics Data System (ADS)

Inglese, V.; Pezzetti, M.; Calore, A.; Modanese, P.; Pengo, R.

2017-02-01

The cryogenic systems of both accelerators, namely HIE ISOLDE (High Intensity and Energy Isotope Separator On Line DEvice) at CERN and ALPI (Acceleratore Lineare Per Ioni) at LNL, have been refurbished. HIE ISOLDE is a major upgrade of the existing ISOLDE facilities, which required the construction of a superconducting linear accelerator consisting of six cryomodules, each containing five superconductive RF cavities and superconducting solenoids. The ALPI linear accelerator, similar to HIE ISOLDE, is located at Legnaro National Laboratories (LNL) and became operational in the early 90’s. It is composed of 74 superconducting RF cavities, assembled inside 22 cryostats. The new control systems are equipped with PLC, developed on the CERN UNICOS framework, which include Schneider and Siemens PLCs and various fieldbuses (Profibus DP and PA, WorldFIP). The control systems were developed in synergy between CERN and LNL in order to build, effectively and with an optimized use of resources, control systems allowing to enhance ease of operation, maintainability, and long-term availability. This paper describes (i) the cryogenic systems, with special focus on the design of the control systems hardware and software, (ii) the strategy adopted in order to achieve a synergic approach, and (iii) the commissioning results after the cool-down to 4.5 K of the cryomodules.

Block iterative restoration of astronomical images with the massively parallel processor

NASA Technical Reports Server (NTRS)

Heap, Sara R.; Lindler, Don J.

1987-01-01

A method is described for algebraic image restoration capable of treating astronomical images. For a typical 500 x 500 image, direct algebraic restoration would require the solution of a 250,000 x 250,000 linear system. The block iterative approach is used to reduce the problem to solving 4900 121 x 121 linear systems. The algorithm was implemented on the Goddard Massively Parallel Processor, which can solve a 121 x 121 system in approximately 0.06 seconds. Examples are shown of the results for various astronomical images.

Control of linear uncertain systems utilizing mismatched state observers

NASA Technical Reports Server (NTRS)

Goldstein, B.

1972-01-01

The control of linear continuous dynamical systems is investigated as a problem of limited state feedback control. The equations which describe the structure of an observer are developed constrained to time-invarient systems. The optimal control problem is formulated, accounting for the uncertainty in the design parameters. Expressions for bounds on closed loop stability are also developed. The results indicate that very little uncertainty may be tolerated before divergence occurs in the recursive computation algorithms, and the derived stability bound yields extremely conservative estimates of regions of allowable parameter variations.

Assessment of Ethylene Vinyl-Acetato Copolymer (EVA) Samples Bombarded by Gamma Radiation via Linearity Analyses

NASA Astrophysics Data System (ADS)

de Oliveira, L. N.; do Nascimento, E. O.; Schimidt, F.; Antonio, P. L.; Caldas, L. V. E.

2018-03-01

Materials with the potential to become dosimeters are of interest in radiation physics. In this research, the materials were analyzed and compared in relation to their linearity ranges. Samples of ethylene vinyl-acetate copolymer (EVA) were irradiated with doses from 10 Gy to 10 kGy using a 60Co Gamma-Cell system 220 and evaluated with the FTIR technique. The linearity analyses were applied through two methodologies, searching for linear regions in their response. The results show that both applied analyses indicate linear regions in defined dose interval. The radiation detectors EVA can be useful for radiation dosimetry in intermediate and high doses.

Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Arteaga, Santiago Egido

1998-12-01

The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the linearization strategies considered and whose computational cost is negligible. The algebraic properties of these systems depend on both the discretization and nonlinear method used. We study in detail the positive definiteness and skewsymmetry of the advection submatrices (essentially, convection-diffusion problems). We propose a discretization based on a new trilinear form for Newton's method. We solve the linear systems using three Krylov subspace methods, GMRES, QMR and TFQMR, and compare the advantages of each. Our emphasis is on parallel algorithms, and so we consider preconditioners suitable for parallel computers such as line variants of the Jacobi and Gauss- Seidel methods, alternating direction implicit methods, and Chebyshev and least squares polynomial preconditioners. These work well for moderate viscosities (moderate Reynolds number). For small viscosities we show that effective parallel solution of the advection subproblem is a critical factor to improve performance. Implementation details on a CM-5 are presented.

Autovibration and chaotic motion of an unbalanced rotor in massive non-linear compliant supports

NASA Astrophysics Data System (ADS)

Pasynkova, I. A.; Stepanova, P. P.

2018-05-01

Stability loss scenarios of an unbalanced rotor with a flexible massless shaft mounted in massive non-linear compliant supports are studied on the example of cylindrical precession. Dyffing type of non-linearity in compliant supports is considered. The system "rotor - supports" has eight degrees of freedom. Internal and external friction are taken into account. Autovibrations and chaotic vibrations are obtained. The results are confirmed by numerical check.

TU-H-BRA-06: Characterization of a Linear Accelerator Operating in a Compact MRIGuided Radiation Therapy System

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

Green, O; Mutic, S; Li, H

2016-06-15

Purpose: To describe the performance of a linear accelerator operating in a compact MRI-guided radiation therapy system. Methods: A commercial linear accelerator was placed in an MRI unit that is employed in a commercial MR-based image guided radiation therapy (IGRT) system. The linear accelerator components were placed within magnetic field-reducing hardware that provided magnetic fields of less than 40 G for the magnetron, gun driver, and port circulator, with 1 G for the linear accelerator. The system did not employ a flattening filter. The test linear accelerator was an industrial 4 MV model that was employed to test the abilitymore » to run an accelerator in the MR environment. An MR-compatible diode detector array was used to measure the beam profiles with the accelerator outside and inside the MR field and with the gradient coils on and off to examine if there was any effect on the delivered dose distribution. The beam profiles and time characteristics of the beam were measured. Results: The beam profiles exhibited characteristic unflattened Bremsstrahlung features with less than ±1.5% differences in the profile magnitude when the system was outside and inside the magnet and less than 1% differences with the gradient coils on and off. The central axis dose rate fluctuated by less than 1% over a 30 second period when outside and inside the MRI. Conclusion: A linaccompatible MR design has been shown to be effective in not perturbing the operation of a commercial linear accelerator. While the accelerator used in the tests was 4MV, there is nothing fundamentally different with the operation of a 6MV unit, implying that the design will enable operation of the proposed clinical unit. Research funding provided by ViewRay, Inc.« less

The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.

1983-09-01

An analysis is presented of the response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric excitation in the presence of an internal resonance of the combination type ω3 ≈ ω2 + ω1, where the ωn are the linear natural frequencies of the systems. In the case of a fundamental resonance of the third mode (i.e., Ω ≈ω 3, where Ω is the frequency of the excitation), one can identify two critical values ζ 1 and ζ 2, where ζ 2 ⩾ ζ 1, of the amplitude F of the excitation. The value F = ζ2 corresponds to the transition from stable to unstable solutions. When F < ζ1, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but the non-linearity limits the motion to a finite amplitude steady state. The amplitude of the third mode, which is directly excited, is independent of F, whereas the amplitudes of the first and second modes, which are indirectly excited through the internal resonance, are functions of F. When ζ1 ⩽ F ⩽ ζ2, the motion decays or achieves a finite amplitude steady state depending on the initial conditions according to the non-linear theory, whereas it decays to zero according to the linear theory. This is an example of subcritical instability. In the case of a fundamental resonance of either the first or second mode, the trivial response is the only possible steady state. When F ⩽ ζ2, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but it is aperiodic according to the non-linear theory. Experiments are being planned to check these theoretical results.

Array of Hall Effect Sensors for Linear Positioning of a Magnet Independently of Its Strength Variation. A Case Study: Monitoring Milk Yield during Milking in Goats

PubMed Central

García-Diego, Fernando-Juan; Sánchez-Quinche, Angel; Merello, Paloma; Beltrán, Pedro; Peris, Cristófol

2013-01-01

In this study we propose an electronic system for linear positioning of a magnet independent of its modulus, which could vary because of aging, different fabrication process, etc. The system comprises a linear array of 24 Hall Effect sensors of proportional response. The data from all sensors are subject to a pretreatment (normalization) by row (position) making them independent on the temporary variation of its magnetic field strength. We analyze the particular case of the individual flow in milking of goats. The multiple regression analysis allowed us to calibrate the electronic system with a percentage of explanation R2 = 99.96%. In our case, the uncertainty in the linear position of the magnet is 0.51 mm that represents 0.019 L of goat milk. The test in farm compared the results obtained by direct reading of the volume with those obtained by the proposed electronic calibrated system, achieving a percentage of explanation of 99.05%. PMID:23793020

The Learning Reconstruction of Particle System and Linear Momentum Conservation in Introductory Physics Course

NASA Astrophysics Data System (ADS)

Karim, S.; Saepuzaman, D.; Sriyansyah, S. P.

2016-08-01

This study is initiated by low achievement of prospective teachers in understanding concepts in introductory physics course. In this case, a problem has been identified that students cannot develop their thinking skills required for building physics concepts. Therefore, this study will reconstruct a learning process, emphasizing a physics concept building. The outcome will design physics lesson plans for the concepts of particle system as well as linear momentum conservation. A descriptive analysis method will be used in order to investigate the process of learning reconstruction carried out by students. In this process, the students’ conceptual understanding will be evaluated using essay tests for concepts of particle system and linear momentum conservation. The result shows that the learning reconstruction has successfully supported the students’ understanding of physics concept.

Synthesis procedure for linear time-varying feedback systems with large parameter ignorance

NASA Technical Reports Server (NTRS)

Mcdonald, T. E., Jr.

1972-01-01

The development of synthesis procedures for linear time-varying feedback systems is considered. It is assumed that the plant can be described by linear differential equations with time-varying coefficients; however, ignorance is associated with the plant in that only the range of the time-variations are known instead of exact functional relationships. As a result of this plant ignorance the use of time-varying compensation is ineffective so that only time-invariant compensation is employed. In addition, there is a noise source at the plant output which feeds noise through the feedback elements to the plant input. Because of this noise source the gain of the feedback elements must be as small as possible. No attempt is made to develop a stability criterion for time-varying systems in this work.

Analysis of periodically excited non-linear systems by a parametric continuation technique

NASA Astrophysics Data System (ADS)

Padmanabhan, C.; Singh, R.

1995-07-01

The dynamic behavior and frequency response of harmonically excited piecewise linear and/or non-linear systems has been the subject of several recent investigations. Most of the prior studies employed harmonic balance or Galerkin schemes, piecewise linear techniques, analog simulation and/or direct numerical integration (digital simulation). Such techniques are somewhat limited in their ability to predict all of the dynamic characteristics, including bifurcations leading to the occurrence of unstable, subharmonic, quasi-periodic and/or chaotic solutions. To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response. Parameter regions exhibiting bifurcations to harmonic, subharmonic or quasi-periodic solutions are obtained quite efficiently and systematically. Unlike other techniques, the proposed scheme can follow period-doubling bifurcations, and with some modifications obtain stable quasi-periodic solutions and their bifurcations. This knowledge is essential in establishing conditions for the occurrence of chaotic oscillations in any non-linear system. The method is first validated through the Duffing oscillator example, the solutions to which are also obtained by conventional one-term harmonic balance and perturbation methods. The second example deals with a clearance non-linearity problem for both harmonic and periodic excitations. Predictions from the proposed scheme match well with available analog simulation data as well as with multi-term harmonic balance results. Potential savings in computational time over direct numerical integration is demonstrated for some of the example cases. Also, this work has filled in some of the solution regimes for an impact pair, which were missed previously in the literature. Finally, one main limitation associated with the proposed procedure is discussed.

Effect of linear energy on the properties of an AL alloy in DPMIG welding

NASA Astrophysics Data System (ADS)

Liao, Tianfa; Jin, Li; Xue, Jiaxiang

2018-01-01

The effect of different linear energy parameters on the DPMIG welding performance of AA1060 aluminium alloy is studied in this paper. The stability of the welding process is verified with a Labview electrical signal acquisition system, and the microstructure and tensile properties of the welded joint are studied via optical microscopy, scanning electron microscopy and electrical tensile tests. The test results show that the welding process for the DPMIG methods stable and that the weld beads appear as scales. Tensile strength results indicate that, with increasing linear energy, the tensile strength first increases and then decreases. The tensile strength of the joint is maximized when the linear energy is 120.5 J / mm-1.

Effect of environmental torques on short-term attitude prediction for a rolling-wheel spacecraft in a sun-synchronous orbit

NASA Technical Reports Server (NTRS)

Hodge, W. F.

1972-01-01

A numerical evaluation and an analysis of the effects of environmental disturbance torques on the attitude of a hexagonal cylinder rolling wheel spacecraft were performed. The resulting perturbations caused by five such torques were found to be very small and exhibited linearity such that linearized equations of motion yielded accurate results over short periods and the separate perturbations contributed by each torque were additive in the sense of superposition. Linearity of the torque perturbations was not affected by moderate system design changes and persisted for torque-to-angular momentum ratios up to 100 times the nominal expected value. As these conditions include many possible applications, similar linear behavior might be anticipated for other rolling-wheel spacecraft.

Axial calibration methods of piezoelectric load sharing dynamometer

NASA Astrophysics Data System (ADS)

Zhang, Jun; Chang, Qingbing; Ren, Zongjin; Shao, Jun; Wang, Xinlei; Tian, Yu

2018-06-01

The relationship between input and output of load sharing dynamometer is seriously non-linear in different loading points of a plane, so it's significant for accutately measuring force to precisely calibrate the non-linear relationship. In this paper, firstly, based on piezoelectric load sharing dynamometer, calibration experiments of different loading points are performed in a plane. And then load sharing testing system is respectively calibrated based on BP algorithm and ELM (Extreme Learning Machine) algorithm. Finally, the results show that the calibration result of ELM is better than BP for calibrating the non-linear relationship between input and output of loading sharing dynamometer in the different loading points of a plane, which verifies that ELM algorithm is feasible in solving force non-linear measurement problem.

Non-linear vibrating systems excited by a nonideal energy source with a large slope characteristic

NASA Astrophysics Data System (ADS)

González-Carbajal, Javier; Domínguez, Jaime

2017-11-01

This paper revisits the problem of an unbalanced motor attached to a fixed frame by means of a nonlinear spring and a linear damper. The excitation provided by the motor is, in general, nonideal, which means it is affected by the vibratory response. Since the system behaviour is highly dependent on the order of magnitude of the motor characteristic slope, the case of large slope is considered herein. Some Perturbation Methods are applied to the system of equations, which allows transforming the original 4D system into a much simpler 2D system. The fixed points of this reduced system and their stability are carefully studied. We find the existence of a Hopf bifurcation which, to the authors' knowledge, has not been addressed before in the literature. These analytical results are supported by numerical simulations. We also compare our approach and results with those published by other authors.

An analysis of a nonlinear instability in the implementation of a VTOL control system

NASA Technical Reports Server (NTRS)

Weber, J. M.

1982-01-01

The contributions to nonlinear behavior and unstable response of the model following yaw control system of a VTOL aircraft during hover were determined. The system was designed as a state rate feedback implicit model follower that provided yaw rate command/heading hold capability and used combined full authority parallel and limited authority series servo actuators to generate an input to the yaw reaction control system of the aircraft. Both linear and nonlinear system models, as well as describing function linearization techniques were used to determine the influence on the control system instability of input magnitude and bandwidth, series servo authority, and system bandwidth. Results of the analysis describe stability boundaries as a function of these system design characteristics.

An Alternative Derivation of the Energy Levels of the "Particle on a Ring" System

NASA Astrophysics Data System (ADS)

Vincent, Alan

1996-10-01

All acceptable wave functions must be continuous mathematical functions. This criterion limits the acceptable functions for a particle in a linear 1-dimensional box to sine functions. If, however, the linear box is bent round into a ring, acceptable wave functions are those which are continuous at the 'join'. On this model some acceptable linear functions become unacceptable for the ring and some unacceptable cosine functions become acceptable. This approach can be used to produce a straightforward derivation of the energy levels and wave functions of the particle on a ring. These simple wave mechanical systems can be used as models of linear and cyclic delocalised systems such as conjugated hydrocarbons or the benzene ring. The promotion energy of an electron can then be used to calculate the wavelength of absorption of uv light. The simple model gives results of the correct order of magnitude and shows that, as the chain length increases, the uv maximum moves to longer wavelengths, as found experimentally.

A novel sensor for two-degree-of-freedom motion measurement of linear nanopositioning stage using knife edge displacement sensing technique

NASA Astrophysics Data System (ADS)

Zolfaghari, Abolfazl; Jeon, Seongkyul; Stepanick, Christopher K.; Lee, ChaBum

2017-06-01

This paper presents a novel method for measuring two-degree-of-freedom (DOF) motion of flexure-based nanopositioning systems based on optical knife-edge sensing (OKES) technology, which utilizes the interference of two superimposed waves: a geometrical wave from the primary source of light and a boundary diffraction wave from the secondary source. This technique allows for two-DOF motion measurement of the linear and pitch motions of nanopositioning systems. Two capacitive sensors (CSs) are used for a baseline comparison with the proposed sensor by simultaneously measuring the motions of the nanopositioning system. The experimental results show that the proposed sensor closely agrees with the fundamental linear motion of the CS. However, the two-DOF OKES technology was shown to be approximately three times more sensitive to the pitch motion than the CS. The discrepancy in the two sensor outputs is discussed in terms of measuring principle, linearity, bandwidth, control effectiveness, and resolution.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Analogue and digital linear modulation techniques for mobile satellite

NASA Technical Reports Server (NTRS)

Whitmarsh, W. J.; Bateman, A.; Mcgeehan, J. P.

1990-01-01

The choice of modulation format for a mobile satellite service is complex. The subjective performance is summarized of candidate schemes and voice coder technologies. It is shown that good performance can be achieved with both analogue and digital voice systems, although the analogue system gives superior performance in fading. The results highlight the need for flexibility in the choice of signaling format. Linear transceiver technology capable of using many forms of narrowband modulation is described.

Full-field fan-beam x-ray fluorescence computed tomography system design with linear-array detectors and pinhole collimation: a rapid Monte Carlo study

NASA Astrophysics Data System (ADS)

Zhang, Siyuan; Li, Liang; Li, Ruizhe; Chen, Zhiqiang

2017-11-01

We present the design concept and initial simulations for a polychromatic full-field fan-beam x-ray fluorescence computed tomography (XFCT) device with pinhole collimators and linear-array photon counting detectors. The phantom is irradiated by a fan-beam polychromatic x-ray source filtered by copper. Fluorescent photons are stimulated and then collected by two linear-array photon counting detectors with pinhole collimators. The Compton scatter correction and the attenuation correction are applied in the data processing, and the maximum-likelihood expectation maximization algorithm is applied for the image reconstruction of XFCT. The physical modeling of the XFCT imaging system was described, and a set of rapid Monte Carlo simulations was carried out to examine the feasibility and sensitivity of the XFCT system. Different concentrations of gadolinium (Gd) and gold (Au) solutions were used as contrast agents in simulations. Results show that 0.04% of Gd and 0.065% of Au can be well reconstructed with the full scan time set at 6 min. Compared with using the XFCT system with a pencil-beam source or a single-pixel detector, using a full-field fan-beam XFCT device with linear-array detectors results in significant scanning time reduction and may satisfy requirements of rapid imaging, such as in vivo imaging experiments.

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.

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

NASA Astrophysics Data System (ADS)

Lu, Yanrong; Liao, Fucheng; Deng, Jiamei; Liu, Huiyang

2017-09-01

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Elastic robot control - Nonlinear inversion and linear stabilization

NASA Technical Reports Server (NTRS)

Singh, S. N.; Schy, A. A.

1986-01-01

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

Renormalization Group for nonlinear oscillators in the absence of linear restoring force

NASA Astrophysics Data System (ADS)

Sarkar, A.; Bhattacharjee, J. K.

2010-09-01

Perturbative Renormalization Group (RG) has been very useful in probing periodic orbits in two-dimensional dynamical systems (Sarkar A., Bhattacharjee J. K., Chakraborty S. and Banerjee D., arXiv:1005.2858v1 (2010)). The method relies on finding a linear center, around which perturbation analysis is done. However it is not obvious as to how systems devoid of any linear terms may be approached using this method. We propose here how RG can be done even in the absence of linear terms. We successfully apply the method to extract correct results for a variant of the second-order Riccati equation. In this variant the periodic orbit disappears as a parameter is varied. Our RG captures this disappearance correctly. We have also applied the technique successfully on the force-free Van der Pol-Duffing oscillator.

SU-E-T-186: Cloud-Based Quality Assurance Application for Linear Accelerator Commissioning

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

Rogers, J

2015-06-15

Purpose: To identify anomalies and safety issues during data collection and modeling for treatment planning systems Methods: A cloud-based quality assurance system (AQUIRE - Automated QUalIty REassurance) has been developed to allow the uploading and analysis of beam data aquired during the treatment planning system commissioning process. In addition to comparing and aggregating measured data, tools have also been developed to extract dose from the treatment planning system for end-to-end testing. A gamma index is perfomed on the data to give a dose difference and distance-to-agreement for validation that a beam model is generating plans consistent with the beam datamore » collection. Results: Over 20 linear accelerators have been commissioning using this platform, and a variety of errors and potential saftey issues have been caught through the validation process. For example, the gamma index of 2% dose, 2mm DTA is quite sufficient to see curves not corrected for effective point of measurement. Also, data imported into the database is analyzed against an aggregate of similar linear accelerators to show data points that are outliers. The resulting curves in the database exhibit a very small standard deviation and imply that a preconfigured beam model based on aggregated linear accelerators will be sufficient in most cases. Conclusion: With the use of this new platform for beam data commissioning, errors in beam data collection and treatment planning system modeling are greatly reduced. With the reduction in errors during acquisition, the resulting beam models are quite similar, suggesting that a common beam model may be possible in the future. Development is ongoing to create routine quality assurance tools to compare back to the beam data acquired during commissioning. I am a medical physicist for Alzyen Medical Physics, and perform commissioning services.« less

Circuit transients due to negative bias arcs-II. [on solar cell power systems in low earth orbit

NASA Technical Reports Server (NTRS)

Metz, R. N.

1986-01-01

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

Nonlinear aeroacoustic characterization of Helmholtz resonators with a local-linear neuro-fuzzy network model

NASA Astrophysics Data System (ADS)

Förner, K.; Polifke, W.

2017-10-01

The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.

Non-Linear Dynamics of Saturn's Rings

NASA Astrophysics Data System (ADS)

Esposito, L. W.

2016-12-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; this requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries determines the power law index, using results of numerical simulations in the tidal environment. Aggregates can explain many dynamic aspects of the rings and can renew rings by shielding and recycling the material within them, depending on how long the mass is sequestered. We can ask: Are Saturn's rings a chaotic non-linear driven system?

Non-Linear Dynamics of Saturn’s Rings

NASA Astrophysics Data System (ADS)

Esposito, Larry W.

2015-11-01

Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects of the rings and can renew rings by shielding and recycling the material within them, depending on how long the mass is sequestered. We can ask: Are Saturn’s rings a chaotic non-linear driven system?

A class of stabilizing controllers for flexible multibody systems

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.; Kelkar, Atul G.; Maghami, Peiman G.

1995-01-01

The problem of controlling a class of nonlinear multibody flexible space systems consisting of a flexible central body to which a number of articulated appendages are attached is considered. Collocated actuators and sensors are assumed, and global asymptotic stability of such systems is established under a nonlinear dissipative control law. The stability is shown to be robust to unmodeled dynamics and parametric uncertainties. For a special case in which the attitude motion of the central body is small, the system, although still nonlinear, is shown to be stabilized by linear dissipative control laws. Two types of linear controllers are considered: static dissipative (constant gain) and dynamic dissipative. The static dissipative control law is also shown to provide robust stability in the presence of certain classes of actuator and sensor nonlinearities and actuator dynamics. The results obtained for this special case can also be readily applied for controlling single-body linear flexible space structures. For this case, a synthesis technique for the design of a suboptimal dynamic dissipative controller is also presented. The results obtained in this paper are applicable to a broad class of multibody and single-body systems such as flexible multilink manipulators, multipayload space platforms, and space antennas. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

Time Delay Estimation

DTIC Science & Technology

1976-04-09

of the signal and noise remain HH ***^-^*--~ 53 h, to r(Mc) h2(r» r(we) Figure 3-2 Sy&toetric Impulse Response for Two FIR Linear Phase...Inputs x,y and Outputs x.j. , 15 2-2 Linear System with Impulse Response h("r) 23 2-3 Model of Error Resulting from Linearly Filtering x(t) to...Corrupted with Additive Noise 42 2-6 Model of Directional Signal Corrupted with Additive Noise and Processed .... 45 2-7 Source Driving Two

Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces

NASA Astrophysics Data System (ADS)

Licht, Christian; Tran Thu Ha

2005-02-01

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity. To cite this article: C. Licht, Tran Thu Ha, C. R. Mecanique 333 (2005).

Linear and nonlinear subspace analysis of hand movements during grasping.

PubMed

Cui, Phil Hengjun; Visell, Yon

2014-01-01

This study investigated nonlinear patterns of coordination, or synergies, underlying whole-hand grasping kinematics. Prior research has shed considerable light on roles played by such coordinated degrees-of-freedom (DOF), illuminating how motor control is facilitated by structural and functional specializations in the brain, peripheral nervous system, and musculoskeletal system. However, existing analyses suppose that the patterns of coordination can be captured by means of linear analyses, as linear combinations of nominally independent DOF. In contrast, hand kinematics is itself highly nonlinear in nature. To address this discrepancy, we sought to to determine whether nonlinear synergies might serve to more accurately and efficiently explain human grasping kinematics than is possible with linear analyses. We analyzed motion capture data acquired from the hands of individuals as they grasped an array of common objects, using four of the most widely used linear and nonlinear dimensionality reduction algorithms. We compared the results using a recently developed algorithm-agnostic quality measure, which enabled us to assess the quality of the dimensional reductions that resulted by assessing the extent to which local neighborhood information in the data was preserved. Although qualitative inspection of this data suggested that nonlinear correlations between kinematic variables were present, we found that linear modeling, in the form of Principle Components Analysis, could perform better than any of the nonlinear techniques we applied.

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

DOE PAGES

Hager, Robert; Yoon, E. S.; Ku, S.; ...

2016-04-04

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computingmore » systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.« less

Directed electromagnetic wave propagation in 1D metamaterial: Projecting operators method

NASA Astrophysics Data System (ADS)

Ampilogov, Dmitrii; Leble, Sergey

2016-07-01

We consider a boundary problem for 1D electrodynamics modeling of a pulse propagation in a metamaterial medium. We build and apply projecting operators to a Maxwell system in time domain that allows to split the linear propagation problem to directed waves for a material relations with general dispersion. Matrix elements of the projectors act as convolution integral operators. For a weak nonlinearity we generalize the linear results still for arbitrary dispersion and derive the system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the popular metamaterial model with Drude formula for both permittivity and permeability coefficients. We also discuss and investigate stationary solutions of the system related to some boundary regimes.

Preliminary results of Linear Induction Accelerator LIA-200

NASA Astrophysics Data System (ADS)

Sharma, Archana; Senthil, K.; Praveen Kumar, D. D.; Mitra, S.; Sharma, V.; Patel, A.; Sharma, D. K.; Rehim, R.; Kolge, T. S.; Saroj, P. C.; Acharya, S.; Amitava, Roy; Rakhee, M.; Nagesh, K. V.; Chakravarthy, D. P.

2010-05-01

Repetitive Pulsed Power Technology is being developed keeping in mind the potential applications of this technology in material modifications, disinfections of water, timber, and food pasteurization etc. BARC has indigenously developed a Linear Induction Accelerator (LIA-200) rated for 200 kV, 4 kA, 100 ns, 10 Hz. The satisfactory performance of all the sub-systems including solid state power modulator, amorphous core based pulsed transformers, magnetic switches, water capacitors, water pulse- forming line, induction adder and field-emission diode have been demonstrated. This paper presents some design details and operational results of this pulsed power system. It also highlights the need for further research and development to build reliable and economic high-average power systems for industrial applications.

Investigation of absolute and relative response for three different liquid chromatography/tandem mass spectrometry systems; the impact of ionization and detection saturation.

PubMed

Nilsson, Lars B; Skansen, Patrik

2012-06-30

The investigations in this article were triggered by two observations in the laboratory; for some liquid chromatography/tandem mass spectrometry (LC/MS/MS) systems it was possible to obtain linear calibration curves for extreme concentration ranges and for some systems seemingly linear calibration curves gave good accuracy at low concentrations only when using a quadratic regression function. The absolute and relative responses were tested for three different LC/MS/MS systems by injecting solutions of a model compound and a stable isotope labeled internal standard. The analyte concentration range for the solutions was 0.00391 to 500 μM (128,000×), giving overload of the chromatographic column at the highest concentrations. The stable isotope labeled internal standard concentration was 0.667 μM in all samples. The absolute response per concentration unit decreased rapidly as higher concentrations were injected. The relative response, the ratio for the analyte peak area to the internal standard peak area, per concentration unit was calculated. For system 1, the ionization process was found to limit the response and the relative response per concentration unit was constant. For systems 2 and 3, the ion detection process was the limiting factor resulting in decreasing relative response at increasing concentrations. For systems behaving like system 1, simple linear regression can be used for any concentration range while, for systems behaving like systems 2 and 3, non-linear regression is recommended for all concentration ranges. Another consequence is that the ionization capacity limited systems will be insensitive to matrix ion suppression when an ideal internal standard is used while the detection capacity limited systems are at risk of giving erroneous results at high concentrations if the matrix ion suppression varies for different samples in a run. Copyright © 2012 John Wiley & Sons, Ltd.

An implicit boundary integral method for computing electric potential of macromolecules in solvent

NASA Astrophysics Data System (ADS)

Zhong, Yimin; Ren, Kui; Tsai, Richard

2018-04-01

A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equation that arises in mathematical models for the electrostatics of molecules in solvent. The proposed method uses an implicit boundary integral formulation to derive a linear system defined on Cartesian nodes in a narrowband surrounding the closed surface that separates the molecule and the solvent. The needed implicit surface is constructed from the given atomic description of the molecules, by a sequence of standard level set algorithms. A fast multipole method is applied to accelerate the solution of the linear system. A few numerical studies involving some standard test cases are presented and compared to other existing results.

Controller design approach based on linear programming.

PubMed

Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa

2013-11-01

This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. © 2013 ISA. Published by ISA. All rights reserved.

Design and analysis of linear oscillatory single-phase permanent magnet generator for free-piston stirling engine systems

NASA Astrophysics Data System (ADS)

Kim, Jeong-Man; Choi, Jang-Young; Lee, Kyu-Seok; Lee, Sung-Ho

2017-05-01

This study focuses on the design and analysis of a linear oscillatory single-phase permanent magnet generator for free-piston stirling engine (FPSE) systems. In order to implement the design of linear oscillatory generator (LOG) for suitable FPSEs, we conducted electromagnetic analysis of LOGs with varying design parameters. Then, detent force analysis was conducted using assisted PM. Using the assisted PM gave us the advantage of using mechanical strength by detent force. To improve the efficiency, we conducted characteristic analysis of eddy-current loss with respect to the PM segment. Finally, the experimental result was analyzed to confirm the prediction of the FEA.

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R.; Sridhar, B.

1976-01-01

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

Linear active disturbance rejection control of underactuated systems: the case of the Furuta pendulum.

PubMed

Ramírez-Neria, M; Sira-Ramírez, H; Garrido-Moctezuma, R; Luviano-Juárez, A

2014-07-01

An Active Disturbance Rejection Control (ADRC) scheme is proposed for a trajectory tracking problem defined on a nonfeedback linearizable Furuta Pendulum example. A desired rest to rest angular position reference trajectory is to be tracked by the horizontal arm while the unactuated vertical pendulum arm stays around its unstable vertical position without falling down during the entire maneuver and long after it concludes. A linear observer-based linear controller of the ADRC type is designed on the basis of the flat tangent linearization of the system around an arbitrary equilibrium. The advantageous combination of flatness and the ADRC method makes it possible to on-line estimate and cancels the undesirable effects of the higher order nonlinearities disregarded by the linearization. These effects are triggered by fast horizontal arm tracking maneuvers driving the pendulum substantially away from the initial equilibrium point. Convincing experimental results, including a comparative test with a sliding mode controller, are presented. © 2013 ISA. Published by ISA. All rights reserved.

Improving biomedical information retrieval by linear combinations of different query expansion techniques.

PubMed

Abdulla, Ahmed AbdoAziz Ahmed; Lin, Hongfei; Xu, Bo; Banbhrani, Santosh Kumar

2016-07-25

Biomedical literature retrieval is becoming increasingly complex, and there is a fundamental need for advanced information retrieval systems. Information Retrieval (IR) programs scour unstructured materials such as text documents in large reserves of data that are usually stored on computers. IR is related to the representation, storage, and organization of information items, as well as to access. In IR one of the main problems is to determine which documents are relevant and which are not to the user's needs. Under the current regime, users cannot precisely construct queries in an accurate way to retrieve particular pieces of data from large reserves of data. Basic information retrieval systems are producing low-quality search results. In our proposed system for this paper we present a new technique to refine Information Retrieval searches to better represent the user's information need in order to enhance the performance of information retrieval by using different query expansion techniques and apply a linear combinations between them, where the combinations was linearly between two expansion results at one time. Query expansions expand the search query, for example, by finding synonyms and reweighting original terms. They provide significantly more focused, particularized search results than do basic search queries. The retrieval performance is measured by some variants of MAP (Mean Average Precision) and according to our experimental results, the combination of best results of query expansion is enhanced the retrieved documents and outperforms our baseline by 21.06 %, even it outperforms a previous study by 7.12 %. We propose several query expansion techniques and their combinations (linearly) to make user queries more cognizable to search engines and to produce higher-quality search results.

Real-Time Parameter Estimation Method Applied to a MIMO Process and its Comparison with an Offline Identification Method

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

Kaplanoglu, Erkan; Safak, Koray K.; Varol, H. Selcuk

2009-01-12

An experiment based method is proposed for parameter estimation of a class of linear multivariable systems. The method was applied to a pressure-level control process. Experimental time domain input/output data was utilized in a gray-box modeling approach. Prior knowledge of the form of the system transfer function matrix elements is assumed to be known. Continuous-time system transfer function matrix parameters were estimated in real-time by the least-squares method. Simulation results of experimentally determined system transfer function matrix compare very well with the experimental results. For comparison and as an alternative to the proposed real-time estimation method, we also implemented anmore » offline identification method using artificial neural networks and obtained fairly good results. The proposed methods can be implemented conveniently on a desktop PC equipped with a data acquisition board for parameter estimation of moderately complex linear multivariable systems.« less

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.

Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching

NASA Technical Reports Server (NTRS)

Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven

2004-01-01

This paper analyzes the stability of hierarchical jump linear systems where the supervisor is driven by a Markovian stochastic process and by the values of the supervised jump linear system s states. The stability framework for this class of systems is developed over infinite and finite time horizons. The framework is then used to derive sufficient stability conditions for a specific class of hybrid jump linear systems with performance supervision. New sufficient stochastic stability conditions for discrete-time jump linear systems are also presented.

An efficient method for model refinement in diffuse optical tomography

NASA Astrophysics Data System (ADS)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

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.

Homogenizing microwave illumination in thermoacoustic tomography by a linear-to-circular polarizer based on frequency selective surfaces

NASA Astrophysics Data System (ADS)

He, Yu; Shen, Yuecheng; Feng, Xiaohua; Liu, Changjun; Wang, Lihong V.

2017-08-01

A circularly polarized antenna, providing more homogeneous illumination compared to a linearly polarized antenna, is more suitable for microwave induced thermoacoustic tomography (TAT). The conventional realization of a circular polarization is by using a helical antenna, but it suffers from low efficiency, low power capacity, and limited aperture in TAT systems. Here, we report an implementation of a circularly polarized illumination method in TAT by inserting a single-layer linear-to-circular polarizer based on frequency selective surfaces between a pyramidal horn antenna and an imaging object. The performance of the proposed method was validated by both simulations and experimental imaging of a breast tumor phantom. The results showed that a circular polarization was achieved, and the resultant thermoacoustic signal-to-noise was twice greater than that in the helical antenna case. The proposed method is more desirable in a waveguide-based TAT system than the conventional method.

Burgers approximation for two-dimensional flow past an ellipse

NASA Technical Reports Server (NTRS)

Dorrepaal, J. M.

1982-01-01

A linearization of the Navier-Stokes equation due to Burgers in which vorticity is transported by the velocity field corresponding to continuous potential flow is examined. The governing equations are solved exactly for the two dimensional steady flow past an ellipse of arbitrary aspect ratio. The requirement of no slip along the surface of the ellipse results in an infinite algebraic system of linear equations for coefficients appearing in the solution. The system is truncated at a point which gives reliable results for Reynolds numbers R in the range 0 R 5. Predictions of the Burgers approximation regarding separation, drag and boundary layer behavior are investigated. In particular, Burgers linearization gives drag coefficients which are closer to observed experimental values than those obtained from Oseen's approximation. In the special case of flow past a circular cylinder, Burgers approximation predicts a boundary layer whose thickness is roughly proportional to R-1/2.

Some Properties and Stability Results for Sector-Bounded LTI Systems

NASA Technical Reports Server (NTRS)

Gupta, Sandeep; Joshi, Suresh M.

1994-01-01

This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector (n, b) in terms of linear matrix inequalities in its state-space realization matrices, which represents a generalization of similar conditions for bounded H(sub infinity)-norm systems. Further, a weaker definition of LTI systems strictly inside closed sector (a, b) is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems.

Structure of 1-alkyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide ionic liquids with linear, branched, and cyclic alkyl groups.

PubMed

Kashyap, Hemant K; Santos, Cherry S; Murthy, N Sanjeeva; Hettige, Jeevapani J; Kerr, Kijana; Ramati, Sharon; Gwon, JinHee; Gohdo, Masao; Lall-Ramnarine, Sharon I; Wishart, James F; Margulis, Claudio J; Castner, Edward W

2013-12-12

X-ray scattering and molecular dynamics simulations have been carried out to investigate structural differences and similarities in the condensed phase between pyrrolidinium-based ionic liquids paired with the bis(trifluoromethylsulfonyl)amide (NTf2(-)) anion where the cationic tail is linear, branched, or cyclic. This is important in light of the charge and polarity type alternations that have recently been shown to be present in the case of liquids with cations of moderately long linear tails. For this study, we have chosen to use the 1-alkyl-1-methylpyrrolidinium, Pyrr(1,n(+)) with n = 5 or 7, as systems with linear tails, 1-(2-ethylhexyl)-1-methylpyrrolidinium, Pyrr(1,EtHx(+)), as a system with a branched tail, and 1-(cyclohexylmethyl)-1-methylpyrrolidinium, Pyrr(1,ChxMe(+)), as a system with a cyclic tail. We put these results into context by comparing these data with recently published results for the Pyrr(1,n(+))/NTf2(-) ionic liquids with n = 4, 6, 8, and 10.1,2 General methods for interpreting the structure function S(q) in terms of q-dependent natural partitionings are described. This allows for an in-depth analysis of the scattering data based on molecular dynamics (MD) trajectories that highlight the effect of modifying the cationic tail.

The cross-over to magnetostrophic convection in planetary dynamo systems

PubMed Central

King, E. M.

2017-01-01

Global scale magnetostrophic balance, in which Lorentz and Coriolis forces comprise the leading-order force balance, has long been thought to describe the natural state of planetary dynamo systems. This argument arises from consideration of the linear theory of rotating magnetoconvection. Here we test this long-held tenet by directly comparing linear predictions against dynamo modelling results. This comparison shows that dynamo modelling results are not typically in the global magnetostrophic state predicted by linear theory. Then, in order to estimate at what scale (if any) magnetostrophic balance will arise in nonlinear dynamo systems, we carry out a simple scaling analysis of the Elsasser number Λ, yielding an improved estimate of the ratio of Lorentz and Coriolis forces. From this, we deduce that there is a magnetostrophic cross-over length scale, LX≈(Λo2/Rmo)D, where Λo is the linear (or traditional) Elsasser number, Rmo is the system scale magnetic Reynolds number and D is the length scale of the system. On scales well above LX, magnetostrophic convection dynamics should not be possible. Only on scales smaller than LX should it be possible for the convective behaviours to follow the predictions for the magnetostrophic branch of convection. Because LX is significantly smaller than the system scale in most dynamo models, their large-scale flows should be quasi-geostrophic, as is confirmed in many dynamo simulations. Estimating Λo≃1 and Rmo≃103 in Earth’s core, the cross-over scale is approximately 1/1000 that of the system scale, suggesting that magnetostrophic convection dynamics exists in the core only on small scales below those that can be characterized by geomagnetic observations. PMID:28413338

The cross-over to magnetostrophic convection in planetary dynamo systems.

PubMed

Aurnou, J M; King, E M

2017-03-01

Global scale magnetostrophic balance, in which Lorentz and Coriolis forces comprise the leading-order force balance, has long been thought to describe the natural state of planetary dynamo systems. This argument arises from consideration of the linear theory of rotating magnetoconvection. Here we test this long-held tenet by directly comparing linear predictions against dynamo modelling results. This comparison shows that dynamo modelling results are not typically in the global magnetostrophic state predicted by linear theory. Then, in order to estimate at what scale (if any) magnetostrophic balance will arise in nonlinear dynamo systems, we carry out a simple scaling analysis of the Elsasser number Λ , yielding an improved estimate of the ratio of Lorentz and Coriolis forces. From this, we deduce that there is a magnetostrophic cross-over length scale, [Formula: see text], where Λ o is the linear (or traditional) Elsasser number, Rm o is the system scale magnetic Reynolds number and D is the length scale of the system. On scales well above [Formula: see text], magnetostrophic convection dynamics should not be possible. Only on scales smaller than [Formula: see text] should it be possible for the convective behaviours to follow the predictions for the magnetostrophic branch of convection. Because [Formula: see text] is significantly smaller than the system scale in most dynamo models, their large-scale flows should be quasi-geostrophic, as is confirmed in many dynamo simulations. Estimating Λ o ≃1 and Rm o ≃10 3 in Earth's core, the cross-over scale is approximately 1/1000 that of the system scale, suggesting that magnetostrophic convection dynamics exists in the core only on small scales below those that can be characterized by geomagnetic observations.

Suspension system vibration analysis with regard to variable type ability to smooth road irregularities

NASA Astrophysics Data System (ADS)

Rykov, S. P.; Rykova, O. A.; Koval, V. S.; Makhno, D. E.; Fedotov, K. V.

2018-03-01

The paper aims to analyze vibrations of the dynamic system equivalent of the suspension system with regard to tyre ability to smooth road irregularities. The research is based on static dynamics for linear systems of automated control, methods of correlation, spectral and numerical analysis. Input of new data on the smoothing effect of the pneumatic tyre reflecting changes of a contact area between the wheel and road under vibrations of the suspension makes the system non-linear which requires using numerical analysis methods. Taking into account the variable smoothing ability of the tyre when calculating suspension vibrations, one can approximate calculation and experimental results and improve the constant smoothing ability of the tyre.

A review on prognostic techniques for non-stationary and non-linear rotating systems

NASA Astrophysics Data System (ADS)

Kan, Man Shan; Tan, Andy C. C.; Mathew, Joseph

2015-10-01

The field of prognostics has attracted significant interest from the research community in recent times. Prognostics enables the prediction of failures in machines resulting in benefits to plant operators such as shorter downtimes, higher operation reliability, reduced operations and maintenance cost, and more effective maintenance and logistics planning. Prognostic systems have been successfully deployed for the monitoring of relatively simple rotating machines. However, machines and associated systems today are increasingly complex. As such, there is an urgent need to develop prognostic techniques for such complex systems operating in the real world. This review paper focuses on prognostic techniques that can be applied to rotating machinery operating under non-linear and non-stationary conditions. The general concept of these techniques, the pros and cons of applying these methods, as well as their applications in the research field are discussed. Finally, the opportunities and challenges in implementing prognostic systems and developing effective techniques for monitoring machines operating under non-stationary and non-linear conditions are also discussed.

Field-programmable gate array-controlled sweep velocity-locked laser pulse generator

NASA Astrophysics Data System (ADS)

Chen, Zhen; Hefferman, Gerald; Wei, Tao

2017-05-01

A field-programmable gate array (FPGA)-controlled sweep velocity-locked laser pulse generator (SV-LLPG) design based on an all-digital phase-locked loop (ADPLL) is proposed. A distributed feedback laser with modulated injection current was used as a swept-frequency laser source. An open-loop predistortion modulation waveform was calibrated using a feedback iteration method to initially improve frequency sweep linearity. An ADPLL control system was then implemented using an FPGA to lock the output of a Mach-Zehnder interferometer that was directly proportional to laser sweep velocity to an on-board system clock. Using this system, linearly chirped laser pulses with a sweep bandwidth of 111.16 GHz were demonstrated. Further testing evaluating the sensing utility of the system was conducted. In this test, the SV-LLPG served as the swept laser source of an optical frequency-domain reflectometry system used to interrogate a subterahertz range fiber structure (sub-THz-FS) array. A static strain test was then conducted and linear sensor results were observed.

Experimental Evaluation of the Free Piston Engine - Linear Alternator (FPLA)

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

Leick, Michael T.; Moses, Ronald W.

2015-03-01

This report describes the experimental evaluation of a prototype free piston engine - linear alternator (FPLA) system developed at Sandia National Laboratories. The opposed piston design wa developed to investigate its potential for use in hybrid electric vehicles (HEVs). The system is mechanically simple with two - stroke uniflow scavenging for gas exchange and timed port fuel injection for fuel delivery, i.e. no complex valving. Electrical power is extracted from piston motion through linear alternators wh ich also provide a means for passive piston synchronization through electromagnetic coupling. In an HEV application, this electrical power would be used to chargemore » the batteries. The engine - alternator system was designed, assembled and operated over a 2 - year period at Sandia National Laboratories in Livermore, CA. This report primarily contains a description of the as - built system, modifications to the system to enable better performance, and experimental results from start - up, motoring, and hydrogen combus tion tests.« less

Incremental harmonic balance method for predicting amplitudes of a multi-d.o.f. non-linear wheel shimmy system with combined Coulomb and quadratic damping

NASA Astrophysics Data System (ADS)

Zhou, J. X.; Zhang, L.

2005-01-01

Incremental harmonic balance (IHB) formulations are derived for general multiple degrees of freedom (d.o.f.) non-linear autonomous systems. These formulations are developed for a concerned four-d.o.f. aircraft wheel shimmy system with combined Coulomb and velocity-squared damping. A multi-harmonic analysis is performed and amplitudes of limit cycles are predicted. Within a large range of parametric variations with respect to aircraft taxi velocity, the IHB method can, at a much cheaper cost, give results with high accuracy as compared with numerical results given by a parametric continuation method. In particular, the IHB method avoids the stiff problems emanating from numerical treatment of aircraft wheel shimmy system equations. The development is applicable to other vibration control systems that include commonly used dry friction devices or velocity-squared hydraulic dampers.

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

DOE PAGES

Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; ...

2016-01-25

We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less

Analysis of the faster-than-Nyquist optimal linear multicarrier system

NASA Astrophysics Data System (ADS)

Marquet, Alexandre; Siclet, Cyrille; Roque, Damien

2017-02-01

Faster-than-Nyquist signalization enables a better spectral efficiency at the expense of an increased computational complexity. Regarding multicarrier communications, previous work mainly relied on the study of non-linear systems exploiting coding and/or equalization techniques, with no particular optimization of the linear part of the system. In this article, we analyze the performance of the optimal linear multicarrier system when used together with non-linear receiving structures (iterative decoding and direct feedback equalization), or in a standalone fashion. We also investigate the limits of the normality assumption of the interference, used for implementing such non-linear systems. The use of this optimal linear system leads to a closed-form expression of the bit-error probability that can be used to predict the performance and help the design of coded systems. Our work also highlights the great performance/complexity trade-off offered by decision feedback equalization in a faster-than-Nyquist context. xml:lang="fr"

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE PAGES

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

2015-12-01

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

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

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Failure detection and identification

NASA Technical Reports Server (NTRS)

Massoumnia, Mohammad-Ali; Verghese, George C.; Willsky, Alan S.

1989-01-01

Using the geometric concept of an unobservability subspace, a solution is given to the problem of detecting and identifying control system component failures in linear, time-invariant systems. Conditions are developed for the existence of a causal, linear, time-invariant processor that can detect and uniquely identify a component failure, first for the case where components can fail simultaneously, and then for the case where they fail only one at a time. Explicit design algorithms are provided when these conditions are satisfied. In addition to time-domain solvability conditions, frequency-domain interpretations of the results are given, and connections are drawn with results already available in the literature.

LMI-based adaptive reliable H∞ static output feedback control against switched actuator failures

NASA Astrophysics Data System (ADS)

An, Liwei; Zhai, Ding; Dong, Jiuxiang; Zhang, Qingling

2017-08-01

This paper investigates the H∞ static output feedback (SOF) control problem for switched linear system under arbitrary switching, where the actuator failure models are considered to depend on switching signal. An active reliable control scheme is developed by combination of linear matrix inequality (LMI) method and adaptive mechanism. First, by exploiting variable substitution and Finsler's lemma, new LMI conditions are given for designing the SOF controller. Compared to the existing results, the proposed design conditions are more relaxed and can be applied to a wider class of no-fault linear systems. Then a novel adaptive mechanism is established, where the inverses of switched failure scaling factors are estimated online to accommodate the effects of actuator failure on systems. Two main difficulties arise: first is how to design the switched adaptive laws to prevent the missing of estimating information due to switching; second is how to construct a common Lyapunov function based on a switched estimate error term. It is shown that the new method can give less conservative results than that for the traditional control design with fixed gain matrices. Finally, simulation results on the HiMAT aircraft are given to show the effectiveness of the proposed approaches.

Foundation stiffness in the linear modeling of wind turbines

NASA Astrophysics Data System (ADS)

Chiang, Chih-Hung; Yu, Chih-Peng; Chen, Yan-Hao; Lai, Jiunnren; Hsu, Keng-Tsang; Cheng, Chia-Chi

2017-04-01

Effects of foundation stiffness on the linear vibrations of wind turbine systems are of concerns for both planning and construction of wind turbine systems. Current study performed numerical modeling for such a problem using linear spectral finite elements. The effects of foundation stiffness were investigated for various combinations of shear wave velocity of soil, size of tower base plate, and pile length. Multiple piles are also included in the models such that the foundation stiffness can be analyzed more realistically. The results indicate that the shear wave velocity of soil and the size of tower base plate have notable effects on the dominant frequency of the turbine-tower system. The larger the lateral dimension, the stiffer the foundation. Large pile cap and multiple spaced piles result in higher stiffness than small pile cap and a mono-pile. The lateral stiffness of a mono-pile mainly depends on the shear wave velocity of soil with the exception for a very short pile that the end constraints may affect the lateral vibration of the superstructure. Effective pile length may be determined by comparing the simulation results of the frictional pile to those of the end-bearing pile.

Predictive IP controller for robust position control of linear servo system.

PubMed

Lu, Shaowu; Zhou, Fengxing; Ma, Yajie; Tang, Xiaoqi

2016-07-01

Position control is a typical application of linear servo system. In this paper, to reduce the system overshoot, an integral plus proportional (IP) controller is used in the position control implementation. To further improve the control performance, a gain-tuning IP controller based on a generalized predictive control (GPC) law is proposed. Firstly, to represent the dynamics of the position loop, a second-order linear model is used and its model parameters are estimated on-line by using a recursive least squares method. Secondly, based on the GPC law, an optimal control sequence is obtained by using receding horizon, then directly supplies the IP controller with the corresponding control parameters in the real operations. Finally, simulation and experimental results are presented to show the efficiency of proposed scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Electron-Phonon Systems on a Universal Quantum Computer

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

Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James

We present an algorithm that extends existing quantum algorithms forsimulating fermion systems in quantum chemistry and condensed matter physics toinclude phonons. The phonon degrees of freedom are represented with exponentialaccuracy on a truncated Hilbert space with a size that increases linearly withthe cutoff of the maximum phonon number. The additional number of qubitsrequired by the presence of phonons scales linearly with the size of thesystem. The additional circuit depth is constant for systems with finite-rangeelectron-phonon and phonon-phonon interactions and linear for long-rangeelectron-phonon interactions. Our algorithm for a Holstein polaron problem wasimplemented on an Atos Quantum Learning Machine (QLM) quantum simulatoremployingmore » the Quantum Phase Estimation method. The energy and the phonon numberdistribution of the polaron state agree with exact diagonalization results forweak, intermediate and strong electron-phonon coupling regimes.« less

Linear time-to-space mapping system using double electrooptic beam deflectors.

PubMed

Hisatake, Shintaro; Tada, Keiji; Nagatsuma, Tadao

2008-12-22

We propose and demonstrate a linear time-to-space mapping system, which is based on two times electrooptic sinusoidal beam deflection. The direction of each deflection is set to be mutually orthogonal with the relative deflection phase of pi/2 rad so that the circular optical beam trajectory can be achieved. The beam spot at the observation plane moves with an uniform velocity and as a result linear time-to-space mapping (an uniform temporal resolution through the mapping) can be realized. The proof-of-concept experiment are carried out and the temporal resolution of 5 ps has been demonstrated using traveling-wave type quasi-velosity-matched electrooptic beam deflectors. The developed system is expected to be applied to characterization of ultrafast optical signal or optical arbitrary waveform shaping for modulated microwave/millimeter-wave generation.

Fast photoacoustic imaging system based on 320-element linear transducer array.

PubMed

Yin, Bangzheng; Xing, Da; Wang, Yi; Zeng, Yaguang; Tan, Yi; Chen, Qun

2004-04-07

A fast photoacoustic (PA) imaging system, based on a 320-transducer linear array, was developed and tested on a tissue phantom. To reconstruct a test tomographic image, 64 time-domain PA signals were acquired from a tissue phantom with embedded light-absorption targets. A signal acquisition was accomplished by utilizing 11 phase-controlled sub-arrays, each consisting of four transducers. The results show that the system can rapidly map the optical absorption of a tissue phantom and effectively detect the embedded light-absorbing target. By utilizing the multi-element linear transducer array and phase-controlled imaging algorithm, we thus can acquire PA tomography more efficiently, compared to other existing technology and algorithms. The methodology and equipment thus provide a rapid and reliable approach to PA imaging that may have potential applications in noninvasive imaging and clinic diagnosis.

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

PubMed Central

Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

2014-01-01

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467

Qualitative properties of large buckled states of spherical shells

NASA Technical Reports Server (NTRS)

Shih, K. G.; Antman, S. S.

1985-01-01

A system of 6th-order quasi-linear Ordinary Differential Equations is analyzed to show the global existence of axisymmetrically buckled states. A surprising nodal property is obtained which shows that everywhere along a branch of solutions that bifurcates from a simple eigenvalue of the linearized equation, the number of simultaneously vanishing points of both shear resultant and circumferential bending moment resultant remains invariant, provided that a certain auxiliary condition is satisfied.

Optimal space communications techniques. [using digital and phase locked systems for signal processing

NASA Technical Reports Server (NTRS)

Schilling, D. L.

1974-01-01

Digital multiplication of two waveforms using delta modulation (DM) is discussed. It is shown that while conventional multiplication of two N bit words requires N2 complexity, multiplication using DM requires complexity which increases linearly with N. Bounds on the signal-to-quantization noise ratio (SNR) resulting from this multiplication are determined and compared with the SNR obtained using standard multiplication techniques. The phase locked loop (PLL) system, consisting of a phase detector, voltage controlled oscillator, and a linear loop filter, is discussed in terms of its design and system advantages. Areas requiring further research are identified.

A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

Optimal control problem for linear fractional-order systems, described by equations with Hadamard-type derivative

NASA Astrophysics Data System (ADS)

Postnov, Sergey

2017-11-01

Two kinds of optimal control problem are investigated for linear time-invariant fractional-order systems with lumped parameters which dynamics described by equations with Hadamard-type derivative: the problem of control with minimal norm and the problem of control with minimal time at given restriction on control norm. The problem setting with nonlocal initial conditions studied. Admissible controls allowed to be the p-integrable functions (p > 1) at half-interval. The optimal control problem studied by moment method. The correctness and solvability conditions for the corresponding moment problem are derived. For several special cases the optimal control problems stated are solved analytically. Some analogies pointed for results obtained with the results which are known for integer-order systems and fractional-order systems describing by equations with Caputo- and Riemann-Liouville-type derivatives.

Energy dynamics in a simulation of LAPD turbulence

NASA Astrophysics Data System (ADS)

Friedman, Brett

2012-10-01

It is often assumed that linear instabilities maintain turbulence in plasmas and some fluids, but this is not always the case. It is well known that many fluids display subcritical turbulence at a Reynolds number well below the threashold of linear instability. Certain plasma models such as drift waves in a sheared slab also exhibit subcritical turbulence [1]. In other instances such as drift-ballooning turbulence in tokamak edge plasmas, linear instabilities exist in a system, but they become subdominant to more robust nonlinear mechanisms that sustain a turbulent state [2, 3]. In our simulation of LAPD turbulence, which was previously analyzed in [4], we diagnose the results using an energy dynamics analysis [5]. This allows us to track energy input into turbulent fluctuations and energy dissipation out of them. We also track conservative energy transfer between different energy types (e.g. from potential to kinetic energy) and between different Fourier waves of the system. The result is that a nonlinear instability drives and maintains the turbulence in the steady state saturated phase of the simulation. While a linear restistive drift wave instability resides in the system, the nonlinear drift wave instability dominates when the fluctuation amplitude becomes large enough. The nonlinear instability is identified by its energy growth rate spectrum, which varies significantly from the linear growth rate spectrum. The main differences are the presence of positive growth rates when k|| = 0 and negative growth rates for nonzero k||, which is opposite that of the linear growth rate spectrum.[4pt] [1] B. D. Scott, Phys. Rev. Lett., 65, 3289 (1990).[0pt] [2] A. Zeiler et al, Phys. Plasmas, 3, 2951 (1996).[0pt] [3] B. D. Scott, Phys. Plasmas, 12, 062314 (2005).[0pt] [4] P. Popovich et al, Phys. Plasmas, 17, 122312 (2010).[0pt] [5] [physics.plasm-ph].

Evolution of the Carter constant for inspirals into a black hole: Effect of the black hole quadrupole

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

Flanagan, Eanna E.; Laboratory for Elementary Particle Physics, Cornell University, Ithaca, New York 14853; Hinderer, Tanja

2007-06-15

We analyze the effect of gravitational radiation reaction on generic orbits around a body with an axisymmetric mass quadrupole moment Q to linear order in Q, to the leading post-Newtonian order, and to linear order in the mass ratio. This system admits three constants of the motion in absence of radiation reaction: energy, angular momentum along the symmetry axis, and a third constant analogous to the Carter constant. We compute instantaneous and time-averaged rates of change of these three constants. For a point particle orbiting a black hole, Ryan has computed the leading order evolution of the orbit's Carter constant,more » which is linear in the spin. Our result, when combined with an interaction quadratic in the spin (the coupling of the black hole's spin to its own radiation reaction field), gives the next to leading order evolution. The effect of the quadrupole, like that of the linear spin term, is to circularize eccentric orbits and to drive the orbital plane towards antialignment with the symmetry axis. In addition we consider a system of two point masses where one body has a single mass multipole or current multipole of order l. To linear order in the mass ratio, to linear order in the multipole, and to the leading post-Newtonian order, we show that there does not exist an analog of the Carter constant for such a system (except for the cases of an l=1 current moment and an l=2 mass moment). Thus, the existence of the Carter constant in Kerr depends on interaction effects between the different multipoles. With mild additional assumptions, this result falsifies the conjecture that all vacuum, axisymmetric spacetimes possess a third constant of the motion for geodesic motion.« less

Application of linear logic to simulation

NASA Astrophysics Data System (ADS)

Clarke, Thomas L.

1998-08-01

Linear logic, since its introduction by Girard in 1987 has proven expressive and powerful. Linear logic has provided natural encodings of Turing machines, Petri nets and other computational models. Linear logic is also capable of naturally modeling resource dependent aspects of reasoning. The distinguishing characteristic of linear logic is that it accounts for resources; two instances of the same variable are considered differently from a single instance. Linear logic thus must obey a form of the linear superposition principle. A proportion can be reasoned with only once, unless a special operator is applied. Informally, linear logic distinguishes two kinds of conjunction, two kinds of disjunction, and also introduces a modal storage operator that explicitly indicates propositions that can be reused. This paper discuses the application of linear logic to simulation. A wide variety of logics have been developed; in addition to classical logic, there are fuzzy logics, affine logics, quantum logics, etc. All of these have found application in simulations of one sort or another. The special characteristics of linear logic and its benefits for simulation will be discussed. Of particular interest is a connection that can be made between linear logic and simulated dynamics by using the concept of Lie algebras and Lie groups. Lie groups provide the connection between the exponential modal storage operators of linear logic and the eigen functions of dynamic differential operators. Particularly suggestive are possible relations between complexity result for linear logic and non-computability results for dynamical systems.

Some estimation formulae for continuous time-invariant linear systems

NASA Technical Reports Server (NTRS)

Bierman, G. J.; Sidhu, G. S.

1975-01-01

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Numerical solution of system of boundary value problems using B-spline with free parameter

NASA Astrophysics Data System (ADS)

Gupta, Yogesh

2017-01-01

This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

Improving linear accelerator service response with a real- time electronic event reporting system.

PubMed

Hoisak, Jeremy D P; Pawlicki, Todd; Kim, Gwe-Ya; Fletcher, Richard; Moore, Kevin L

2014-09-08

To track linear accelerator performance issues, an online event recording system was developed in-house for use by therapists and physicists to log the details of technical problems arising on our institution's four linear accelerators. In use since October 2010, the system was designed so that all clinical physicists would receive email notification when an event was logged. Starting in October 2012, we initiated a pilot project in collaboration with our linear accelerator vendor to explore a new model of service and support, in which event notifications were also sent electronically directly to dedicated engineers at the vendor's technical help desk, who then initiated a response to technical issues. Previously, technical issues were reported by telephone to the vendor's call center, which then disseminated information and coordinated a response with the Technical Support help desk and local service engineers. The purpose of this work was to investigate the improvements to clinical operations resulting from this new service model. The new and old service models were quantitatively compared by reviewing event logs and the oncology information system database in the nine months prior to and after initiation of the project. Here, we focus on events that resulted in an inoperative linear accelerator ("down" machine). Machine downtime, vendor response time, treatment cancellations, and event resolution were evaluated and compared over two equivalent time periods. In 389 clinical days, there were 119 machine-down events: 59 events before and 60 after introduction of the new model. In the new model, median time to service response decreased from 45 to 8 min, service engineer dispatch time decreased 44%, downtime per event decreased from 45 to 20 min, and treatment cancellations decreased 68%. The decreased vendor response time and reduced number of on-site visits by a service engineer resulted in decreased downtime and decreased patient treatment cancellations.

Benefits of incorporating the adaptive dynamic range optimization amplification scheme into an assistive listening device for people with mild or moderate hearing loss.

PubMed

Chang, Hung-Yue; Luo, Ching-Hsing; Lo, Tun-Shin; Chen, Hsiao-Chuan; Huang, Kuo-You; Liao, Wen-Huei; Su, Mao-Chang; Liu, Shu-Yu; Wang, Nan-Mai

2017-08-28

This study investigated whether a self-designed assistive listening device (ALD) that incorporates an adaptive dynamic range optimization (ADRO) amplification strategy can surpass a commercially available monaurally worn linear ALD, SM100. Both subjective and objective measurements were implemented. Mandarin Hearing-In-Noise Test (MHINT) scores were the objective measurement, whereas participant satisfaction was the subjective measurement. The comparison was performed in a mixed design (i.e., subjects' hearing status being mild or moderate, quiet versus noisy, and linear versus ADRO scheme). The participants were two groups of hearing-impaired subjects, nine mild and eight moderate, respectively. The results of the ADRO system revealed a significant difference in the MHINT sentence reception threshold (SRT) in noisy environments between monaurally aided and unaided conditions, whereas the linear system did not. The benchmark results showed that the ADRO scheme is effectively beneficial to people who experience mild or moderate hearing loss in noisy environments. The satisfaction rating regarding overall speech quality indicated that the participants were satisfied with the speech quality of both ADRO and linear schemes in quiet environments, and they were more satisfied with ADRO than they with the linear scheme in noisy environments.

Implementation of software-based sensor linearization algorithms on low-cost microcontrollers.

PubMed

Erdem, Hamit

2010-10-01

Nonlinear sensors and microcontrollers are used in many embedded system designs. As the input-output characteristic of most sensors is nonlinear in nature, obtaining data from a nonlinear sensor by using an integer microcontroller has always been a design challenge. This paper discusses the implementation of six software-based sensor linearization algorithms for low-cost microcontrollers. The comparative study of the linearization algorithms is performed by using a nonlinear optical distance-measuring sensor. The performance of the algorithms is examined with respect to memory space usage, linearization accuracy and algorithm execution time. The implementation and comparison results can be used for selection of a linearization algorithm based on the sensor transfer function, expected linearization accuracy and microcontroller capacity. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Linear algebraic methods applied to intensity modulated radiation therapy.

PubMed

Crooks, S M; Xing, L

2001-10-01

Methods of linear algebra are applied to the choice of beam weights for intensity modulated radiation therapy (IMRT). It is shown that the physical interpretation of the beam weights, target homogeneity and ratios of deposited energy can be given in terms of matrix equations and quadratic forms. The methodology of fitting using linear algebra as applied to IMRT is examined. Results are compared with IMRT plans that had been prepared using a commercially available IMRT treatment planning system and previously delivered to cancer patients.

AESOP: An interactive computer program for the design of linear quadratic regulators and Kalman filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L. C.

1984-01-01

AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.

The Absolute Stability Analysis in Fuzzy Control Systems with Parametric Uncertainties and Reference Inputs

NASA Astrophysics Data System (ADS)

Wu, Bing-Fei; Ma, Li-Shan; Perng, Jau-Woei

This study analyzes the absolute stability in P and PD type fuzzy logic control systems with both certain and uncertain linear plants. Stability analysis includes the reference input, actuator gain and interval plant parameters. For certain linear plants, the stability (i.e. the stable equilibriums of error) in P and PD types is analyzed with the Popov or linearization methods under various reference inputs and actuator gains. The steady state errors of fuzzy control systems are also addressed in the parameter plane. The parametric robust Popov criterion for parametric absolute stability based on Lur'e systems is also applied to the stability analysis of P type fuzzy control systems with uncertain plants. The PD type fuzzy logic controller in our approach is a single-input fuzzy logic controller and is transformed into the P type for analysis. In our work, the absolute stability analysis of fuzzy control systems is given with respect to a non-zero reference input and an uncertain linear plant with the parametric robust Popov criterion unlike previous works. Moreover, a fuzzy current controlled RC circuit is designed with PSPICE models. Both numerical and PSPICE simulations are provided to verify the analytical results. Furthermore, the oscillation mechanism in fuzzy control systems is specified with various equilibrium points of view in the simulation example. Finally, the comparisons are also given to show the effectiveness of the analysis method.

Differences between measured and linearly interpolated synoptic variables over a 12-h period during AVE 4

NASA Technical Reports Server (NTRS)

Dupuis, L. R.; Scoggins, J. R.

1979-01-01

Results of analyses revealed that nonlinear changes or differences formed centers or systems, that were mesosynoptic in nature. These systems correlated well in space with upper level short waves, frontal zones, and radar observed convection, and were very systematic in time and space. Many of the centers of differences were well established in the vertical, extending up to the tropopause. Statistical analysis showed that on the average nonlinear changes were larger in convective areas than nonconvective regions. Errors often exceeding 100 percent were made by assuming variables to change linearly through a 12-h period in areas of thunderstorms, indicating that these nonlinear changes are important in the development of severe weather. Linear changes, however, accounted for more and more of an observed change as the time interval (within the 12-h interpolation period) increased, implying that the accuracy of linear interpolation increased over larger time intervals.

A linear induction motor with a coated conductor superconducting secondary

NASA Astrophysics Data System (ADS)

Chen, Xin; Zheng, Shijun; Li, Jing; Ma, Guang Tong; Yen, Fei

2018-07-01

A linear induction motor system composed of a high-Tc superconducting secondary with close-ended coils made of REBCO coated conductor wire was designed and tested experimentally. The measured thrust, normal force and power loss are presented and explained by combining the flux dynamics inside superconductors with existing linear drive theory. It is found that an inherent capacitive component associated to the flux motion of vortices in the Type-II superconductor reduces the impedance of the coils; from such, the associated Lorentz forces are drastically increased. The resulting breakout thrust of the designed linear motor system was found to be extremely high (up to 4.7 kN/m2) while the associated normal forces only a fraction of the thrust. Compared to its conventional counterparts, high-Tc superconducting secondaries appear to be more feasible for use in maglev propulsion and electromagnetic launchers.

Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

NASA Astrophysics Data System (ADS)

Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

2018-05-01

In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

Seeking Space Aliens and the Strong Approximation Property: A (disjoint) Study in Dust Plumes on Planetary Satellites and Nonsymmetric Algebraic Multigrid

NASA Astrophysics Data System (ADS)

Southworth, Benjamin Scott

PART I: One of the most fascinating questions to humans has long been whether life exists outside of our planet. To our knowledge, water is a fundamental building block of life, which makes liquid water on other bodies in the universe a topic of great interest. In fact, there are large bodies of water right here in our solar system, underneath the icy crust of moons around Saturn and Jupiter. The NASA-ESA Cassini Mission spent two decades studying the Saturnian system. One of the many exciting discoveries was a "plume" on the south pole of Enceladus, emitting hundreds of kg/s of water vapor and frozen water-ice particles from Enceladus' subsurface ocean. It has since been determined that Enceladus likely has a global liquid water ocean separating its rocky core from icy surface, with conditions that are relatively favorable to support life. The plume is of particular interest because it gives direct access to ocean particles from space, by flying through the plume. Recently, evidence has been found for similar geological activity occurring on Jupiter's moon Europa, long considered one of the most likely candidate bodies to support life in our solar system. Here, a model for plume-particle dynamics is developed based on studies of the Enceladus plume and data from the Cassini Cosmic Dust Analyzer. A C++, OpenMP/MPI parallel software package is then built to run large scale simulations of dust plumes on planetary satellites. In the case of Enceladus, data from simulations and the Cassini mission provide insight into the structure of emissions on the surface, the total mass production of the plume, and the distribution of particles being emitted. Each of these are fundamental to understanding the plume and, for Europa and Enceladus, simulation data provide important results for the planning of future missions to these icy moons. In particular, this work has contributed to the Europa Clipper mission and proposed Enceladus Life Finder. PART II: Solving large, sparse linear systems arises often in the modeling of biological and physical phenomenon, data analysis through graphs and networks, and other scientific applications. This work focuses primarily on linear systems resulting from the discretization of partial differential equations (PDEs). Because solving linear systems is the bottleneck of many large simulation codes, there is a rich field of research in developing "fast" solvers, with the ultimate goal being a method that solves an n x n linear system in O(n) operations. One of the most effective classes of solvers is algebraic multigrid (AMG), which is a multilevel iterative method based on projecting the problem into progressively smaller spaces, and scales like O(n) or O(nlog n) for certain classes of problems. The field of AMG is well-developed for symmetric positive definite matrices, and is typically most effective on linear systems resulting from the discretization of scalar elliptic PDEs, such as the heat equation. Systems of PDEs can add additional difficulties, but the underlying linear algebraic theory is consistent and, in many cases, an elliptic system of PDEs can be handled well by AMG with appropriate modifications of the solver. Solving general, nonsymmetric linear systems remains the wild west of AMG (and other fast solvers), lacking significant results in convergence theory as well as robust methods. Here, we develop new theoretical motivation and practical variations of AMG to solve nonsymmetric linear systems, often resulting from the discretization of hyperbolic PDEs. In particular, multilevel convergence of AMG for nonsymmetric systems is proven for the first time. A new nonsymmetric AMG solver is also developed based on an approximate ideal restriction, referred to as AIR, which is able to solve advection-dominated, hyperbolic-type problems that are outside the scope of existing AMG solvers and other fast iterative methods. AIR demonstrates scalable convergence on unstructured meshes, in multiple dimensions, and with high-order finite elements, expanding the applicability of AMG to a new class of problems.

Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators.

PubMed

Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao

2014-10-06

Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.

Fit Point-Wise AB Initio Calculation Potential Energies to a Multi-Dimension Long-Range Model

NASA Astrophysics Data System (ADS)

Zhai, Yu; Li, Hui; Le Roy, Robert J.

2016-06-01

A potential energy surface (PES) is a fundamental tool and source of understanding for theoretical spectroscopy and for dynamical simulations. Making correct assignments for high-resolution rovibrational spectra of floppy polyatomic and van der Waals molecules often relies heavily on predictions generated from a high quality ab initio potential energy surface. Moreover, having an effective analytic model to represent such surfaces can be as important as the ab initio results themselves. For the one-dimensional potentials of diatomic molecules, the most successful such model to date is arguably the ``Morse/Long-Range'' (MLR) function developed by R. J. Le Roy and coworkers. It is very flexible, is everywhere differentiable to all orders. It incorporates correct predicted long-range behaviour, extrapolates sensibly at both large and small distances, and two of its defining parameters are always the physically meaningful well depth {D}_e and equilibrium distance r_e. Extensions of this model, called the Multi-Dimension Morse/Long-Range (MD-MLR) function, linear molecule-linear molecule systems and atom-non-linear molecule system. have been applied successfully to atom-plus-linear molecule, linear molecule-linear molecule and atom-non-linear molecule systems. However, there are several technical challenges faced in modelling the interactions of general molecule-molecule systems, such as the absence of radial minima for some relative alignments, difficulties in fitting short-range potential energies, and challenges in determining relative-orientation dependent long-range coefficients. This talk will illustrate some of these challenges and describe our ongoing work in addressing them. Mol. Phys. 105, 663 (2007); J. Chem. Phys. 131, 204309 (2009); Mol. Phys. 109, 435 (2011). Phys. Chem. Chem. Phys. 10, 4128 (2008); J. Chem. Phys. 130, 144305 (2009) J. Chem. Phys. 132, 214309 (2010) J. Chem. Phys. 140, 214309 (2010)

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

Linear maps preserving maximal deviation and the Jordan structure of quantum systems

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

Hamhalter, Jan

2012-12-15

In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable is the largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or a minus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only onemore » numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviation in the case of self-adjoint parts of von Neumann algebras proved by Molnar.« less

A new look at the robust control of discrete-time Markov jump linear systems

NASA Astrophysics Data System (ADS)

Todorov, M. G.; Fragoso, M. D.

2016-03-01

In this paper, we make a foray in the role played by a set of four operators on the study of robust H2 and mixed H2/H∞ control problems for discrete-time Markov jump linear systems. These operators appear in the study of mean square stability for this class of systems. By means of new linear matrix inequality (LMI) characterisations of controllers, which include slack variables that, to some extent, separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of H2 performance. Since each operator provides a different degree of conservatism, the results are unified in the form of an iterative LMI technique for designing robust H2 controllers, whose convergence is attained in a finite number of steps. The method yields a new way of computing mixed H2/H∞ controllers, whose conservatism decreases with iteration. Two numerical examples illustrate the applicability of the proposed results for the control of a small unmanned aerial vehicle, and for an underactuated robotic arm.

Application of Multiregressive Linear Models, Dynamic Kriging Models and Neural Network Models to Predictive Maintenance of Hydroelectric Power Systems

NASA Astrophysics Data System (ADS)

Lucifredi, A.; Mazzieri, C.; Rossi, M.

2000-05-01

Since the operational conditions of a hydroelectric unit can vary within a wide range, the monitoring system must be able to distinguish between the variations of the monitored variable caused by variations of the operation conditions and those due to arising and progressing of failures and misoperations. The paper aims to identify the best technique to be adopted for the monitoring system. Three different methods have been implemented and compared. Two of them use statistical techniques: the first, the linear multiple regression, expresses the monitored variable as a linear function of the process parameters (independent variables), while the second, the dynamic kriging technique, is a modified technique of multiple linear regression representing the monitored variable as a linear combination of the process variables in such a way as to minimize the variance of the estimate error. The third is based on neural networks. Tests have shown that the monitoring system based on the kriging technique is not affected by some problems common to the other two models e.g. the requirement of a large amount of data for their tuning, both for training the neural network and defining the optimum plane for the multiple regression, not only in the system starting phase but also after a trivial operation of maintenance involving the substitution of machinery components having a direct impact on the observed variable. Or, in addition, the necessity of different models to describe in a satisfactory way the different ranges of operation of the plant. The monitoring system based on the kriging statistical technique overrides the previous difficulties: it does not require a large amount of data to be tuned and is immediately operational: given two points, the third can be immediately estimated; in addition the model follows the system without adapting itself to it. The results of the experimentation performed seem to indicate that a model based on a neural network or on a linear multiple regression is not optimal, and that a different approach is necessary to reduce the amount of work during the learning phase using, when available, all the information stored during the initial phase of the plant to build the reference baseline, elaborating, if it is the case, the raw information available. A mixed approach using the kriging statistical technique and neural network techniques could optimise the result.

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

NASA Astrophysics Data System (ADS)

Abramov, R. V.

2011-12-01

Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger chaotic system would result in general increase of chaos at the slow variables.

Method of Conjugate Radii for Solving Linear and Nonlinear Systems

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.

1999-01-01

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate

NASA Astrophysics Data System (ADS)

Bianchi, Eugenio; Hackl, Lucas; Yokomizo, Nelson

2018-03-01

The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate h KS given by the sum of all positive Lyapunov exponents of the system. We prove a quantum version of this result valid for bosonic systems with unstable quadratic Hamiltonian. The derivation takes into account the case of time-dependent Hamiltonians with Floquet instabilities. We show that the entanglement entropy S A of a Gaussian state grows linearly for large times in unstable systems, with a rate Λ A ≤ h KS determined by the Lyapunov exponents and the choice of the subsystem A. We apply our results to the analysis of entanglement production in unstable quadratic potentials and due to periodic quantum quenches in many-body quantum systems. Our results are relevant for quantum field theory, for which we present three applications: a scalar field in a symmetry-breaking potential, parametric resonance during post-inflationary reheating and cosmological perturbations during inflation. Finally, we conjecture that the same rate Λ A appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.

PubMed

Li, Pu; Chen, Bing

2011-04-01

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk. Copyright © 2010 Elsevier Ltd. All rights reserved.

The role of model dynamics in ensemble Kalman filter performance for chaotic systems

USGS Publications Warehouse

Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.

2011-01-01

The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

NASA Astrophysics Data System (ADS)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

Linear control of the flywheel inverted pendulum.

PubMed

Olivares, Manuel; Albertos, Pedro

2014-09-01

The flywheel inverted pendulum is an underactuated mechanical system with a nonlinear model but admitting a linear approximation around the unstable equilibrium point in the upper position. Although underactuated systems usually require nonlinear controllers, the easy tuning and understanding of linear controllers make them more attractive for designers and final users. In a recent paper, a simple PID controller was proposed by the authors, leading to an internally unstable controlled plant. To achieve global stability, two options are developed here: first by introducing an internal stabilizing controller and second by replacing the PID controller by an observer-based state feedback control. Simulation and experimental results show the effectiveness of the design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Study of optical nonlinearities in Se-Te-Bi thin films

NASA Astrophysics Data System (ADS)

Sharma, Ambika; Yadav, Preeti; Kumari, Anshu

2014-04-01

The present work reports the nonlinear refractive index of Se85-xTe15Bix thin films calculated by Ticha and Tichy relation. The nonlinear refractive index of Chalcogenide amorphous semiconductor is well correlated with the linear refractive index and WDD parameters which in turn depend on the density and molar volume of the system. The density of the system is calculated theoretical as well as experimentally by using Archimedes principle. The linear refractive index and WDD parameters are calculated using single transmission spectra in the spectral range of 400-1500 nm. It is observed that linear as well as nonlinear refractive index increases with Bi content. The results are analyzed on the basis of increasing polarizability due to larger radii of Bi.

Symbolic discrete event system specification

NASA Technical Reports Server (NTRS)

Zeigler, Bernard P.; Chi, Sungdo

1992-01-01

Extending discrete event modeling formalisms to facilitate greater symbol manipulation capabilities is important to further their use in intelligent control and design of high autonomy systems. An extension to the DEVS formalism that facilitates symbolic expression of event times by extending the time base from the real numbers to the field of linear polynomials over the reals is defined. A simulation algorithm is developed to generate the branching trajectories resulting from the underlying nondeterminism. To efficiently manage symbolic constraints, a consistency checking algorithm for linear polynomial constraints based on feasibility checking algorithms borrowed from linear programming has been developed. The extended formalism offers a convenient means to conduct multiple, simultaneous explorations of model behaviors. Examples of application are given with concentration on fault model analysis.

Harmonic-phase path-integral approximation of thermal quantum correlation functions

NASA Astrophysics Data System (ADS)

Robertson, Christopher; Habershon, Scott

2018-03-01

We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

Loop shaping design for tracking performance in machine axes.

PubMed

Schinstock, Dale E; Wei, Zhouhong; Yang, Tao

2006-01-01

A modern interpretation of classical loop shaping control design methods is presented in the context of tracking control for linear motor stages. Target applications include noncontacting machines such as laser cutters and markers, water jet cutters, and adhesive applicators. The methods are directly applicable to the common PID controller and are pertinent to many electromechanical servo actuators other than linear motors. In addition to explicit design techniques a PID tuning algorithm stressing the importance of tracking is described. While the theory behind these techniques is not new, the analysis of their application to modern systems is unique in the research literature. The techniques and results should be important to control practitioners optimizing PID controller designs for tracking and in comparing results from classical designs to modern techniques. The methods stress high-gain controller design and interpret what this means for PID. Nothing in the methods presented precludes the addition of feedforward control methods for added improvements in tracking. Laboratory results from a linear motor stage demonstrate that with large open-loop gain very good tracking performance can be achieved. The resultant tracking errors compare very favorably to results from similar motions on similar systems that utilize much more complicated controllers.

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

Møller, Jacob Schach

These notes provide an introduction to the spectral analysis of Pauli-Fierz systems at zero and positive temperature. More precisely, we study finite dimensional quantum systems linearly coupled to a single reservoir, a massless scalar quantum field. We emphasize structure results valid at arbitrary system-reservoir coupling strength. The notes contain a mixture of known, refined, and new results and each section ends with a discussion of open problems.

Comparative study of microwave radiation-induced magnetoresistive oscillations induced by circularly- and linearly- polarized photo-excitation

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

Ye, Tianyu; Liu, Han -Chun; Wang, Zhuo

A comparative study of the radiation-induced magnetoresistance oscillations in the high mobility GaAs/AlGaAs heterostructure two dimensional electron system (2DES) under linearly- and circularly- polarized microwave excitation indicates a profound difference in the response observed upon rotating the microwave launcher for the two cases, although circularly polarized microwave radiation induced magnetoresistance oscillations observed at low magnetic fields are similar to the oscillations observed with linearly polarized radiation. For the linearly polarized radiation, the magnetoresistive response is a strong sinusoidal function of the launcher rotation (or linear polarization) angle, θ. As a result, for circularly polarized radiation, the oscillatory magnetoresistive response ismore » hardly sensitive to θ.« less

Comparative study of microwave radiation-induced magnetoresistive oscillations induced by circularly- and linearly- polarized photo-excitation

DOE PAGES

Ye, Tianyu; Liu, Han -Chun; Wang, Zhuo; ...

2015-10-09

A comparative study of the radiation-induced magnetoresistance oscillations in the high mobility GaAs/AlGaAs heterostructure two dimensional electron system (2DES) under linearly- and circularly- polarized microwave excitation indicates a profound difference in the response observed upon rotating the microwave launcher for the two cases, although circularly polarized microwave radiation induced magnetoresistance oscillations observed at low magnetic fields are similar to the oscillations observed with linearly polarized radiation. For the linearly polarized radiation, the magnetoresistive response is a strong sinusoidal function of the launcher rotation (or linear polarization) angle, θ. As a result, for circularly polarized radiation, the oscillatory magnetoresistive response ismore » hardly sensitive to θ.« less

Analytical Solution of Steady State Equations for Chemical Reaction Networks with Bilinear Rate Laws

PubMed Central

Halász, Ádám M.; Lai, Hong-Jian; McCabe, Meghan M.; Radhakrishnan, Krishnan; Edwards, Jeremy S.

2014-01-01

True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher dimensional space. We show that the linearized version of the steady state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1. PMID:24334389

On the Effect of Variability on Fermi, Pasta and Ulam Matrices

NASA Astrophysics Data System (ADS)

Nelson, Heather; Choubey, Bhaskar

The first numerical experiment by Fermi, Pasta, Ulam and Tsingou in 1955 observed recurrence in an array of non-linear systems. This has led to a large number of nonlinear numerical experiments with various new results from a chain of ideal oscillators. FPUT arrays consists of linear oscillators connected nonlinearly which leads to recurrence of energy mode with time. However, if such a system were to be physically constructed, inherent process variations would introduce a manufacturing tolerance into the parameters of the system. This abstract reports investigation into the effects of these tolerances on the FPU matrices. It has been observed that tolerance in the oscillators can degrade the observance of recurrence and with a chain of even 64 oscillators, recurrence cannot be observed with tolerances more than 10%. It has also been observed that linear oscillators tolerances have more effects on recurrence than those of the nonlinear coupling. Even with very small tolerances of +/- 1% on the linear components, one start to observe variations in the quality and magnitude of the recurrence and at +/- 5%, recurrence is starting to break down.

Linearized Poststall Aerodynamic and Control Law Models of the X-31A Aircraft and Comparison with Flight Data

NASA Technical Reports Server (NTRS)

Stoliker, Patrick C.; Bosworth, John T.; Georgie, Jennifer

1997-01-01

The X-31A aircraft has a unique configuration that uses thrust-vector vanes and aerodynamic control effectors to provide an operating envelope to a maximum 70 deg angle of attack, an inherently nonlinear portion of the flight envelope. This report presents linearized versions of the X-31A longitudinal and lateral-directional control systems, with aerodynamic models sufficient to evaluate characteristics in the poststall envelope at 30 deg, 45 deg, and 60 deg angle of attack. The models are presented with detail sufficient to allow the reader to reproduce the linear results or perform independent control studies. Comparisons between the responses of the linear models and flight data are presented in the time and frequency domains to demonstrate the strengths and weaknesses of the ability to predict high-angle-of-attack flight dynamics using linear models. The X-31A six-degree-of-freedom simulation contains a program that calculates linear perturbation models throughout the X-31A flight envelope. The models include aerodynamics and flight control system dynamics that are used for stability, controllability, and handling qualities analysis. The models presented in this report demonstrate the ability to provide reasonable linear representations in the poststall flight regime.

Broadband linearisation of high-efficiency power amplifiers

NASA Technical Reports Server (NTRS)

Kenington, Peter B.; Parsons, Kieran J.; Bennett, David W.

1993-01-01

A feedforward-based amplifier linearization technique is presented which is capable of yielding significant improvements in both linearity and power efficiency over conventional amplifier classes (e.g. class-A or class-AB). Theoretical and practical results are presented showing that class-C stages may be used for both the main and error amplifiers yielding practical efficiencies well in excess of 30 percent, with theoretical efficiencies of much greater than 40 percent being possible. The levels of linearity which may be achieved are required for most satellite systems, however if greater linearity is required, the technique may be used in addition to conventional pre-distortion techniques.

Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems.

PubMed

Amaral, Gleison F V; Letellier, Christophe; Aguirre, Luis Antonio

2006-03-01

This paper proposes a procedure by which it is possible to synthesize Rossler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.

Using integrated models to minimize environmentally induced wavefront error in optomechanical design and analysis

NASA Astrophysics Data System (ADS)

Genberg, Victor L.; Michels, Gregory J.

2017-08-01

The ultimate design goal of an optical system subjected to dynamic loads is to minimize system level wavefront error (WFE). In random response analysis, system WFE is difficult to predict from finite element results due to the loss of phase information. In the past, the use of ystem WFE was limited by the difficulty of obtaining a linear optics model. In this paper, an automated method for determining system level WFE using a linear optics model is presented. An error estimate is included in the analysis output based on fitting errors of mode shapes. The technique is demonstrated by example with SigFit, a commercially available tool integrating mechanical analysis with optical analysis.

A spline-based non-linear diffeomorphism for multimodal prostate registration.

PubMed

Mitra, Jhimli; Kato, Zoltan; Martí, Robert; Oliver, Arnau; Lladó, Xavier; Sidibé, Désiré; Ghose, Soumya; Vilanova, Joan C; Comet, Josep; Meriaudeau, Fabrice

2012-08-01

This paper presents a novel method for non-rigid registration of transrectal ultrasound and magnetic resonance prostate images based on a non-linear regularized framework of point correspondences obtained from a statistical measure of shape-contexts. The segmented prostate shapes are represented by shape-contexts and the Bhattacharyya distance between the shape representations is used to find the point correspondences between the 2D fixed and moving images. The registration method involves parametric estimation of the non-linear diffeomorphism between the multimodal images and has its basis in solving a set of non-linear equations of thin-plate splines. The solution is obtained as the least-squares solution of an over-determined system of non-linear equations constructed by integrating a set of non-linear functions over the fixed and moving images. However, this may not result in clinically acceptable transformations of the anatomical targets. Therefore, the regularized bending energy of the thin-plate splines along with the localization error of established correspondences should be included in the system of equations. The registration accuracies of the proposed method are evaluated in 20 pairs of prostate mid-gland ultrasound and magnetic resonance images. The results obtained in terms of Dice similarity coefficient show an average of 0.980±0.004, average 95% Hausdorff distance of 1.63±0.48 mm and mean target registration and target localization errors of 1.60±1.17 mm and 0.15±0.12 mm respectively. Copyright © 2012 Elsevier B.V. All rights reserved.

Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ku, R. T.

1972-01-01

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Reliability enhancement of common module systems

NASA Astrophysics Data System (ADS)

Schellenberger, Gisbert; Ruehlich, Ingo; Korf, Herbert; Petrie, Juergen J.; Muenter, Rolf

2004-08-01

Several thousands of 1st Gen IR Systems operated by Integral Stirling Cooler HD1033 are still in service worldwide. Replacing the HD 1033 Stirling by a Linear Drive Cooler will result in a significant reliability enhancement of these IR system of about a factor of three. These attempts had been unsuccessful in the past due to excessive EMI noise induced by the linear cooler compressor. So a main goal for such a development is the elimination of various EMI distortions in the IR system by EMI filtering and shielding. Additionally, the synchronization of the cooler power to the predominant scanning frequency of the IR system significantly improves the image quality. Technical details of the solution, MTTF data and performance data are described in detail.

Variable structure control of nonlinear systems through simplified uncertain models

NASA Technical Reports Server (NTRS)

Sira-Ramirez, Hebertt

1986-01-01

A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.

Holographic representation of space-variant systems: system theory.

PubMed

Marks Ii, R J; Krile, T F

1976-09-01

System theory for holographic representation of linear space-variant systems is derived. The utility of the resulting piecewise isoplanatic approximation (PIA) is illustrated by example application to the invariant system, ideal magnifier, and Fourier transformer. A method previously employed to holographically represent a space-variant system, the discrete approximation, is shown to be a special case of the PIA.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

PubMed

Metzler, Holger; Müller, Markus; Sierra, Carlos A

2018-02-06

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems

NASA Astrophysics Data System (ADS)

Li, Zhifu; Hu, Yueming; Li, Di

2016-08-01

For a class of linear discrete-time uncertain systems, a feedback feed-forward iterative learning control (ILC) scheme is proposed, which is comprised of an iterative learning controller and two current iteration feedback controllers. The iterative learning controller is used to improve the performance along the iteration direction and the feedback controllers are used to improve the performance along the time direction. First of all, the uncertain feedback feed-forward ILC system is presented by an uncertain two-dimensional Roesser model system. Then, two robust control schemes are proposed. One can ensure that the feedback feed-forward ILC system is bounded-input bounded-output stable along time direction, and the other can ensure that the feedback feed-forward ILC system is asymptotically stable along time direction. Both schemes can guarantee the system is robust monotonically convergent along the iteration direction. Third, the robust convergent sufficient conditions are given, which contains a linear matrix inequality (LMI). Moreover, the LMI can be used to determine the gain matrix of the feedback feed-forward iterative learning controller. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed schemes.

Identification of single-input-single-output quantum linear systems

NASA Astrophysics Data System (ADS)

Levitt, Matthew; GuÅ£ǎ, Mǎdǎlin

2017-03-01

The purpose of this paper is to investigate system identification for single-input-single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realization from sufficient input-output data? We show that for time-dependent inputs, the systems which cannot be distinguished are related by symplectic transformations acting on the space of system modes. This complements a previous result of Guţă and Yamamoto [IEEE Trans. Autom. Control 61, 921 (2016), 10.1109/TAC.2015.2448491] for passive linear systems. In the regime of stationary quantum noise input, the output is completely determined by the power spectrum. We define the notion of global minimality for a given power spectrum, and characterize globally minimal systems as those with a fully mixed stationary state. We show that in the case of systems with a cascade realization, the power spectrum completely fixes the transfer function, so the system can be identified up to a symplectic transformation. We give a method for constructing a globally minimal subsystem direct from the power spectrum. Restricting to passive systems the analysis simplifies so that identifiability may be completely understood from the eigenvalues of a particular system matrix.

Self-optimizing Pitch Control for Large Scale Wind Turbine Based on ADRC

NASA Astrophysics Data System (ADS)

Xia, Anjun; Hu, Guoqing; Li, Zheng; Huang, Dongxiao; Wang, Fengxiang

2018-01-01

Since wind turbine is a complex nonlinear and strong coupling system, traditional PI control method can hardly achieve good control performance. A self-optimizing pitch control method based on the active-disturbance-rejection control theory is proposed in this paper. A linear model of the wind turbine is derived by linearizing the aerodynamic torque equation and the dynamic response of wind turbine is transformed into a first-order linear system. An expert system is designed to optimize the amplification coefficient according to the pitch rate and the speed deviation. The purpose of the proposed control method is to regulate the amplification coefficient automatically and keep the variations of pitch rate and rotor speed in proper ranges. Simulation results show that the proposed pitch control method has the ability to modify the amplification coefficient effectively, when it is not suitable, and keep the variations of pitch rate and rotor speed in proper ranges

Magnetization of a quantum spin system induced by a linear polarized laser

NASA Astrophysics Data System (ADS)

Zvyagin, A. A.

2015-08-01

It is shown that a linear polarized laser can cause magnetization of a spin system with magnetic anisotropy, the distinguished axis of which is perpendicular to the polarization of the laser field. In the dynamical regime the magnetization oscillates around the nonzero value determined by the parameters of the system. Oscillations have the frequency of the laser field, modulated by the lower Rabi-like frequencies. In the steady-state regime, for a large time scale greater than the characteristic relaxation time, the Rabi-like oscillations are damped, and the magnetization oscillates with the frequency of the laser field around the value which is determined by the relaxation rate also. Analytic results are presented for the spin-1/2 chain. The most direct manifestation of such a behavior can be observed in spin-1/2 Ising chain materials if the linear polarization of the laser field is chosen to be perpendicular to the Ising axis.

Integrated Control Modeling for Propulsion Systems Using NPSS

NASA Technical Reports Server (NTRS)

Parker, Khary I.; Felder, James L.; Lavelle, Thomas M.; Withrow, Colleen A.; Yu, Albert Y.; Lehmann, William V. A.

2004-01-01

The Numerical Propulsion System Simulation (NPSS), an advanced engineering simulation environment used to design and analyze aircraft engines, has been enhanced by integrating control development tools into it. One of these tools is a generic controller interface that allows NPSS to communicate with control development software environments such as MATLAB and EASY5. The other tool is a linear model generator (LMG) that gives NPSS the ability to generate linear, time-invariant state-space models. Integrating these tools into NPSS enables it to be used for control system development. This paper will discuss the development and integration of these tools into NPSS. In addition, it will show a comparison of transient model results of a generic, dual-spool, military-type engine model that has been implemented in NPSS and Simulink. It will also show the linear model generator s ability to approximate the dynamics of a nonlinear NPSS engine model.

Photocathode device that replenishes photoemissive coating

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

Moody, Nathan A.; Lizon, David C.

2016-06-14

A photocathode device may replenish its photoemissive coating to replace coating material that desorbs/evaporates during photoemission. A linear actuator system may regulate the release of a replenishment material vapor, such as an alkali metal, from a chamber inside the photocathode device to a porous cathode substrate. The replenishment material deposits on the inner surface of a porous membrane and effuses through the membrane to the outer surface, where it replenishes the photoemissive coating. The rate of replenishment of the photoemissive coating may be adjusted using the linear actuator system to regulate performance of the photocathode device during photoemission. Alternatively, themore » linear actuator system may adjust a plasma discharge gap between a cartridge containing replenishment material and a metal grid. A potential is applied between the cartridge and the grid, resulting in ejection of metal ions from the cartridge that similarly replenish the photoemissive coating.« less

Robust consensus control with guaranteed rate of convergence using second-order Hurwitz polynomials

NASA Astrophysics Data System (ADS)

Fruhnert, Michael; Corless, Martin

2017-10-01

This paper considers homogeneous networks of general, linear time-invariant, second-order systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilisable. We show that consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. To achieve this, we provide a new and simple derivation of the conditions for a second-order polynomial with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback.

Computation of output feedback gains for linear stochastic systems using the Zangnill-Powell Method

NASA Technical Reports Server (NTRS)

Kaufman, H.

1975-01-01

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Linear quadratic servo control of a reusable rocket engine

NASA Technical Reports Server (NTRS)

Musgrave, Jeffrey L.

1991-01-01

A design method for a servo compensator is developed in the frequency domain using singular values. The method is applied to a reusable rocket engine. An intelligent control system for reusable rocket engines was proposed which includes a diagnostic system, a control system, and an intelligent coordinator which determines engine control strategies based on the identified failure modes. The method provides a means of generating various linear multivariable controllers capable of meeting performance and robustness specifications and accommodating failure modes identified by the diagnostic system. Command following with set point control is necessary for engine operation. A Kalman filter reconstructs the state while loop transfer recovery recovers the required degree of robustness while maintaining satisfactory rejection of sensor noise from the command error. The approach is applied to the design of a controller for a rocket engine satisfying performance constraints in the frequency domain. Simulation results demonstrate the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation.

Development of a Bolometer Detector System for the NIST High Accuracy Infrared Spectrophotometer

PubMed Central

Zong, Y.; Datla, R. U.

1998-01-01

A bolometer detector system was developed for the high accuracy infrared spectrophotometer at the National Institute of Standards and Technology to provide maximum sensitivity, spatial uniformity, and linearity of response covering the entire infrared spectral range. The spatial response variation was measured to be within 0.1 %. The linearity of the detector output was measured over three decades of input power. After applying a simple correction procedure, the detector output was found to deviate less than 0.2 % from linear behavior over this range. The noise equivalent power (NEP) of the bolometer system was 6 × 10−12 W/Hz at the frequency of 80 Hz. The detector output 3 dB roll-off frequency was 200 Hz. The detector output was stable to within ± 0.05 % over a 15 min period. These results demonstrate that the bolometer detector system will serve as an excellent detector for the high accuracy infrared spectrophotometer. PMID:28009364

Tidal evolution of the Galilean satellites - A linearized theory

NASA Technical Reports Server (NTRS)

Greenberg, R.

1981-01-01

The Laplace resonance among the Galilean satellites Io, Europa, and Ganymede is traditionally reduced to a pendulum-like dynamical problem by neglecting short-period variations of several orbital elements. However, some of these variations that can now be neglected may once have had longer periods, comparable to the 'pendulum' period, if the system was formerly in deep resonance (pairs of periods even closer to the ratio 2:1 than they are now). In that case, the dynamical system cannot be reduced to fewer than nine dimensions. The nine-dimensional system is linearized here in order to study small variations about equilibrium. When tidal effects are included, the resulting evolution is substantially the same as was indicated by the pendulum approach, except that evolution out of deep resonance is found to be somewhat slower than suggested by extrapolation of the pendulum results. This slower rate helps support the hypothesis that the system may have evolved from deep resonance.

Rail Brake System Using a Linear Induction Motor for Dynamic Braking

NASA Astrophysics Data System (ADS)

Sakamoto, Yasuaki; Kashiwagi, Takayuki; Tanaka, Minoru; Hasegawa, Hitoshi; Sasakawa, Takashi; Fujii, Nobuo

One type of braking system for railway vehicles is the eddy current brake. Because this type of brake has the problem of rail heating, it has not been used for practical applications in Japan. Therefore, we proposed the use of a linear induction motor (LIM) for dynamic braking in eddy current brake systems. The LIM reduces rail heating and uses an inverter for self excitation. In this paper, we estimated the performance of an LIM from experimental results of a fundamental test machine and confirmed that the LIM generates an approximately constant braking force under constant current excitation. At relatively low frequencies, this braking force remains unaffected by frequency changes. The reduction ratio of rail heating is also approximately proportional to the frequency. We also confirmed that dynamic braking resulting in no electrical output can be used for drive control of the LIM. These characteristics are convenient for the realization of the LIM rail brake system.

A High-Order, Linear Time-Invariant Model for Application to Higher Harmonic Control and Flight Control System Interaction

NASA Technical Reports Server (NTRS)

Cheng, Rendy P.; Tischler, Mark B.; Celi, Roberto

2006-01-01

This research describes a new methodology for the extraction of a high-order, linear time invariant model, which allows the periodicity of the helicopter response to be accurately captured. This model provides the needed level of dynamic fidelity to permit an analysis and optimization of the AFCS and HHC algorithms. The key results of this study indicate that the closed-loop HHC system has little influence on the AFCS or on the vehicle handling qualities, which indicates that the AFCS does not need modification to work with the HHC system. However, the results show that the vibration response to maneuvers must be considered during the HHC design process, and this leads to much higher required HHC loop crossover frequencies. This research also demonstrates that the transient vibration responses during maneuvers can be reduced by optimizing the closed-loop higher harmonic control algorithm using conventional control system analyses.

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.

Controlling the Size and Shape of the Elastin-Like Polypeptide based Micelles

NASA Astrophysics Data System (ADS)

Streletzky, Kiril; Shuman, Hannah; Maraschky, Adam; Holland, Nolan

Elastin-like polypeptide (ELP) trimer constructs make reliable environmentally responsive micellar systems because they exhibit a controllable transition from being water-soluble at low temperatures to aggregating at high temperatures. It has been shown that depending on the specific details of the ELP design (length of the ELP chain, pH and salt concentration) micelles can vary in size and shape between spherical micelles with diameter 30-100 nm to elongated particles with an aspect ratio of about 10. This makes ELP trimers a convenient platform for developing potential drug delivery and bio-sensing applications as well as for understanding micelle formation in ELP systems. Since at a given salt concentration, the headgroup area for each foldon should be constant, the size of the micelles is expected to be proportional to the volume of the linear ELP available per foldon headgroup. Therefore, adding linear ELPs to a system of ELP-foldon should result in changes of the micelle volume allowing to control micelle size and possibly shape. The effects of addition of linear ELPs on size, shape, and molecular weight of micelles at different salt concentrations were studied by a combination of Dynamic Light Scattering and Static Light Scattering. The initial results on 50 µM ELP-foldon samples (at low salt) show that Rh of mixed micelles increases more than 5-fold as the amount of linear ELP raised from 0 to 50 µM. It was also found that a given mixture of linear and trimer constructs has two temperature-based transitions and therefore displays three predominant size regimes.

Decentralization, stabilization, and estimation of large-scale linear systems

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Vukcevic, M. B.

1976-01-01

In this short paper we consider three closely related aspects of large-scale systems: decentralization, stabilization, and estimation. A method is proposed to decompose a large linear system into a number of interconnected subsystems with decentralized (scalar) inputs or outputs. The procedure is preliminary to the hierarchic stabilization and estimation of linear systems and is performed on the subsystem level. A multilevel control scheme based upon the decomposition-aggregation method is developed for stabilization of input-decentralized linear systems Local linear feedback controllers are used to stabilize each decoupled subsystem, while global linear feedback controllers are utilized to minimize the coupling effect among the subsystems. Systems stabilized by the method have a tolerance to a wide class of nonlinearities in subsystem coupling and high reliability with respect to structural perturbations. The proposed output-decentralization and stabilization schemes can be used directly to construct asymptotic state estimators for large linear systems on the subsystem level. The problem of dimensionality is resolved by constructing a number of low-order estimators, thus avoiding a design of a single estimator for the overall system.

LINEAR - DERIVATION AND DEFINITION OF A LINEAR AIRCRAFT MODEL

NASA Technical Reports Server (NTRS)

Duke, E. L.

1994-01-01

The Derivation and Definition of a Linear Model program, LINEAR, provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models. LINEAR was developed to provide a standard, documented, and verified tool to derive linear models for aircraft stability analysis and control law design. Linear system models define the aircraft system in the neighborhood of an analysis point and are determined by the linearization of the nonlinear equations defining vehicle dynamics and sensors. LINEAR numerically determines a linear system model using nonlinear equations of motion and a user supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. LINEAR is capable of extracting both linearized engine effects, such as net thrust, torque, and gyroscopic effects and including these effects in the linear system model. The point at which this linear model is defined is determined either by completely specifying the state and control variables, or by specifying an analysis point on a trajectory and directing the program to determine the control variables and the remaining state variables. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to provide easy selection of state, control, and observation variables to be used in a particular model. Thus, the order of the system model is completely under user control. Further, the program provides the flexibility of allowing alternate formulations of both the state and observation equations. Data describing the aircraft and the test case is input to the program through a terminal or formatted data files. All data can be modified interactively from case to case. The aerodynamic model can be defined in two ways: a set of nondimensional stability and control derivatives for the flight point of interest, or a full non-linear aerodynamic model as used in simulations. LINEAR is written in FORTRAN and has been implemented on a DEC VAX computer operating under VMS with a virtual memory requirement of approximately 296K of 8 bit bytes. Both an interactive and batch version are included. LINEAR was developed in 1988.

Introducing linear functions: an alternative statistical approach

NASA Astrophysics Data System (ADS)

Nolan, Caroline; Herbert, Sandra

2015-12-01

The introduction of linear functions is the turning point where many students decide if mathematics is useful or not. This means the role of parameters and variables in linear functions could be considered to be `threshold concepts'. There is recognition that linear functions can be taught in context through the exploration of linear modelling examples, but this has its limitations. Currently, statistical data is easily attainable, and graphics or computer algebra system (CAS) calculators are common in many classrooms. The use of this technology provides ease of access to different representations of linear functions as well as the ability to fit a least-squares line for real-life data. This means these calculators could support a possible alternative approach to the introduction of linear functions. This study compares the results of an end-of-topic test for two classes of Australian middle secondary students at a regional school to determine if such an alternative approach is feasible. In this study, test questions were grouped by concept and subjected to concept by concept analysis of the means of test results of the two classes. This analysis revealed that the students following the alternative approach demonstrated greater competence with non-standard questions.

Bullous dermatosis associated with vancomycin extravasation.

PubMed

Bohm, Nicole M; Wong, Jeffrey G

2012-02-01

Cutaneous side effects related to vancomycin therapy have been reported including histamine-related reactions, linear IgA bullous dermatosis, Stevens-Johnson syndrome, maculopapular rash and drug rash with eosinophilia and systemic symptoms. In all instances, these reports were due to the systemic administration of vancomycin and subsequent immunological reactions to the medication. Drug extravasation into soft tissues can result in a variety of clinical outcomes usually related to physiochemical properties of the drug extravasated and its diluents or pharmacologic effects on the vasculature and tissue. The authors report a patient who experienced vancomycin extravasation that resulted in a localized bullous eruption resembling linear IgA bullous dermatosis, a phenomenon not previously described in the literature.

Parallel computation using boundary elements in solid mechanics

NASA Technical Reports Server (NTRS)

Chien, L. S.; Sun, C. T.

1990-01-01

The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.

Structural and lithologic study of northern coast ranges and Sacramento Valley, California

NASA Technical Reports Server (NTRS)

Rich, E. I. (Principal Investigator)

1973-01-01

The author has identified the following significant results. The pattern of linear systems within the project area has been extended into the western foothill belt of the Sierra Nevada. The chief pattern of linear features in the western Sierran foothill belt trends about N. 10 - 15 deg W., but in the vicinity of the Feather River the trend of the features abruptly changes to about N. 50-60 deg W and appears to be contiguous across the Sacramento Valley with a similar system of linear features in the Coast Ranges. The linear features in the Modoc Plateau and Klamath Mt. areas appear unrelated to the systems detected in the Coast Ranges of Sierran foothill belt. Although the change in trend of the Sierran structural features has been previously suggested and the interrelationship of the Klamath Mt. region with the northern Sierra Nevadas has been postulated, the data obtained from the ERTS-1 imagery strengthens these notions and provides for the first time evidence of a direct connection of the structural trends within the alluviated part of the Sacramento Valley. In addition rocks of Pleistocene and Holocene age are offset by some of the linear features seen on ERTS-1 imagery and hence may record the latest episode of geologic deformation in north-central California.

On analyticity of linear waves scattered by a layered medium

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

Application of Nearly Linear Solvers to Electric Power System Computation

NASA Astrophysics Data System (ADS)

Grant, Lisa L.

To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

Dual solutions of three-dimensional flow and heat transfer over a non-linearly stretching/shrinking sheet

NASA Astrophysics Data System (ADS)

Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan

2018-05-01

This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.

A scaling theory for linear systems

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Krishnaprasad, P. S.

1980-01-01

A theory of scaling for rational (transfer) functions in terms of transformation groups is developed. Two different four-parameter scaling groups which play natural roles in studying linear systems are identified and the effect of scaling on Fisher information and related statistical measures in system identification are studied. The scalings considered include change of time scale, feedback, exponential scaling, magnitude scaling, etc. The scaling action of the groups studied is tied to the geometry of transfer functions in a rather strong way as becomes apparent in the examination of the invariants of scaling. As a result, the scaling process also provides new insight into the parameterization question for rational functions.

Observability Analysis of a Matrix Kalman Filter-Based Navigation System Using Visual/Inertial/Magnetic Sensors

PubMed Central

Feng, Guohu; Wu, Wenqi; Wang, Jinling

2012-01-01

A matrix Kalman filter (MKF) has been implemented for an integrated navigation system using visual/inertial/magnetic sensors. The MKF rearranges the original nonlinear process model in a pseudo-linear process model. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system is observable. It has been proved that such observability conditions are: (a) at least one degree of rotational freedom is excited, and (b) at least two linearly independent horizontal lines and one vertical line are observed. Experimental results have validated the correctness of these observability conditions. PMID:23012523

Linear laser diode arrays for improvement in optical disk recording for space stations

NASA Technical Reports Server (NTRS)

Alphonse, G. A.; Carlin, D. B.; Connolly, J. C.

1990-01-01

The design and fabrication of individually addressable laser diode arrays for high performance magneto-optic recording systems are presented. Ten diode arrays with 30 mW cW light output, linear light vs. current characteristics and single longitudinal mode spectrum were fabricated using channel substrate planar (CSP) structures. Preliminary results on the inverse CSP structure, whose fabrication is less critically dependent on device parameters than the CSP, are also presented. The impact of systems parameters and requirements, in particular, the effect of feedback on laser design is assessed, and techniques to reduce feedback or minimize its effect on systems performance, including mode-stabilized structures, are evaluated.

Modern digital flight control system design for VTOL aircraft

NASA Technical Reports Server (NTRS)

Broussard, J. R.; Berry, P. W.; Stengel, R. F.

1979-01-01

Methods for and results from the design and evaluation of a digital flight control system (DFCS) for a CH-47B helicopter are presented. The DFCS employed proportional-integral control logic to provide rapid, precise response to automatic or manual guidance commands while following conventional or spiral-descent approach paths. It contained altitude- and velocity-command modes, and it adapted to varying flight conditions through gain scheduling. Extensive use was made of linear systems analysis techniques. The DFCS was designed, using linear-optimal estimation and control theory, and the effects of gain scheduling are assessed by examination of closed-loop eigenvalues and time responses.

Study on the characters of control valve for ammonia injection in selective catalytic reduction (SCR) system of coal-fired power plant

NASA Astrophysics Data System (ADS)

Yao, Che; Li, Tao; Zhang, Hong; Zhou, Yanming

2017-08-01

In this paper, the characters of two control valves used for ammonia injection in SCR system are discussed. The linear/quadratic character between pressure drop/outlet flow rate and valve opening/dynamic pressure inlet are investigated using computational fluid dynamic (CFD) and response surface analysis (RSA) methods. The results show that the linear character of brake valve is significantly better than butterfly valve, which means that the brake valve is more suitable for ammonia injection adjustment than the butterfly valve.

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

NASA Technical Reports Server (NTRS)

Ghosh, Amitabha

1997-01-01

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunnel. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally some results of the current investigation are presented.

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

NASA Technical Reports Server (NTRS)

Ghosh, Amitabha

1997-01-01

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunell. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally, some results of the current investigation are presented.

Efficient loads analyses of Shuttle-payloads using dynamic models with linear or nonlinear interfaces

NASA Technical Reports Server (NTRS)

Spanos, P. D.; Cao, T. T.; Hamilton, D. A.; Nelson, D. A. R.

1989-01-01

An efficient method for the load analysis of Shuttle-payload systems with linear or nonlinear attachment interfaces is presented which allows the kinematics of the interface degrees of freedom at a given time to be evaluated without calculating the combined system modal representation of the Space Shuttle and its payload. For the case of a nonlinear dynamic model, an iterative procedure is employed to converge the nonlinear terms of the equations of motion to reliable values. Results are presented for a Shuttle abort landing event.

Comparison of linear and nonlinear models for coherent hemodynamics spectroscopy (CHS)

NASA Astrophysics Data System (ADS)

Sassaroli, Angelo; Kainerstorfer, Jana; Fantini, Sergio

2015-03-01

A recently proposed linear time-invariant hemodynamic model for coherent hemodynamics spectroscopy1 (CHS) relates the tissue concentrations of oxy- and deoxy-hemoglobin (outputs of the system) to given dynamics of the tissue blood volume, blood flow and rate constant of oxygen diffusion (inputs of the system). This linear model was derived in the limit of "small" perturbations in blood flow velocity. We have extended this model to a more general model (which will be referred to as the nonlinear extension to the original model) that yields the time-dependent changes of oxy and deoxy-hemoglobin concentrations in response to arbitrary dynamic changes in capillary blood flow velocity. The nonlinear extension to the model relies on a general solution of the partial differential equation that governs the spatio-temporal behavior of oxygen saturation of hemoglobin in capillaries and venules on the basis of dynamic (or time resolved) blood transit time. We show preliminary results where the CHS spectra obtained from the linear and nonlinear models are compared to quantify the limits of applicability of the linear model.

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

Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modularmore » In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.« less

A dynamic model of the human postural control system

NASA Technical Reports Server (NTRS)

Hill, J. C.

1972-01-01

A digital simulation of the pitch axis dynamics of a stick man of figures is described. Difficulties encountered in linearizing the equations of motion are discussed; the conclusion reached is that a completely linear simulation is of such restricted validity that only a nonlinear simulation is of any practical use. Typical simulation results obtained from the full nonlinear model are presented.

A dynamic model of the human postural control system.

NASA Technical Reports Server (NTRS)

Hill, J. C.

1971-01-01

Description of a digital simulation of the pitch axis dynamics of a stick man. The difficulties encountered in linearizing the equations of motion are discussed; the conclusion reached is that a completely linear simulation is of such restricted validity that only a nonlinear simulation is of any practical use. Typical simulation results obtained from the full nonlinear model are illustrated.

A Study on Linear Programming Applications for the Optimization of School Lunch Menus. Summation Report.

ERIC Educational Resources Information Center

Findorff, Irene K.

This document summarizes the results of a project at Tulane University that was designed to adapt, test, and evaluate a computerized information and menu planning system utilizing linear programing techniques for use in school lunch food service operations. The objectives of the menu planning were to formulate menu items into a palatable,…

Stochastic stability properties of jump linear systems

NASA Technical Reports Server (NTRS)

Feng, Xiangbo; Loparo, Kenneth A.; Ji, Yuandong; Chizeck, Howard J.

1992-01-01

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.

Dissipative open systems theory as a foundation for the thermodynamics of linear systems.

PubMed

Delvenne, Jean-Charles; Sandberg, Henrik

2017-03-06

In this paper, we advocate the use of open dynamical systems, i.e. systems sharing input and output variables with their environment, and the dissipativity theory initiated by Jan Willems as models of thermodynamical systems, at the microscopic and macroscopic level alike. We take linear systems as a study case, where we show how to derive a global Lyapunov function to analyse networks of interconnected systems. We define a suitable notion of dynamic non-equilibrium temperature that allows us to derive a discrete Fourier law ruling the exchange of heat between lumped, discrete-space systems, enriched with the Maxwell-Cattaneo correction. We complete these results by a brief recall of the steps that allow complete derivation of the dissipation and fluctuation in macroscopic systems (i.e. at the level of probability distributions) from lossless and deterministic systems.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Inclusion of Linearized Moist Physics in Nasa's Goddard Earth Observing System Data Assimilation Tools

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Errico, Ronald; Gelaro, Ronaldo; Kim, Jong G.

2013-01-01

Inclusion of moist physics in the linearized version of a weather forecast model is beneficial in terms of variational data assimilation. Further, it improves the capability of important tools, such as adjoint-based observation impacts and sensitivity studies. A linearized version of the relaxed Arakawa-Schubert (RAS) convection scheme has been developed and tested in NASA's Goddard Earth Observing System data assimilation tools. A previous study of the RAS scheme showed it to exhibit reasonable linearity and stability. This motivates the development of a linearization of a near-exact version of the RAS scheme. Linearized large-scale condensation is included through simple conversion of supersaturation into precipitation. The linearization of moist physics is validated against the full nonlinear model for 6- and 24-h intervals, relevant to variational data assimilation and observation impacts, respectively. For a small number of profiles, sudden large growth in the perturbation trajectory is encountered. Efficient filtering of these profiles is achieved by diagnosis of steep gradients in a reduced version of the operator of the tangent linear model. With filtering turned on, the inclusion of linearized moist physics increases the correlation between the nonlinear perturbation trajectory and the linear approximation of the perturbation trajectory. A month-long observation impact experiment is performed and the effect of including moist physics on the impacts is discussed. Impacts from moist-sensitive instruments and channels are increased. The effect of including moist physics is examined for adjoint sensitivity studies. A case study examining an intensifying Northern Hemisphere Atlantic storm is presented. The results show a significant sensitivity with respect to moisture.

Interaction between mantle and crustal detachments: a non-linear system controlling lithospheric extension

NASA Astrophysics Data System (ADS)

Rosenbaum, G.; Regenauer-Lieb, K.; Weinberg, R. F.

2009-12-01

We use numerical modelling to investigate the development of crustal and mantle detachment faults during lithospheric extension. Our models simulate a wide range of rift systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles, which grow in response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation at different levels of the lithosphere. Crustal detachment faults are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW/m2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate (60-70 mW/m2) heat flow. Results show a non-linear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometime unexpected switches in extension modes (e.g. from diffuse rifting to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this non-linearity to result from the interference of doming wavelengths. Disharmony of crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonious crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged rifting history prior to continental breakup.

Robustness in linear quadratic feedback design with application to an aircraft control problem

NASA Technical Reports Server (NTRS)

Patel, R. V.; Sridhar, B.; Toda, M.

1977-01-01

Some new results concerning robustness and asymptotic properties of error bounds of a linear quadratic feedback design are applied to an aircraft control problem. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed based on Linear Quadratic (LQ) theory and the results developed in this paper. The variation of the error bounds to changes in the weighting matrices in the LQ design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable error bound for variations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.

Controllability in nonlinear systems

NASA Technical Reports Server (NTRS)

Hirschorn, R. M.

1975-01-01

An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

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

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Dynamic analysis and electronic circuit implementation of a novel 3D autonomous system without linear terms

NASA Astrophysics Data System (ADS)

Kengne, J.; Jafari, S.; Njitacke, Z. T.; Yousefi Azar Khanian, M.; Cheukem, A.

2017-11-01

Mathematical models (ODEs) describing the dynamics of almost all continuous time chaotic nonlinear systems (e.g. Lorenz, Rossler, Chua, or Chen system) involve at least a nonlinear term in addition to linear terms. In this contribution, a novel (and singular) 3D autonomous chaotic system without linear terms is introduced. This system has an especial feature of having two twin strange attractors: one ordinary and one symmetric strange attractor when the time is reversed. The complex behavior of the model is investigated in terms of equilibria and stability, bifurcation diagrams, Lyapunov exponent plots, time series and Poincaré sections. Some interesting phenomena are found including for instance, period-doubling bifurcation, antimonotonicity (i.e. the concurrent creation and annihilation of periodic orbits) and chaos while monitoring the system parameters. Compared to the (unique) case previously reported by Xu and Wang (2014) [31], the system considered in this work displays a more 'elegant' mathematical expression and experiences richer dynamical behaviors. A suitable electronic circuit (i.e. the analog simulator) is designed and used for the investigations. Pspice based simulation results show a very good agreement with the theoretical analysis.

Evaluation of Beckman Coulter DxI 800 immunoassay system using clinically oriented performance goals.

PubMed

Akbas, Neval; Schryver, Patricia G; Algeciras-Schimnich, Alicia; Baumann, Nikola A; Block, Darci R; Budd, Jeffrey R; Gaston, S J Stephen; Klee, George G

2014-11-01

We evaluated the analytical performance of 24 immunoassays using the Beckman Coulter DxI 800 immunoassay systems at Mayo Clinic, Rochester, MN for trueness, precision, detection limits, linearity, and consistency (across instruments and reagent lots). Clinically oriented performance goals were defined using the following methods: trueness-published desirable accuracy limits, precision-published desirable biologic variation; detection limits - 0.1 percentile of patient test values, linearity - 50% of total error, and consistency-percentage test values crossing key decision points. Local data were collected for precision, linearity, and consistency. Data were provided by Beckman Coulter, Inc. for trueness and detection limits. All evaluated assays except total thyroxine were within the proposed goals for trueness. Most of the assays met the proposed goals for precision (86% of intra-assay results and 75% of inter-assay results). Five assays had more than 15% of the test results below the minimum detection limits. Carcinoembryonic antigen, total thyroxine and free triiodothyronine exceeded the proposed goals of ±6.3%, ±5% and ±5.7% for dilution linearity. All evaluated assays were within the proposed goals for instrument consistency. Lot-to-lot consistency results for cortisol, ferritin and total thyroxine exceeded the proposed goals of 3.3%, 11.4% and 7% at one medical decision level, while vitamin B12 exceeded the proposed goals of 5.2% and 3.8% at two decision levels. The Beckman Coulter DxI 800 immunoassay system meets most of these proposed goals, even though these clinically focused performance goals represent relatively stringent limits. Copyright © 2014 The Canadian Society of Clinical Chemists. Published by Elsevier Inc. All rights reserved.

Linear Aerospike SR-71 Experiment (LASRE): Aerospace Propulsion Hazard Mitigation Systems

NASA Technical Reports Server (NTRS)

Mizukami, Masashi; Corpening, Griffin P.; Ray, Ronald J.; Hass, Neal; Ennix, Kimberly A.; Lazaroff, Scott M.

1998-01-01

A major hazard posed by the propulsion system of hypersonic and space vehicles is the possibility of fire or explosion in the vehicle environment. The hazard is mitigated by minimizing or detecting, in the vehicle environment, the three ingredients essential to producing fire: fuel, oxidizer, and an ignition source. The Linear Aerospike SR-71 Experiment (LASRE) consisted of a linear aerospike rocket engine integrated into one-half of an X-33-like lifting body shape, carried on top of an SR-71 aircraft. Gaseous hydrogen and liquid oxygen were used as propellants. Although LASRE is a one-of-a-kind experimental system, it must be rated for piloted flight, so this test presented a unique challenge. To help meet safety requirements, the following propulsion hazard mitigation systems were incorporated into the experiment: pod inert purge, oxygen sensors, a hydrogen leak detection algorithm, hydrogen sensors, fire detection and pod temperature thermocouples, water misting, and control room displays. These systems are described, and their development discussed. Analyses, ground test, and flight test results are presented, as are findings and lessons learned.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Adaptive Failure Compensation for Aircraft Flight Control Using Engine Differentials: Regulation

NASA Technical Reports Server (NTRS)

Yu, Liu; Xidong, Tang; Gang, Tao; Joshi, Suresh M.

2005-01-01

The problem of using engine thrust differentials to compensate for rudder and aileron failures in aircraft flight control is addressed in this paper in a new framework. A nonlinear aircraft model that incorporates engine di erentials in the dynamic equations is employed and linearized to describe the aircraft s longitudinal and lateral motion. In this model two engine thrusts of an aircraft can be adjusted independently so as to provide the control flexibility for rudder or aileron failure compensation. A direct adaptive compensation scheme for asymptotic regulation is developed to handle uncertain actuator failures in the linearized system. A design condition is specified to characterize the system redundancy needed for failure compensation. The adaptive regulation control scheme is applied to the linearized model of a large transport aircraft in which the longitudinal and lateral motions are coupled as the result of using engine thrust differentials. Simulation results are presented to demonstrate the effectiveness of the adaptive compensation scheme.

Vibration Control Using a State Observer that Considers Disturbances of a Golf Swing Robot

NASA Astrophysics Data System (ADS)

Hoshino, Yohei; Kobayashi, Yukinori; Yamada, Gen

In this paper, optimal control of a golf swing robot that is used to evaluate the performance of golf clubs is described. The robot has two joints, a rigid link and a flexible link that is a golf club. A mathematical model of the golf club is derived by Hamilton’s principle in consideration of bending and torsional stiffness and in consideration of eccentricity of the center of gravity of the club head on the shaft axis. A linear quadratic regulator (LQR) that considers the vibration of the club shaft is used to stop the robot during the follow-through. Since the robot moves fast and has strong non-linearity, an ordinary state observer for a linear system cannot accurately estimate the states of the system. A state observer that considers disturbances accurately estimates the state variables that cannot be measured. The results of numerical simulation are compared with experimental results obtained by using a swing robot.

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

NASA Astrophysics Data System (ADS)

Sinou, J.-J.; Thouverez, F.; Jezequel, L.

2003-08-01

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.

Linear quadratic optimization for positive LTI system

NASA Astrophysics Data System (ADS)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Noise studies of communication systems using the SYSTID computer aided analysis program

NASA Technical Reports Server (NTRS)

Tranter, W. H.; Dawson, C. T.

1973-01-01

SYSTID computer aided design is a simple program for simulating data systems and communication links. A trial of the efficiency of the method was carried out by simulating a linear analog communication system to determine its noise performance and by comparing the SYSTID result with the result arrived at by theoretical calculation. It is shown that the SYSTID program is readily applicable to the analysis of these types of systems.

Evaluation of different operating strategies to integrate storage in a linear Fresnel ORC power plant

NASA Astrophysics Data System (ADS)

Zoschke, Theda; Seubert, Bernhard; Fluri, Thomas

2017-06-01

An existing linear Fresnel power plant with ORC process located in Ben Guerir, Morocco, is retrofitted with a thermal energy storage system and additional collector loops. Two different plant configurations are investigated in this paper. In the first configuration two separate solar fields are built and only the minor one can charge the storage. In the second configuration, there is only one large solar field which offers more flexibility. Two different control strategies are assessed by comparing simulation results. It shows that the simulations of the systems with two solar fields results in higher energy yields throughout the year, but the power production of the system with one solar field is much more flexible and demand oriented. Also it offers great potential for improvement when it comes to weather forecasting.

Variationally consistent discretization schemes and numerical algorithms for contact problems

NASA Astrophysics Data System (ADS)

Wohlmuth, Barbara

We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of possible applications and show the performance of the space discretization scheme, non-linear solver, adaptive refinement process and time integration.

Optical analysis and thermal management of 2-cell strings linear concentrating photovoltaic system

NASA Astrophysics Data System (ADS)

Reddy, K. S.; Kamnapure, Nikhilesh R.

2015-09-01

This paper presents the optical and thermal analyses for a linear concentrating photovoltaic/thermal collector under different operating conditions. Linear concentrating photovoltaic system (CPV) consists of a highly reflective mirror, a receiver and semi-dual axis tracking mechanism. The CPV receiver embodies two strings of triple-junction cells (100 cells in each string) adhered to a mild steel circular tube mounted at the focal length of trough. This system provides 560 W of electricity and 1580 W of heat which needs to be dissipated by active cooling. The Al2O3/Water nanofluid is used as heat transfer fluid (HTF) flowing through circular receiver for CPV cells cooling. Optical analysis of linear CPV system with 3.35 m2 aperture and geometric concentration ratio (CR) of 35 is carried out using Advanced System Analysis Program (ASAP) an optical simulation tool. Non-uniform intensity distribution model of solar disk is used to model the sun in ASAP. The impact of random errors including slope error (σslope), tracking error (σtrack) and apparent change in sun's width (σsun) on optical performance of collector is shown. The result from the optical simulations shows the optical efficiency (ηo) of 88.32% for 2-cell string CPV concentrator. Thermal analysis of CPV receiver is carried out with conjugate heat transfer modeling in ANSYS FLUENT-14. Numerical simulations of Al2O3/Water nanofluid turbulent forced convection are performed for various parameters such as nanoparticle volume fraction (φ), Reynolds number (Re). The addition of the nanoparticle in water enhances the heat transfer in the ranges of 3.28% - 35.6% for φ = 1% - 6%. Numerical results are compared with literature data which shows the reasonable agreement.

SU-G-JeP3-09: Tumor Location Prediction Using Natural Respiratory Volume for Respiratory Gated Radiation Therapy (RGRT): System Verification Study

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

Kim, M; Jung, J; Yoon, D

Purpose: Respiratory gated radiation therapy (RGRT) gives accurate results when a patient’s breathing is stable and regular. Thus, the patient should be fully aware during respiratory pattern training before undergoing the RGRT treatment. In order to bypass the process of respiratory pattern training, we propose a target location prediction system for RGRT that uses only natural respiratory volume, and confirm its application. Methods: In order to verify the proposed target location prediction system, an in-house phantom set was used. This set involves a chest phantom including target, external markers, and motion generator. Natural respiratory volume signals were generated using themore » random function in MATLAB code. In the chest phantom, the target takes a linear motion based on the respiratory signal. After a four-dimensional computed tomography (4DCT) scan of the in-house phantom, the motion trajectory was derived as a linear equation. The accuracy of the linear equation was compared with that of the motion algorithm used by the operating motion generator. In addition, we attempted target location prediction using random respiratory volume values. Results: The correspondence rate of the linear equation derived from the 4DCT images with the motion algorithm of the motion generator was 99.41%. In addition, the average error rate of target location prediction was 1.23% for 26 cases. Conclusion: We confirmed the applicability of our proposed target location prediction system for RGRT using natural respiratory volume. If additional clinical studies can be conducted, a more accurate prediction system can be realized without requiring respiratory pattern training.« less

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

NASA Technical Reports Server (NTRS)

Molenaar, J.

1996-01-01

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Prediction uncertainty and data worth assessment for groundwater transport times in an agricultural catchment

NASA Astrophysics Data System (ADS)

Zell, Wesley O.; Culver, Teresa B.; Sanford, Ward E.

2018-06-01

Uncertainties about the age of base-flow discharge can have serious implications for the management of degraded environmental systems where subsurface pathways, and the ongoing release of pollutants that accumulated in the subsurface during past decades, dominate the water quality signal. Numerical groundwater models may be used to estimate groundwater return times and base-flow ages and thus predict the time required for stakeholders to see the results of improved agricultural management practices. However, the uncertainty inherent in the relationship between (i) the observations of atmospherically-derived tracers that are required to calibrate such models and (ii) the predictions of system age that the observations inform have not been investigated. For example, few if any studies have assessed the uncertainty of numerically-simulated system ages or evaluated the uncertainty reductions that may result from the expense of collecting additional subsurface tracer data. In this study we combine numerical flow and transport modeling of atmospherically-derived tracers with prediction uncertainty methods to accomplish four objectives. First, we show the relative importance of head, discharge, and tracer information for characterizing response times in a uniquely data rich catchment that includes 266 age-tracer measurements (SF6, CFCs, and 3H) in addition to long term monitoring of water levels and stream discharge. Second, we calculate uncertainty intervals for model-simulated base-flow ages using both linear and non-linear methods, and find that the prediction sensitivity vector used by linear first-order second-moment methods results in much larger uncertainties than non-linear Monte Carlo methods operating on the same parameter uncertainty. Third, by combining prediction uncertainty analysis with multiple models of the system, we show that data-worth calculations and monitoring network design are sensitive to variations in the amount of water leaving the system via stream discharge and irrigation withdrawals. Finally, we demonstrate a novel model-averaged computation of potential data worth that can account for these uncertainties in model structure.

Collision Based Blood Cell Distribution of the Blood Flow

NASA Astrophysics Data System (ADS)

Cinar, Yildirim

2003-11-01

Introduction: The goal of the study is the determination of the energy transferring process between colliding masses and the application of the results to the distribution of the cell, velocity and kinetic energy in arterial blood flow. Methods: Mathematical methods and models were used to explain the collision between two moving systems, and the distribution of linear momentum, rectilinear velocity, and kinetic energy in a collision. Results: According to decrease of mass of the second system, the velocity and momentum of constant mass of the first system are decreased, and linearly decreasing mass of the second system captures a larger amount of the kinetic energy and the rectilinear velocity of the collision system on a logarithmic scale. Discussion: The cause of concentration of blood cells at the center of blood flow an artery is not explained by Bernoulli principle alone but the kinetic energy and velocity distribution due to collision between the big mass of the arterial wall and the small mass of blood cells must be considered as well.

Linear-constraint wavefront control for exoplanet coronagraphic imaging systems

NASA Astrophysics Data System (ADS)

Sun, He; Eldorado Riggs, A. J.; Kasdin, N. Jeremy; Vanderbei, Robert J.; Groff, Tyler Dean

2017-01-01

A coronagraph is a leading technology for achieving high-contrast imaging of exoplanets in a space telescope. It uses a system of several masks to modify the diffraction and achieve extremely high contrast in the image plane around target stars. However, coronagraphic imaging systems are very sensitive to optical aberrations, so wavefront correction using deformable mirrors (DMs) is necessary to avoid contrast degradation in the image plane. Electric field conjugation (EFC) and Stroke minimization (SM) are two primary high-contrast wavefront controllers explored in the past decade. EFC minimizes the average contrast in the search areas while regularizing the strength of the control inputs. Stroke minimization calculates the minimum DM commands under the constraint that a target average contrast is achieved. Recently in the High Contrast Imaging Lab at Princeton University (HCIL), a new linear-constraint wavefront controller based on stroke minimization was developed and demonstrated using numerical simulation. Instead of only constraining the average contrast over the entire search area, the new controller constrains the electric field of each single pixel using linear programming, which could led to significant increases in speed of the wavefront correction and also create more uniform dark holes. As a follow-up of this work, another linear-constraint controller modified from EFC is demonstrated theoretically and numerically and the lab verification of the linear-constraint controllers is reported. Based on the simulation and lab results, the pros and cons of linear-constraint controllers are carefully compared with EFC and stroke minimization.

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Benchmarking a Soil Moisture Data Assimilation System for Agricultural Drought Monitoring

NASA Technical Reports Server (NTRS)

Hun, Eunjin; Crow, Wade T.; Holmes, Thomas; Bolten, John

2014-01-01

Despite considerable interest in the application of land surface data assimilation systems (LDAS) for agricultural drought applications, relatively little is known about the large-scale performance of such systems and, thus, the optimal methodological approach for implementing them. To address this need, this paper evaluates an LDAS for agricultural drought monitoring by benchmarking individual components of the system (i.e., a satellite soil moisture retrieval algorithm, a soil water balance model and a sequential data assimilation filter) against a series of linear models which perform the same function (i.e., have the same basic inputoutput structure) as the full system component. Benchmarking is based on the calculation of the lagged rank cross-correlation between the normalized difference vegetation index (NDVI) and soil moisture estimates acquired for various components of the system. Lagged soil moistureNDVI correlations obtained using individual LDAS components versus their linear analogs reveal the degree to which non-linearities andor complexities contained within each component actually contribute to the performance of the LDAS system as a whole. Here, a particular system based on surface soil moisture retrievals from the Land Parameter Retrieval Model (LPRM), a two-layer Palmer soil water balance model and an Ensemble Kalman filter (EnKF) is benchmarked. Results suggest significant room for improvement in each component of the system.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Formal methods for modeling and analysis of hybrid systems

NASA Technical Reports Server (NTRS)

Tiwari, Ashish (Inventor); Lincoln, Patrick D. (Inventor)

2009-01-01

A technique based on the use of a quantifier elimination decision procedure for real closed fields and simple theorem proving to construct a series of successively finer qualitative abstractions of hybrid automata is taught. The resulting abstractions are always discrete transition systems which can then be used by any traditional analysis tool. The constructed abstractions are conservative and can be used to establish safety properties of the original system. The technique works on linear and non-linear polynomial hybrid systems: the guards on discrete transitions and the continuous flows in all modes can be specified using arbitrary polynomial expressions over the continuous variables. An exemplar tool in the SAL environment built over the theorem prover PVS is detailed. The technique scales well to large and complex hybrid systems.

Contrast changes in fluoroscopic imaging systems and statistical variations of these changes

NASA Technical Reports Server (NTRS)

Bailey, N. A.

1973-01-01

Experimental studies have indicated that: (1) The response of digitized fluoroscopic imaging systems is linear systems is linear with contrast over a rather wide range of absorber and cavity thicknesses. (2) Contrast changes associated with the addition of aluminum, iodine containing contrast agents and air of thicknesses 1mm or less can be detected with a 95% confidence level. (3) The standard deviation associated with such determination using clinically available X-ray generators and video disc recording is less than 1 percent. A large flat screen X-ray image intensifier has been constructed and some preliminary results obtained. Sensitivity achieved makes dose reduction a factor often greater than previously reported for a system using a conventional X-ray image intensifier.

Electronic Non-Contacting Linear Position Measuring System

DOEpatents

Post, Richard F.

2005-06-14

A non-contacting linear position location system employs a special transmission line to encode and transmit magnetic signals to a receiver on the object whose position is to be measured. The invention is useful as a non-contact linear locator of moving objects, e.g., to determine the location of a magnetic-levitation train for the operation of the linear-synchronous motor drive system.

Analysis of Nonlinear Dynamics in Linear Compressors Driven by Linear Motors

NASA Astrophysics Data System (ADS)

Chen, Liangyuan

2018-03-01

The analysis of dynamic characteristics of the mechatronics system is of great significance for the linear motor design and control. Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically based on the linearized and nonlinear models. First, the influence factors considering the nonlinear gas force load were analyzed. Then, a simple linearized model was set up to analyze the influence on the stroke and resonance frequency. Finally, the nonlinear model was set up to analyze the effects of piston mass, spring stiffness, driving force as an example of design parameter variation. The simulating results show that the stroke can be obtained by adjusting the excitation amplitude, frequency and other adjustments, the equilibrium position can be adjusted by adjusting the DC input, and to make the more efficient operation, the operating frequency must always equal to the resonance frequency.

The determination of third order linear models from a seventh order nonlinear jet engine model

NASA Technical Reports Server (NTRS)

Lalonde, Rick J.; Hartley, Tom T.; De Abreu-Garcia, J. Alex

1989-01-01

Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.

A Differential Monolithically Integrated Inductive Linear Displacement Measurement Microsystem

PubMed Central

Podhraški, Matija; Trontelj, Janez

2016-01-01

An inductive linear displacement measurement microsystem realized as a monolithic Application-Specific Integrated Circuit (ASIC) is presented. The system comprises integrated microtransformers as sensing elements, and analog front-end electronics for signal processing and demodulation, both jointly fabricated in a conventional commercially available four-metal 350-nm CMOS process. The key novelty of the presented system is its full integration, straightforward fabrication, and ease of application, requiring no external light or magnetic field source. Such systems therefore have the possibility of substituting certain conventional position encoder types. The microtransformers are excited by an AC signal in MHz range. The displacement information is modulated into the AC signal by a metal grating scale placed over the microsystem, employing a differential measurement principle. Homodyne mixing is used for the demodulation of the scale displacement information, returned by the ASIC as a DC signal in two quadrature channels allowing the determination of linear position of the target scale. The microsystem design, simulations, and characterization are presented. Various system operating conditions such as frequency, phase, target scale material and distance have been experimentally evaluated. The best results have been achieved at 4 MHz, demonstrating a linear resolution of 20 µm with steel and copper scale, having respective sensitivities of 0.71 V/mm and 0.99 V/mm. PMID:26999146

A Differential Monolithically Integrated Inductive Linear Displacement Measurement Microsystem.

PubMed

Podhraški, Matija; Trontelj, Janez

2016-03-17

An inductive linear displacement measurement microsystem realized as a monolithic Application-Specific Integrated Circuit (ASIC) is presented. The system comprises integrated microtransformers as sensing elements, and analog front-end electronics for signal processing and demodulation, both jointly fabricated in a conventional commercially available four-metal 350-nm CMOS process. The key novelty of the presented system is its full integration, straightforward fabrication, and ease of application, requiring no external light or magnetic field source. Such systems therefore have the possibility of substituting certain conventional position encoder types. The microtransformers are excited by an AC signal in MHz range. The displacement information is modulated into the AC signal by a metal grating scale placed over the microsystem, employing a differential measurement principle. Homodyne mixing is used for the demodulation of the scale displacement information, returned by the ASIC as a DC signal in two quadrature channels allowing the determination of linear position of the target scale. The microsystem design, simulations, and characterization are presented. Various system operating conditions such as frequency, phase, target scale material and distance have been experimentally evaluated. The best results have been achieved at 4 MHz, demonstrating a linear resolution of 20 µm with steel and copper scale, having respective sensitivities of 0.71 V/mm and 0.99 V/mm.

Nonequilibrium molecular dynamics study of ring polymer melts under shear and elongation flows: A comparison with their linear analogs

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

Yoon, Jeongha; Kim, Jinseong; Baig, Chunggi, E-mail: cbaig@unist.ac.kr

We present detailed results for the structural and rheological properties of unknotted and unconcatenated ring polyethylene (PE) melts under shear and elongation flows via direct atomistic nonequilibrium molecular dynamics simulations. Short (C{sub 78}H{sub 156}) and long (C{sub 400}H{sub 800}) ring PE melts were subjected to planar Couette flow (PCF) and planar elongational flow (PEF) across a wide range of strain rates from linear to highly nonlinear flow regimes. The results are analyzed in detail through a direct comparison with those of the corresponding linear polymers. We found that, in comparison to their linear analogs, ring melts possess rather compact chainmore » structures at or near the equilibrium state and exhibit a considerably lesser degree of structural deformation with respect to the applied flow strength under both PCF and PEF. The large structural resistance of ring polymers against an external flow field is attributed to the intrinsic closed-loop configuration of the ring and the topological constraint of nonconcatenation between ring chains in the melt. As a result, there appears to be a substantial discrepancy between ring and linear systems in terms of their structural and rheological properties such as chain orientation, the distribution of chain dimensions, viscosity, flow birefringence, hydrostatic pressure, the pair correlation function, and potential interaction energies. The findings and conclusions drawn in this work would be a useful guide in future exploration of the characteristic dynamical and relaxation mechanisms of ring polymers in bulk or confined systems under flowing conditions.« less

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

ORACLS: A system for linear-quadratic-Gaussian control law design

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1978-01-01

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

NASA Astrophysics Data System (ADS)

Antown, Fadi; Dragičević, Davor; Froyland, Gary

2018-03-01

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

Formation of Linear Gradient of Antibiotics on Microfluidic Chips for High-throughput Antibiotic Susceptibility Testing

NASA Astrophysics Data System (ADS)

Kim, Seunggyu; Lee, Seokhun; Jeon, Jessie S.

2017-11-01

To determine the most effective antimicrobial treatments of infectious pathogen, high-throughput antibiotic susceptibility test (AST) is critically required. However, the conventional AST requires at least 16 hours to reach the minimum observable population. Therefore, we developed a microfluidic system that allows maintenance of linear antibiotic concentration and measurement of local bacterial density. Based on the Stokes-Einstein equation, the flow rate in the microchannel was optimized so that linearization was achieved within 10 minutes, taking into account the diffusion coefficient of each antibiotic in the agar gel. As a result, the minimum inhibitory concentration (MIC) of each antibiotic against P. aeruginosa could be immediately determined 6 hours after treatment of the linear antibiotic concentration. In conclusion, our system proved the efficacy of a high-throughput AST platform through MIC comparison with Clinical and Laboratory Standards Institute (CLSI) range of antibiotics. This work was supported by the Climate Change Research Hub (Grant No. N11170060) of the KAIST and by the Brain Korea 21 Plus project.

Applying linear programming to estimate fluxes in ecosystems or food webs: An example from the herpetological assemblage of the freshwater Everglades

USGS Publications Warehouse

Diffendorfer, James E.; Richards, Paul M.; Dalrymple, George H.; DeAngelis, Donald L.

2001-01-01

We present the application of Linear Programming for estimating biomass fluxes in ecosystem and food web models. We use the herpetological assemblage of the Everglades as an example. We developed food web structures for three common Everglades freshwater habitat types: marsh, prairie, and upland. We obtained a first estimate of the fluxes using field data, literature estimates, and professional judgment. Linear programming was used to obtain a consistent and better estimate of the set of fluxes, while maintaining mass balance and minimizing deviations from point estimates. The results support the view that the Everglades is a spatially heterogeneous system, with changing patterns of energy flux, species composition, and biomasses across the habitat types. We show that a food web/ecosystem perspective, combined with Linear Programming, is a robust method for describing food webs and ecosystems that requires minimal data, produces useful post-solution analyses, and generates hypotheses regarding the structure of energy flow in the system.

Joint Services Electronics Program.

DTIC Science & Technology

1983-09-30

environment. The research is under three interrelated heads: (1) algebraic Methodologies for Control Systems design , both linear and non -linear, (2) robust...properties of the device. After study of these experimental results, we plan to design a millimeter- wave version of the Gunn device. This will...appropriate dose discretization level for an adju- stable width beam. 2) Experimental Device Fabrication In a collaborative effort with the IC design group

Mass Optimization of Battery/Supercapacitors Hybrid Systems Based on a Linear Programming Approach

NASA Astrophysics Data System (ADS)

Fleury, Benoit; Labbe, Julien

2014-08-01

The objective of this paper is to show that, on a specific launcher-type mission profile, a 40% gain of mass is expected using a battery/supercapacitors active hybridization instead of a single battery solution. This result is based on the use of a linear programming optimization approach to perform the mass optimization of the hybrid power supply solution.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1989-01-01

transform provides a linearization.’ Well known systems include the Kadomtsev - Petviashvili , Davey-Stewartson and Self-Dual Yang-Mills equations . The d...which employs inverse scattering theory in order to linearize the given nonlinear equation . I.S.T. has led to new developments in both fields: inverse...scattering and nonlinear wave equations . Listed below are some of the problems studied and a short description of results. - Multidimensional

Linear and Logarithmic Speed-Accuracy Trade-Offs in Reciprocal Aiming Result from Task-Specific Parameterization of an Invariant Underlying Dynamics

ERIC Educational Resources Information Center

Bongers, Raoul M.; Fernandez, Laure; Bootsma, Reinoud J.

2009-01-01

The authors examined the origins of linear and logarithmic speed-accuracy trade-offs from a dynamic systems perspective on motor control. In each experiment, participants performed 2 reciprocal aiming tasks: (a) a velocity-constrained task in which movement time was imposed and accuracy had to be maximized, and (b) a distance-constrained task in…

Using Kalman Filters to Reduce Noise from RFID Location System

PubMed Central

Xavier, José; Reis, Luís Paulo; Petry, Marcelo

2014-01-01

Nowadays, there are many technologies that support location systems involving intrusive and nonintrusive equipment and also varying in terms of precision, range, and cost. However, the developers some time neglect the noise introduced by these systems, which prevents these systems from reaching their full potential. Focused on this problem, in this research work a comparison study between three different filters was performed in order to reduce the noise introduced by a location system based on RFID UWB technology with an associated error of approximately 18 cm. To achieve this goal, a set of experiments was devised and executed using a miniature train moving at constant velocity in a scenario with two distinct shapes—linear and oval. Also, this train was equipped with a varying number of active tags. The obtained results proved that the Kalman Filter achieved better results when compared to the other two filters. Also, this filter increases the performance of the location system by 15% and 12% for the linear and oval paths respectively, when using one tag. For a multiple tags and oval shape similar results were obtained (11–13% of improvement). PMID:24592186

Optimization of damping in the passive automotive suspension system with using two quarter-car models

NASA Astrophysics Data System (ADS)

Lozia, Z.; Zdanowicz, P.

2016-09-01

The paper presents the optimization of damping in the passive suspension system of a motor vehicle moving rectilinearly with a constant speed on a road with rough surface of random irregularities, described according to the ISO classification. Two quarter-car 2DoF models, linear and non-linear, were used; in the latter, nonlinearities of spring characteristics of the suspension system and pneumatic tyres, sliding friction in the suspension system, and wheel lift-off were taken into account. The smoothing properties of vehicle tyres were represented in both models. The calculations were carried out for three roads of different quality, with simulating four vehicle speeds. Statistical measures of vertical vehicle body vibrations and of changes in the vertical tyre/road contact force were used as the criteria of system optimization and model comparison. The design suspension displacement limit was also taken into account. The optimum suspension damping coefficient was determined and the impact of undesirable sliding friction in the suspension system on the calculation results was estimated. The results obtained make it possible to evaluate the impact of the structure and complexity of the model used on the results of the optimization.

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

Dynamic modelling and simulation of linear Fresnel solar field model based on molten salt heat transfer fluid

NASA Astrophysics Data System (ADS)

Hakkarainen, Elina; Tähtinen, Matti

2016-05-01

Demonstrations of direct steam generation (DSG) in linear Fresnel collectors (LFC) have given promising results related to higher steam parameters compared to the current state-of-the-art parabolic trough collector (PTC) technology using oil as heat transfer fluid (HTF). However, DSG technology lacks feasible solution for long-term thermal energy storage (TES) system. This option is important for CSP technology in order to offer dispatchable power. Recently, molten salts have been proposed to be used as HTF and directly as storage medium in both line-focusing solar fields, offering storage capacity of several hours. This direct molten salt (DMS) storage concept has already gained operational experience in solar tower power plant, and it is under demonstration phase both in the case of LFC and PTC systems. Dynamic simulation programs offer a valuable effort for design and optimization of solar power plants. In this work, APROS dynamic simulation program is used to model a DMS linear Fresnel solar field with two-tank TES system, and example simulation results are presented in order to verify the functionality of the model and capability of APROS for CSP modelling and simulation.

A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles.

PubMed

Kitayama, Tomoya; Kinoshita, Ayako; Sugimoto, Masahiro; Nakayama, Yoichi; Tomita, Masaru

2006-07-17

In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles.

Real Time Digital Control of a Magnetostrictive Actuator

NASA Technical Reports Server (NTRS)

Zrostlik, Rick L.; Hall, David L.; Flatau, Alison B.

1996-01-01

The use of the magnetostrictive material Terfenol-D as a motion source in active vibration control (AVC) systems are being studied. Currently it is of limited use due to the nonlinear nature of the strain versus magnetization curve and the magnetic hysteresis in the Terfenol-D. One manifestation of these nonlinearities is waveform distortion in the output velocity of the transducer. For Terfenol-D to be used in ever greater numbers of AVC systems, these nonlinearities must be addressed. In this study the nonlinearities are treated as disturbances to a linear system. The acceleration output is used in simple analog and digital feedback control schemes to improve linearity of the transducer. In addition, the use of a Terfenol-D actuator in an AVC system is verified. Both analog and digital controllers are implemented and results compared. A cantilever beam system is considered for AVC applications. The second thrust of this presentation is the reduction of harmonic distortions. Two conclusions can be reached from this work. One, the linearization of Terfenol-D transducers is possible with the use of feedback controllers, both digital and analog. Second, Terfenol-D is a viable motion source in active vibration control systems utilizing either analog or digital controllers.

Linear systems on balancing chemical reaction problem

NASA Astrophysics Data System (ADS)

Kafi, R. A.; Abdillah, B.

2018-01-01

The concept of linear systems appears in a variety of applications. This paper presents a small sample of the wide variety of real-world problems regarding our study of linear systems. We show that the problem in balancing chemical reaction can be described by homogeneous linear systems. The solution of the systems is obtained by performing elementary row operations. The obtained solution represents the finding coefficients of chemical reaction. In addition, we present a computational calculation to show that mathematical software such as Matlab can be used to simplify completion of the systems, instead of manually using row operations.

Development of fault tolerant adaptive control laws for aerospace systems

NASA Astrophysics Data System (ADS)

Perez Rocha, Andres E.

The main topic of this dissertation is the design, development and implementation of intelligent adaptive control techniques designed to maintain healthy performance of aerospace systems subjected to malfunctions, external parameter changes and/or unmodeled dynamics. The dissertation is focused on the development of novel adaptive control configurations that rely on non-linear functions that appear in the immune system of living organisms as main source of adaptation. One of the main goals of this dissertation is to demonstrate that these novel adaptive control architectures are able to improve overall performance and protect the system while reducing control effort and maintaining adequate operation outside bounds of nominal design. This research effort explores several phases, ranging from theoretical stability analysis, simulation and hardware implementation on different types of aerospace systems including spacecraft, aircraft and quadrotor vehicles. The results presented in this dissertation are focused on two main adaptivity approaches, the first one is intended for aerospace systems that do not attain large angles and use exact feedback linearization of Euler angle kinematics. A proof of stability is presented by means of the circle Criterion and Lyapunov's direct method. The second approach is intended for aerospace systems that can attain large attitude angles (e.g. space systems in gravity-less environments), the adaptation is incorporated on a baseline architecture that uses partial feedback linearization of quaternions kinematics. In this case, the closed loop stability was analyzed using Lyapunov's direct method and Barbalat's Lemma. It is expected that some results presented in this dissertation can contribute towards the validation and certification of direct adaptive controllers.

Fault detection for discrete-time LPV systems using interval observers

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Hui; Yang, Guang-Hong

2017-10-01

This paper is concerned with the fault detection (FD) problem for discrete-time linear parameter-varying systems subject to bounded disturbances. A parameter-dependent FD interval observer is designed based on parameter-dependent Lyapunov and slack matrices. The design method is presented by translating the parameter-dependent linear matrix inequalities (LMIs) into finite ones. In contrast to the existing results based on parameter-independent and diagonal Lyapunov matrices, the derived disturbance attenuation, fault sensitivity and nonnegative conditions lead to less conservative LMI characterisations. Furthermore, without the need to design the residual evaluation functions and thresholds, the residual intervals generated by the interval observers are used directly for FD decision. Finally, simulation results are presented for showing the effectiveness and superiority of the proposed method.

Computer simulation results of attitude estimation of earth orbiting satellites

NASA Technical Reports Server (NTRS)

Kou, S. R.

1976-01-01

Computer simulation results of attitude estimation of Earth-orbiting satellites (including Space Telescope) subjected to environmental disturbances and noises are presented. Decomposed linear recursive filter and Kalman filter were used as estimation tools. Six programs were developed for this simulation, and all were written in the basic language and were run on HP 9830A and HP 9866A computers. Simulation results show that a decomposed linear recursive filter is accurate in estimation and fast in response time. Furthermore, for higher order systems, this filter has computational advantages (i.e., less integration errors and roundoff errors) over a Kalman filter.

Dynamic imperfections and optimized feedback design in the Compact Linear Collider main linac

NASA Astrophysics Data System (ADS)

Eliasson, Peder

2008-05-01

The Compact Linear Collider (CLIC) main linac is sensitive to dynamic imperfections such as element jitter, injected beam jitter, and ground motion. These effects cause emittance growth that, in case of ground motion, has to be counteracted by a trajectory feedback system. The feedback system itself will, due to jitter effects and imperfect beam position monitors (BPMs), indirectly cause emittance growth. Fast and accurate simulations of both the direct and indirect effects are desirable, but due to the many elements of the CLIC main linac, simulations may become very time consuming. In this paper, an efficient way of simulating linear (or nearly linear) dynamic effects is described. The method is also shown to facilitate the analytic determination of emittance growth caused by the different dynamic imperfections while using a trajectory feedback system. Emittance growth expressions are derived for quadrupole, accelerating structure, and beam jitter, for ground motion, and for noise in the feedback BPMs. Finally, it is shown how the method can be used to design a feedback system that is optimized for the optics of the machine and the ground motion spectrum of the particular site. This feedback system gives an emittance growth rate that is approximately 10 times lower than that of traditional trajectory feedbacks. The robustness of the optimized feedback system is studied for a number of additional imperfections, e.g., dipole corrector imperfections and faulty knowledge about the machine optics, with promising results.

Flight control optimization from design to assessment application on the Cessna Citation X business aircraft =

NASA Astrophysics Data System (ADS)

Boughari, Yamina

New methodologies have been developed to optimize the integration, testing and certification of flight control systems, an expensive process in the aerospace industry. This thesis investigates the stability of the Cessna Citation X aircraft without control, and then optimizes two different flight controllers from design to validation. The aircraft's model was obtained from the data provided by the Research Aircraft Flight Simulator (RAFS) of the Cessna Citation business aircraft. To increase the stability and control of aircraft systems, optimizations of two different flight control designs were performed: 1) the Linear Quadratic Regulation and the Proportional Integral controllers were optimized using the Differential Evolution algorithm and the level 1 handling qualities as the objective function. The results were validated for the linear and nonlinear aircraft models, and some of the clearance criteria were investigated; and 2) the Hinfinity control method was applied on the stability and control augmentation systems. To minimize the time required for flight control design and its validation, an optimization of the controllers design was performed using the Differential Evolution (DE), and the Genetic algorithms (GA). The DE algorithm proved to be more efficient than the GA. New tools for visualization of the linear validation process were also developed to reduce the time required for the flight controller assessment. Matlab software was used to validate the different optimization algorithms' results. Research platforms of the aircraft's linear and nonlinear models were developed, and compared with the results of flight tests performed on the Research Aircraft Flight Simulator. Some of the clearance criteria of the optimized H-infinity flight controller were evaluated, including its linear stability, eigenvalues, and handling qualities criteria. Nonlinear simulations of the maneuvers criteria were also investigated during this research to assess the Cessna Citation X's flight controller clearance, and therefore, for its anticipated certification.

A novel methodology for non-linear system identification of battery cells used in non-road hybrid electric vehicles

NASA Astrophysics Data System (ADS)

Unger, Johannes; Hametner, Christoph; Jakubek, Stefan; Quasthoff, Marcus

2014-12-01

An accurate state of charge (SoC) estimation of a traction battery in hybrid electric non-road vehicles, which possess higher dynamics and power densities than on-road vehicles, requires a precise battery cell terminal voltage model. This paper presents a novel methodology for non-linear system identification of battery cells to obtain precise battery models. The methodology comprises the architecture of local model networks (LMN) and optimal model based design of experiments (DoE). Three main novelties are proposed: 1) Optimal model based DoE, which aims to high dynamically excite the battery cells at load ranges frequently used in operation. 2) The integration of corresponding inputs in the LMN to regard the non-linearities SoC, relaxation, hysteresis as well as temperature effects. 3) Enhancements to the local linear model tree (LOLIMOT) construction algorithm, to achieve a physical appropriate interpretation of the LMN. The framework is applicable for different battery cell chemistries and different temperatures, and is real time capable, which is shown on an industrial PC. The accuracy of the obtained non-linear battery model is demonstrated on cells with different chemistries and temperatures. The results show significant improvement due to optimal experiment design and integration of the battery non-linearities within the LMN structure.

Time of flight dependent linearity in diffuse imaging: how effective is it to evaluate the spatial resolution by measuring the edge response function?

PubMed

Ortiz-Rascón, E; Bruce, N C; Rodríguez-Rosales, A A; Garduño-Mejía, J

2016-03-01

We describe the behavior of linearity in diffuse imaging by evaluating the differences between time-resolved images produced by photons arriving at the detector at different times. Two approaches are considered: Monte Carlo simulations and experimental results. The images of two complete opaque bars embedded in a transparent or in a turbid medium with a slab geometry are analyzed; the optical properties of the turbid medium sample are close to those of breast tissue. A simple linearity test was designed involving a direct comparison between the intensity profile produced by two bars scanned at the same time and the intensity profile obtained by adding two profiles of each bar scanned one at a time. It is shown that the linearity improves substantially when short time of flight photons are used in the imaging process, but even then the nonlinear behavior prevails. As the edge response function (ERF) has been used widely for testing the spatial resolution in imaging systems, the main implication of a time dependent linearity is the weakness of the linearity assumption when evaluating the spatial resolution through the ERF in diffuse imaging systems, and the need to evaluate the spatial resolution by other methods.

Dc microgrid stabilization through fuzzy control of interleaved, heterogeneous storage elements

NASA Astrophysics Data System (ADS)

Smith, Robert David

As microgrid power systems gain prevalence and renewable energy comprises greater and greater portions of distributed generation, energy storage becomes important to offset the higher variance of renewable energy sources and maximize their usefulness. One of the emerging techniques is to utilize a combination of lead-acid batteries and ultracapacitors to provide both short and long-term stabilization to microgrid systems. The different energy and power characteristics of batteries and ultracapacitors imply that they ought to be utilized in different ways. Traditional linear controls can use these energy storage systems to stabilize a power grid, but cannot effect more complex interactions. This research explores a fuzzy logic approach to microgrid stabilization. The ability of a fuzzy logic controller to regulate a dc bus in the presence of source and load fluctuations, in a manner comparable to traditional linear control systems, is explored and demonstrated. Furthermore, the expanded capabilities (such as storage balancing, self-protection, and battery optimization) of a fuzzy logic system over a traditional linear control system are shown. System simulation results are presented and validated through hardware-based experiments. These experiments confirm the capabilities of the fuzzy logic control system to regulate bus voltage, balance storage elements, optimize battery usage, and effect self-protection.

Precision Pointing in Space Using Arrays of Shape Memory Based Linear Actuators

NASA Astrophysics Data System (ADS)

Sonawane, Nikhil

Space systems such as communication satellites, earth observation satellites and telescope require accurate pointing to observe fixed targets over prolonged time. These systems typically use reaction wheels to slew the spacecraft and gimballing systems containing motors to achieve precise pointing. Motor based actuators have limited life as they contain moving parts that require lubrication in space. Alternate methods have utilized piezoelectric actuators. This paper presents Shape memory alloys (SMA) actuators for control of a deployable antenna placed on a satellite. The SMAs are operated as a series of distributed linear actuators. These distributed linear actuators are not prone to single point failures and although each individual actuator is imprecise due to hysteresis and temperature variation, the system as a whole achieves reliable results. The SMAs can be programmed to perform a series of periodic motion and operate as a mechanical guidance system that is not prone to damage from radiation or space weather. Efforts are focused on developing a system that can achieve 1 degree pointing accuracy at first, with an ultimate goal of achieving a few arc seconds accuracy. Bench top model of the actuator system has been developed and working towards testing the system under vacuum. A demonstration flight of the technology is planned aboard a CubeSat.

Parameter identification for nonlinear aerodynamic systems

NASA Technical Reports Server (NTRS)

Pearson, Allan E.

1991-01-01

Work continues on frequency analysis for transfer function identification, both with respect to the continued development of the underlying algorithms and in the identification study of two physical systems. Some new results of a theoretical nature were recently obtained that lend further insight into the frequency domain interpretation of the research. Progress in each of those areas is summarized. Although not related to the system identification problem, some new results were obtained on the feedback stabilization of linear time lag systems.

Linear System Control Using Stochastic Learning Automata

NASA Technical Reports Server (NTRS)

Ziyad, Nigel; Cox, E. Lucien; Chouikha, Mohamed F.

1998-01-01

This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.

Linear systems with structure group and their feedback invariants

NASA Technical Reports Server (NTRS)

Martin, C.; Hermann, R.

1977-01-01

A general method described by Hermann and Martin (1976) for the study of the feedback invariants of linear systems is considered. It is shown that this method, which makes use of ideas of topology and algebraic geometry, is very useful in the investigation of feedback problems for which the classical methods are not suitable. The transfer function as a curve in the Grassmanian is examined. The general concepts studied in the context of specific systems and applications are organized in terms of the theory of Lie groups and algebraic geometry. Attention is given to linear systems which have a structure group, linear mechanical systems, and feedback invariants. The investigation shows that Lie group techniques are powerful and useful tools for analysis of the feedback structure of linear systems.

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

Technical notes and correspondence: Stochastic robustness of linear time-invariant control systems

NASA Technical Reports Server (NTRS)

Stengel, Robert F.; Ray, Laura R.

1991-01-01

A simple numerical procedure for estimating the stochastic robustness of a linear time-invariant system is described. Monte Carlo evaluations of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variation. Confidence intervals for the scalar probability of instability address computational issues inherent in Monte Carlo simulation. Trivial extensions of the procedure admit consideration of alternate discriminants; thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions can also be estimated. Results are particularly amenable to graphical presentation.

Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems.

PubMed

Li, Jianfeng; Huang, Zhitong; Liu, Xiaoshuang; Ji, Yuefeng

2015-01-12

A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (N-TDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced.

Desired Accuracy Estimation of Noise Function from ECG Signal by Fuzzy Approach

PubMed Central

Vahabi, Zahra; Kermani, Saeed

2012-01-01

Unknown noise and artifacts present in medical signals with non-linear fuzzy filter will be estimated and then removed. An adaptive neuro-fuzzy interference system which has a non-linear structure presented for the noise function prediction by before Samples. This paper is about a neuro-fuzzy method to estimate unknown noise of Electrocardiogram signal. Adaptive neural combined with Fuzzy System to construct a fuzzy Predictor. For this system setting parameters such as the number of Membership Functions for each input and output, training epochs, type of MFs for each input and output, learning algorithm and etc. is determined by learning data. At the end simulated experimental results are presented for proper validation. PMID:23717810

A methodology for designing robust multivariable nonlinear control systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Grunberg, D. B.

1986-01-01

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Linear system identification via backward-time observer models

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Phan, Minh

1993-01-01

This paper presents an algorithm to identify a state-space model of a linear system using a backward-time approach. The procedure consists of three basic steps. First, the Markov parameters of a backward-time observer are computed from experimental input-output data. Second, the backward-time observer Markov parameters are decomposed to obtain the backward-time system Markov parameters (backward-time pulse response samples) from which a backward-time state-space model is realized using the Eigensystem Realization Algorithm. Third, the obtained backward-time state space model is converted to the usual forward-time representation. Stochastic properties of this approach will be discussed. Experimental results are given to illustrate when and to what extent this concept works.

Linear decentralized systems with special structure. [for twin lift helicopters

NASA Technical Reports Server (NTRS)

Martin, C. F.

1982-01-01

Certain fundamental structures associated with linear systems having internal symmetries are outlined. It is shown that the theory of finite-dimensional algebras and their representations are closely related to such systems. It is also demonstrated that certain problems in the decentralized control of symmetric systems are equivalent to long-standing problems of linear systems theory. Even though the structure imposed arose in considering the problems of twin-lift helicopters, any large system composed of several identical intercoupled control systems can be modeled by a linear system that satisfies the constraints imposed. Internal symmetry can be exploited to yield new system-theoretic invariants and a better understanding of the way in which the underlying structure affects overall system performance.

SU-G-BRB-14: Uncertainty of Radiochromic Film Based Relative Dose Measurements

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

Devic, S; Tomic, N; DeBlois, F

2016-06-15

Purpose: Due to inherently non-linear dose response, measurement of relative dose distribution with radiochromic film requires measurement of absolute dose using a calibration curve following previously established reference dosimetry protocol. On the other hand, a functional form that converts the inherently non-linear dose response curve of the radiochromic film dosimetry system into linear one has been proposed recently [Devic et al, Med. Phys. 39 4850–4857 (2012)]. However, there is a question what would be the uncertainty of such measured relative dose. Methods: If the relative dose distribution is determined going through the reference dosimetry system (conversion of the response bymore » using calibration curve into absolute dose) the total uncertainty of such determined relative dose will be calculated by summing in quadrature total uncertainties of doses measured at a given and at the reference point. On the other hand, if the relative dose is determined using linearization method, the new response variable is calculated as ζ=a(netOD)n/ln(netOD). In this case, the total uncertainty in relative dose will be calculated by summing in quadrature uncertainties for a new response function (σζ) for a given and the reference point. Results: Except at very low doses, where the measurement uncertainty dominates, the total relative dose uncertainty is less than 1% for the linear response method as compared to almost 2% uncertainty level for the reference dosimetry method. The result is not surprising having in mind that the total uncertainty of the reference dose method is dominated by the fitting uncertainty, which is mitigated in the case of linearization method. Conclusion: Linearization of the radiochromic film dose response provides a convenient and a more precise method for relative dose measurements as it does not require reference dosimetry and creation of calibration curve. However, the linearity of the newly introduced function must be verified. Dave Lewis is inventor and runs a consulting company for radiochromic films.« less

Bisimulation equivalence of differential-algebraic systems

NASA Astrophysics Data System (ADS)

Megawati, Noorma Yulia; Schaft, Arjan van der

2018-01-01

In this paper, the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterisation of bisimulation relations, and an algorithm for computing the maximal bisimulation relation between two linear DAE systems. The general definition is specialised to the case where the matrix pencil sE - A is regular. Furthermore, by developing a one-sided version of bisimulation, characterisations of simulation and abstraction are obtained.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions

NASA Astrophysics Data System (ADS)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-04-01

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. We also show that the strategy is efficient and scales optimally with problem size.

Decoupling analysis for a powertrain mounting system with a combination of hydraulic mounts

NASA Astrophysics Data System (ADS)

Hu, Jinfang; Chen, Wuwei; Huang, He

2013-07-01

The existing torque roll axis(TRA) decoupling theories for a powertrain mounting system assume that the stiffness and viscous damping properties are constant. However, real-life mounts exhibit considerable spectrally varying stiffness and damping characteristics, and the influence of the spectrally-varying properties of the hydraulic mounts on the powertrain system cannot be ignored. To overcome the deficiency, an analytical quasi-linear model of the hydraulic mount and the coupled properties of the powertrain and hydraulic mounts system are formulated. The influence of the hydraulic mounts on the TRA decoupling of a powertrain system is analytically examined in terms of eigensolutions, frequency, and impulse responses, and then a new analytical axiom is proposed based on the TRA decoupling indices. With the experimental setup of a fixed decoupler hydraulic mount in the context of non-resonant dynamic stiffness testing procedure, the quasi-linear model of the hydraulic mount is verified by comparing the predictions with the measurement. And the quasi-linear formulation of the coupled system is also verified by comparing the frequency responses with the numerical results obtained by the direct inversion method. Finally, the mounting system with a combination of hydraulic mounts is redesigned in terms of the stiffness, damping and mount locations by satisfying the new axiom. The frequency and time domain results of the redesigned system demonstrate that the torque roll axis of the redesigned powertrain mounting system is indeed decoupled in the presence of hydraulic mounts (given oscillating torque or impulsive torque excitation). The proposed research provides an important basis and method for the research on a powertrain system with spectrally-varying mount properties, especially for the TRA decoupling.

Controllable outrigger damping system for high rise building with MR dampers

NASA Astrophysics Data System (ADS)

Wang, Zhihao; Chang, Chia-Ming; Spencer, Billie F., Jr.; Chen, Zhengqing

2010-04-01

A novel energy dissipation system that can achieve the amplified damping ratio for a frame-core tube structures is explored, where vertical dampers are equipped between the outrigger and perimeter columns. The modal characteristics of the structural system with linear viscous dampers are theoretically analyzed from the simplified finite element model by parametric analysis. The result shows that modal damping ratios of the first several modes can increase a lot with this novel damping system. To improve the control performance of system, the semi-active control devices, magnetorheological (MR) dampers, are adopted to develop a controllable outrigger damping system. The clipped optimal control with the linear-quadratic Gaussian (LQG) acceleration feedback is adopted in this paper. The effectiveness of both passive and semi-active control outrigger damping systems is evaluated through the numerical simulation of a representative tall building subjected to two typical earthquake records.

An improved conjugate gradient scheme to the solution of least squares SVM.

PubMed

Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya

2005-03-01

The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.

The Lick Observatory image-dissector scanner.

NASA Technical Reports Server (NTRS)

Robinson, L. B.; Wampler, E. J.

1972-01-01

A scanner that uses an image dissector to scan the output screen of an image tube has proven to be a sensitive and linear detector for faint astronomical spectra. The image-tube phosphor screen acts as a short-term storage element and allows the system to approach the performance of an ideal multichannel photon counter. Pulses resulting from individual photons, emitted from the output phosphor and detected by the image dissector, trigger an amplifier-discriminator and are counted in a 24-bit, 4096-word circulating memory. Aspects of system performance are discussed, giving attention to linearity, dynamic range, sensitivity, stability, and scattered light properties.

Slip control for LIM propelled transit vehicles

NASA Astrophysics Data System (ADS)

Wallace, A. K.; Parker, J. H.; Dawson, G. E.

1980-09-01

Short stator linear induction motors, with an iron-backed aluminum sheet reaction rail and powered by a controlled inverter, have been selected as the propulsion system for transit vehicles in an intermediate capacity system (12-20,000 pphpd). The linear induction motor is capable of adhesion independent braking and acceleration levels which permit safe, close headways. In addition, simple control is possible allowing moving block automatic train control. This paper presents a slip frequency control scheme for the LIM. Experimental results for motoring and braking obtained from a test vehicle are also presented. These values are compared with theoretical predictions.

Detecting both melanoma depth and volume in vivo with a handheld photoacoustic probe

NASA Astrophysics Data System (ADS)

Zhou, Yong; Li, Guo; Zhu, Liren; Li, Chiye; Cornelius, Lynn A.; Wang, Lihong V.

2016-03-01

We applied a linear-array-based photoacoustic probe to detect the tumor depth and volume of melanin-containing melanoma in nude mice in vivo. We demonstrated the ability of this linear-array-based system to measure both the depth and volume of melanoma through phantom, ex vivo, and in vivo experiments. The volume detection ability also enables us to accurately calculate the rate of growth of the tumor, which is important in quantifying tumor activity. Our results show that this system can be used for clinical melanoma diagnosis and treatment at the bedside.

Accelerate quasi Monte Carlo method for solving systems of linear algebraic equations through shared memory

NASA Astrophysics Data System (ADS)

Lai, Siyan; Xu, Ying; Shao, Bo; Guo, Menghan; Lin, Xiaola

2017-04-01

In this paper we study on Monte Carlo method for solving systems of linear algebraic equations (SLAE) based on shared memory. Former research demostrated that GPU can effectively speed up the computations of this issue. Our purpose is to optimize Monte Carlo method simulation on GPUmemoryachritecture specifically. Random numbers are organized to storein shared memory, which aims to accelerate the parallel algorithm. Bank conflicts can be avoided by our Collaborative Thread Arrays(CTA)scheme. The results of experiments show that the shared memory based strategy can speed up the computaions over than 3X at most.

Some New Properties of Quantum Correlations

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Fei; Wei, Yunxia

2017-02-01

Quantum coherence measures the correlation between different measurement results in a single-system, while entanglement and quantum discord measure the correlation among different subsystems in a multipartite system. In this paper, we focus on the relative entropy form of them, and obtain three new properties of them as follows: 1) General forms of maximally coherent states for the relative entropy coherence, 2) Linear monogamy of the relative entropy entanglement, and 3) Subadditivity of quantum discord. Here, the linear monogamy is defined as there is a small constant as the upper bound on the sum of the relative entropy entanglement in subsystems.

Linear CCD attitude measurement system based on the identification of the auxiliary array CCD

NASA Astrophysics Data System (ADS)

Hu, Yinghui; Yuan, Feng; Li, Kai; Wang, Yan

2015-10-01

Object to the high precision flying target attitude measurement issues of a large space and large field of view, comparing existing measurement methods, the idea is proposed of using two array CCD to assist in identifying the three linear CCD with multi-cooperative target attitude measurement system, and to address the existing nonlinear system errors and calibration parameters and more problems with nine linear CCD spectroscopic test system of too complicated constraints among camera position caused by excessive. The mathematical model of binocular vision and three linear CCD test system are established, co-spot composition triangle utilize three red LED position light, three points' coordinates are given in advance by Cooperate Measuring Machine, the red LED in the composition of the three sides of a triangle adds three blue LED light points as an auxiliary, so that array CCD is easier to identify three red LED light points, and linear CCD camera is installed of a red filter to filter out the blue LED light points while reducing stray light. Using array CCD to measure the spot, identifying and calculating the spatial coordinates solutions of red LED light points, while utilizing linear CCD to measure three red LED spot for solving linear CCD test system, which can be drawn from 27 solution. Measured with array CCD coordinates auxiliary linear CCD has achieved spot identification, and has solved the difficult problems of multi-objective linear CCD identification. Unique combination of linear CCD imaging features, linear CCD special cylindrical lens system is developed using telecentric optical design, the energy center of the spot position in the depth range of convergence in the direction is perpendicular to the optical axis of the small changes ensuring highprecision image quality, and the entire test system improves spatial object attitude measurement speed and precision.

A comprehensive inversion approach for feedforward compensation of piezoactuator system at high frequency

NASA Astrophysics Data System (ADS)

Tian, Lizhi; Xiong, Zhenhua; Wu, Jianhua; Ding, Han

2016-09-01

Motion control of the piezoactuator system over broadband frequencies is limited due to its inherent hysteresis and system dynamics. One of the suggested ways is to use feedforward controller to linearize the input-output relationship of the piezoactuator system. Although there have been many feedforward approaches, it is still a challenge to develop feedforward controller for the piezoactuator system at high frequency. Hence, this paper presents a comprehensive inversion approach in consideration of the coupling of hysteresis and dynamics. In this work, the influence of dynamics compensation on the input-output relationship of the piezoactuator system is investigated first. With system dynamics compensation, the input-output relationship of the piezoactuator system will be further represented as rate-dependent nonlinearity due to the inevitable dynamics compensation error, especially at high frequency. Base on this result, the feedforward controller composed by a cascade of linear dynamics inversion and rate-dependent nonlinearity inversion is developed. Then, the system identification of the comprehensive inversion approach is proposed. Finally, experimental results show that the proposed approach can improve the performance on tracking of both periodic and non-periodic trajectories at medium and high frequency compared with the conventional feedforward approaches.

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.

Assessment of Advanced Logistics Delivery System (ALDS) Launch Systems Concepts

DTIC Science & Technology

2004-10-01

highest force vs. rotor weight required, allows much higher magnetic field generation than the linear induction or linear permanent magnet motors , and...provides the highest force vs. rotor weight required, allows much higher magnetic generation than the linear induction or linear permanent magnet motors , and

Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

NASA Astrophysics Data System (ADS)

Chunodkar, Apurva A.; Akella, Maruthi R.

2013-12-01

This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

Three-dimensional finite amplitude electroconvection in dielectric liquids

NASA Astrophysics Data System (ADS)

Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

2018-02-01

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Active control of acoustic pressure fields using smart material technologies

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, R. C.

1993-01-01

An overview describing the use of piezoceramic patches in reducing noise in a structural acoustics setting is presented. The passive and active contributions due to patches which are bonded to an Euler-Bernoulli beam or thin shell are briefly discussed and the results are incorporated into a 2-D structural acoustics model. In this model, an exterior noise source causes structural vibrations which in turn lead to interior noise as a result of nonlinear fluid/structure coupling mechanism. Interior sound pressure levels are reduced via patches bonded to the flexible boundary (a beam in this case) which generate pure bending moments when an out-of-phase voltage is applied. Well-posedness results for the infinite dimensional system are discussed and a Galerkin scheme for approximating the system dynamics is outlined. Control is implemented by using linear quadratic regulator (LQR) optimal control theory to calculate gains for the linearized system and then feeding these gains back into the nonlinear system of interest. The effectiveness of this strategy for this problem is illustrated in an example.

Multi-static MIMO along track interferometry (ATI)

NASA Astrophysics Data System (ADS)

Knight, Chad; Deming, Ross; Gunther, Jake

2016-05-01

Along-track interferometry (ATI) has the ability to generate high-quality synthetic aperture radar (SAR) images and concurrently detect and estimate the positions of ground moving target indicators (GMTI) with moderate processing requirements. This paper focuses on several different ATI system configurations, with an emphasis on low-cost configurations employing no active electronic scanned array (AESA). The objective system has two transmit phase centers and four receive phase centers and supports agile adaptive radar behavior. The advantages of multistatic, multiple input multiple output (MIMO) ATI system configurations are explored. The two transmit phase centers can employ a ping-pong configuration to provide the multistatic behavior. For example, they can toggle between an up and down linear frequency modulated (LFM) waveform every other pulse. The four receive apertures are considered in simple linear spatial configurations. Simulated examples are examined to understand the trade space and verify the expected results. Finally, actual results are collected with the Space Dynamics Laboratorys (SDL) FlexSAR system in diverse configurations. The theory, as well as the simulated and actual SAR results, are presented and discussed.

Analysis on the Effect of Sensor Views in Image Reconstruction Produced by Optical Tomography System Using Charge-Coupled Device.

PubMed

Jamaludin, Juliza; Rahim, Ruzairi Abdul; Fazul Rahiman, Mohd Hafiz; Mohd Rohani, Jemmy

2018-04-01

Optical tomography (OPT) is a method to capture a cross-sectional image based on the data obtained by sensors, distributed around the periphery of the analyzed system. This system is based on the measurement of the final light attenuation or absorption of radiation after crossing the measured objects. The number of sensor views will affect the results of image reconstruction, where the high number of sensor views per projection will give a high image quality. This research presents an application of charge-coupled device linear sensor and laser diode in an OPT system. Experiments in detecting solid and transparent objects in crystal clear water were conducted. Two numbers of sensors views, 160 and 320 views are evaluated in this research in reconstructing the images. The image reconstruction algorithms used were filtered images of linear back projection algorithms. Analysis on comparing the simulation and experiments image results shows that, with 320 image views giving less area error than 160 views. This suggests that high image view resulted in the high resolution of image reconstruction.

A game theoretic controller for a linear time-invariant system with parameter uncertainty and its application to the Space Station

NASA Technical Reports Server (NTRS)

Rhee, Ihnseok; Speyer, Jason L.

1990-01-01

A game theoretic controller is developed for a linear time-invariant system with parameter uncertainties in system and input matrices. The input-output decomposition modeling for the plant uncertainty is adopted. The uncertain dynamic system is represented as an internal feedback loop in which the system is assumed forced by fictitious disturbance caused by the parameter uncertainty. By considering the input and the fictitious disturbance as two noncooperative players, a differential game problem is constructed. It is shown that the resulting time invariant controller stabilizes the uncertain system for a prescribed uncertainty bound. This game theoretic controller is applied to the momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Inclusion of the external disturbance torque to the design procedure results in a dynamical feedback controller which consists of conventional PID control and cyclic disturbance rejection filter. It is shown that the game theoretic design, comparing to the LQR design or pole placement design, improves the stability robustness with respect to inertia variations.

Effect of a crystal-melt interface on Taylor-vortex flow

NASA Technical Reports Server (NTRS)

Mcfadden, G. B.; Coriell, S. R.; Murray, B. T.; Glicksman, M. E.; Selleck, M. E.

1990-01-01

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal-melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n = 1; the stability of these n = 1 modes is sensitive to the latent heat of fusion.

Dynamic Stiffness Transfer Function of an Electromechanical Actuator Using System Identification

NASA Astrophysics Data System (ADS)

Kim, Sang Hwa; Tahk, Min-Jea

2018-04-01

In the aeroelastic analysis of flight vehicles with electromechanical actuators (EMAs), an accurate prediction of flutter requires dynamic stiffness characteristics of the EMA. The dynamic stiffness transfer function of the EMA with brushless direct current (BLDC) motor can be obtained by conducting complicated mathematical calculations of control algorithms and mechanical/electrical nonlinearities using linearization techniques. Thus, system identification approaches using experimental data, as an alternative, have considerable advantages. However, the test setup for system identification is expensive and complex, and experimental procedures for data collection are time-consuming tasks. To obtain the dynamic stiffness transfer function, this paper proposes a linear system identification method that uses information obtained from a reliable dynamic stiffness model with a control algorithm and nonlinearities. The results of this study show that the system identification procedure is compact, and the transfer function is able to describe the dynamic stiffness characteristics of the EMA. In addition, to verify the validity of the system identification method, the simulation results of the dynamic stiffness transfer function and the dynamic stiffness model were compared with the experimental data for various external loads.

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

NASA Astrophysics Data System (ADS)

Chavarette, Fábio Roberto; Balthazar, José Manoel; Felix, Jorge L. P.; Rafikov, Marat

2009-05-01

This paper analyzes the non-linear dynamics, with a chaotic behavior of a particular micro-electro-mechanical system. We used a technique of the optimal linear control for reducing the irregular (chaotic) oscillatory movement of the non-linear systems to a periodic orbit. We use the mathematical model of a (MEMS) proposed by Luo and Wang.

An equivalent frequency approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice

2018-05-01

Pre-tensioned cable braces are widely used as bracing systems in various structural typologies. This technology is fundamentally utilized for stiffening purposes in the case of steel and timber structures. The pre-stressing force imparted to the braces provides to the system a remarkable increment of stiffness. On the other hand, the pre-tensioning force in the braces must be properly calibrated in order to satisfactorily meet both serviceability and ultimate limit states. Dynamic properties of these systems are however affected by non-linear behavior due to potential slackening of the pre-tensioned brace. In the recent years the author has been working on a similar problem regarding the non-linear response of cables in cable-stayed bridges and braced structures. In the present paper a displacement-based approach is used to examine the non-linear behavior of a building system. The methodology operates through linearization and allows obtaining an equivalent linearized frequency to approximately characterize, mode by mode, the dynamic behavior of the system. The equivalent frequency depends on both the mechanical characteristics of the system, the pre-tensioning level assigned to the braces and a characteristic vibration amplitude. The proposed approach can be used as a simplified technique, capable of linearizing the response of structural systems, characterized by non-linearity induced by the slackening of pre-tensioned braces.

Second-order discrete Kalman filtering equations for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.

1991-01-01

A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.