Simulation Of Nonlinear Systems Research Articles

Indirect self-tuning control using multiple models for non-affine nonlinear systems

In this article, for a class of discrete time non-affine nonlinear systems, a multiple-model-based indirect self-tuning control method is developed. The indirect self-tuning control method is composed of a linear robust indirect self-tuning controller, a nonlinear neural network indirect self-tuning controller and a switching mechanism. By introducing a modified Clarke index, the indirect self-tuning control method can tolerate properties of non-minimum phase and open-loop instability of the controlled system and attenuate the disturbance caused by the higher order nonlinear term. By resorting to the time-varying operation, it is proved without the assumption on the boundedness of the nonlinear term or its differential term that the proposed multiple-model-based nonlinear indirect self-tuning control method can guarantee the bounded-input–bounded-output stability of the closed-loop system and improve the system performance simultaneously. To illustrate the effectiveness of the proposed method, simulations for a synthetic nonlinear system and a realistic nonlinear system are conducted.

System-Oriented Harmonic-Balance Algorithms for Circuit-Level Simulation

This paper discusses a self-consistent set of modern computational concepts providing an effective approach to the circuit-level harmonic-balance (HB) simulation of nonlinear microwave systems of complex topology. The system is automatically split into the interconnection of a near-optimal number of nonlinear blocks at run time. The resulting structure is then exploited by the domain-partitioning concept. A block-wise constant spectrum is used rather than a common spectrum by considering for each block only the set of spectral lines that are relevant to its electrical function, which leads to a very significant reduction in the number of problem unknowns. System simulation under digitally modulated RF drive is reduced to a sequence of modified multitone HB analyses that are backward coupled through the envelope dynamics. Besides providing high numerical efficiency, this set of techniques opens the way to an effective co-simulation of RF and baseband transceiver sections.

Combined Nonlinear Tokamak Plasma Current Profile Control System Design and Simulation with Input Constraints

AbstractThe paper presents the design and simulation results of the combined multivariable control system with the plant input constraints for a plasma current profile in a tokamak. The plasma kinetic model was used in terms of the Grad-Shafranov plasma equilibrium equation and the poloidal magnetic flux diffusion equation. The model is square specifically contains 5 inputs and 5 outputs. Actuators are external current drive sources. Output is plasma current density measured at five points of the minor radius. A set of linear models for controller design was obtained by a state subspace identification approach. A set of H∞ controllers was synthesized by a loop shaping methodology at various values of the plasma electron temperature on the magnetic axis. Controllers designed were applied by the numerical simulation to the original model to change the current profile from one state to another. In the presence of plant input constraints a special logic block was developed in addition to the linear robust controller and used when plant inputs saturated. The plasma current profile control system designed showed its operability in the tokamak plasma electron temperature range on the magnetic axis from 0.1 to 18 keV.

A probabilistic indirect adaptive control for systems with input‐dependent noise

AbstractA probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system. Copyright © 2010 John Wiley & Sons, Ltd.

Model order reduction for object-oriented models: a control systems perspective

In recent years several concepts and tools for modelling and simulation of non-linear heterogeneous and multi-domain systems have been developed, speeding up to a great extent the process of an accurate analysis by simulation of increasingly complex technological systems. In parallel, for dimensioning and, above all, for control system design purposes, the need of models of reduced complexity has emerged; together with the need of tools capable of extracting, from the overall dynamic model, reduced models representing the dominant behaviour. This article reviews recent results in non-linear model order reduction method (NORM), originally developed with reference to computer-aided analysis and design of electronic circuits, and puts them in a control system design-oriented perspective, pointing out interesting future research directions.

Observer-feedback fuzzy control with passivity property for discrete-time affine Takagi-Sugeno fuzzy models

By considering discrete-time affine Takagi-Sugeno fuzzy models, this paper presents an observer-feedback fuzzy control approach for achieving the passivity property of closed-loop systems. The passivity property of the system is used to deal with all external disturbances. The proposed observer-feedback fuzzy controller is developed based on the parallel distribution compensation technique. Also, an iterative linear matrix inequality algorithm is used to obtain a feasible solution for the proposed observer-feedback fuzzy control problem. Finally, two numerical simulations of discrete-time nonl-inear systems are presented that highlight the application of the proposed observer-feedback fuzzy controller design approach.

Modeling switched circuits based on wavelet decomposition and neural networks

Abstract In this paper, switched circuits are modeled based on wavelet decomposition and neural network. Also describes the usage of wavelet decomposition and neural network for modeling and simulation of nonlinear systems. The switched circuits are piecewise-linear circuits. At each position of switch the circuit is linear but when considered all switching positions of the circuit it becomes nonlinear. An important problem which arises in modeling switched circuit is high structural complexity. In this study, wavelet decomposition is used for feature extracting from input signals and neural network is used as an intelligent modeling tool. Two performance measures root-mean-square (RMS) and the coefficient of multiple determinations (R2) are given to compare the predicted and computed values for model validation. The evaluated R2 value is 0.9985 and RMS value is 0.0099. All simulations showed that the proposed method is more effective and can be used for analyzing and modeling switched circuits. When we consider obtained performance, we can easily say that the proposed method can be used efficiently for modeling any other nonlinear dynamical systems.

LQ control of coupled hyperbolic PDEs and ODEs: Application to a CSTR-PFR system

In this paper an infinite-dimensional LQR control-based design for a system containing linear hyperbolic partial differential equations coupled with linear ordinary differential equations is presented. The design is based on an infinite-dimensional Hilbert state-space representation of the coupled system. The feedback control gain is obtained by solving algebraic and differential matrix Riccati equations that result from an operator Riccati equation solution. The designed LQR control is applied to a system containing a continuous stirred tank reactor (CSTR) and a plug flow reactor (PFR) in series with the recycle-rate from PFR to CSTR as controlled variable. The LQR controller's performance is evaluated by numerical simulation of the original nonlinear system.

Limit Cycle Prediction for Fractional Order Systems with Static Nonlinearities

This paper deals with limit cycle prediction for nonlinear systems which have fractional order transfer functions. Describing function method is used for the analysis of fractional order nonlinear systems. It is observed that the limit cycle frequencies obtained from the simulation of the fractional order nonlinear systems, agree with the theoretical values of the limit cycle frequencies obtained from Nyquist plots of the fractional order plant and complex plot of the negative inverse of describing function. The critical gain of the system is estimated from Nyquist plot. The fractional order nonlinear system becomes stable for the gain smaller than the critical gain value. System starts to oscillate for the gain bigger than the critical gain value.

Stochastic Sparse-Grid Collocation Algorithm for Steady-State Analysis of Nonlinear System with Process Variations

In this paper, a Stochastic Collocation Algorithm combined with Sparse Grid technique (SSCA) is proposed to deal with the periodic steady-state analysis for nonlinear systems with process variations. Compared to the existing approaches, SSCA has several considerable merits. Firstly, compared with the moment-matching parameterized model order reduction (PMOR) which equally treats the circuit response on process variables and frequency parameter by Taylor approximation, SSCA employs Homogeneous Chaos to capture the impact of process variations with exponential convergence rate and adopts Fourier series or Wavelet Bases to model the steady-state behavior in time domain. Secondly, contrary to Stochastic Galerkin Algorithm (SGA), which is efficient for stochastic linear system analysis, the complexity of SSCA is much smaller than that of SGA for nonlinear case. Thirdly, different from Efficient Collocation Method, the heuristic approach which may result in “Rank deficient problem” and “Runge phenomenon,” Sparse Grid technique is developed to select the collocation points needed in SSCA in order to reduce the complexity while guaranteing the approximation accuracy. Furthermore, though SSCA is proposed for the stochastic nonlinear steady-state analysis, it can be applied to any other kind of nonlinear system simulation with process variations, such as transient analysis, etc..

Modeling and simulation of chaotic phenomena in electrical power systems

Modeling and simulation of nonlinear systems under chaotic behavior is presented. Nonlinear systems and their relation to chaos as a result of nonlinear interaction of different elements in the system are presented. Application of chaotic theory for power systems is discussed through simulation results. Simulation of some mathematical equations, e.g. Vander Pol's equation, Lorenz's equation, Duffing's equation and double scroll equations are presented. Theoretical aspects of dynamical systems, the existence of chaos in power system and their dependency on system parameters and initial conditions using computer simulations are discussed. From the results one can easily understand the strange attractor and transient stages to voltage collapse, angle instability or voltage collapse and angle divergence simultaneously. Important simulation results of chaos for a model three bus system are presented and discussed.

Dynamic Simulations of Nonlinear Multi-Domain Systems Based on Genetic Programming and Bond Graphs

A dynamic simulation method for non-linear systems based on genetic programming (GP) and bond graphs (BG) was developed to improve the design of nonlinear multi-domain energy conversion systems. The genetic operators enable the embryo bond graph to evolve towards the target graph according to the fitness function. Better simulation requires analysis of the optimization of the eigenvalue and the filter circuit evolution. The open topological design and space search ability of this method not only gives a more optimized convergence for the operation, but also reduces the generation time for the new circuit graph for the design of nonlinear multi-domain systems.

Modeling, analysis and motion control of a pan tilt platform based on linear and nonlinear systems

This paper deals with the modeling, analysis and controlled motion control of a two degree of freedom pan tilt platform (PTP) for positioning or aiming a device. The PTP has two revolute joints. The PTP is a device that makes it possible for the camera to point in a desired direction when mounted under a carrier such as an aircraft. The objective of this research work is to derive a linear and nonlinear control system of the PTP to point in a desired direction within allowable specifications. To perform the analysis and simulation, all the parameters involved in the system dynamics were identified. To achieve the motion control a feedback control system with PD controllers was simulated and tested for the position control of pan and tilt mechanism. These PD controllers were derived from linear system model were used in nonlinear control system simulation and tested with real system. The nonlinear control system developed in this paper is nearest to the physical system. The motion controller results matched closely with the simulation results.

A Support Vector Regression Approach for Recursive Simultaneous Data Reconciliation and Gross Error Detection in Nonlinear Dynamical Systems

The quality of process data in a chemical plant significantly affects the performance and benefits gained from activities like performance monitoring, online optimization, and control. Since many chemical processes often show nonlinear dynamics, techniques like extended Kalman filter (EKF) and nonlinear dynamic data reconciliation (NDDR) have been developed to improve the data quality. Recently, the recursive nonlinear dynamic data reconciliation (RNDDR) technique has been proposed, which combines the merits of EKF and NDDR techniques. However, the RNDDR technique cannot handle measurements with gross errors. In this paper, a support vector (SV) regression approach for recursive simultaneous data reconciliation and gross error detection in nonlinear dynamical systems is proposed. SV regression is a compromise between the empirical risk and the model complexity, and for data reconciliation it is robust to random and gross errors. By minimizing the regularized risk instead of the maximum likelihood in the RNDDR, our approach could achieve not only recursive nonlinear dynamic data reconciliation but also gross error detection simultaneously. The nonlinear dynamic system simulation results in this paper show that the proposed approach is robust, efficient, stable, and accurate for simultaneous data reconciliation and gross error detection in nonlinear dynamic systems within a recursive real-time estimation framework. It can also give better performance of control.

Robust adaptive tracking controller design for non-affine non-linear systems with state time-varying delay and unknown dead-zone

A novel Neural Network (NN)-based dead-zone compensation scheme for a class of non-affine Multiple-Input Multiple-Output (MIMO) non-linear systems with state time-varying delay is presented. A static NN is introduced to approximate and adaptively cancel the unknown nonlinear dynamic of the subsystems and unknown dead-zone after its existence proved by implicit function theorem. The control law and adaptive laws for the weights of the hidden layer and output layer of NNs are established by Lyapunov analysis of the whole closed-loop system. The tracking error is proved to be Uniformly Ultimately Bounded (UUB) via introducing an additional robust control term. The effectiveness of the proposed control scheme is verified by the simulation of an MIMO non-affine non-linear system with state time-varying delay.

HHT-based nonlinear signal processing method for parametric and non-parametric identification of dynamical systems

This paper presents a time–frequency signal processing method based on Hilbert–Huang transform (HHT) and a sliding-window fitting (SWF) technique for parametric and non-parametric identification of nonlinear dynamical systems. The SWF method is developed to reveal the limitations of conventional signal processing methods and to perform further decomposition of signals. Similar to the short-time Fourier transform and wavelet transform, the SWF uses windowed regular harmonics and function orthogonality to extract time-localized regular and/or distorted harmonics. On the other hand, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales, starting from high- to low-frequency ones. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. Methods are developed to reduce the end effect caused by Gibbs’ phenomenon and other mathematical and numerical problems of HHT analysis. For parametric identification of a nonlinear one-degree-of-freedom system, the method processes one free damped transient response and one steady-state response and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. For non-parametric identification, the method uses the maximum displacement states to determine the displacement–stiffness curve and the maximum velocity states to determine the velocity-damping curve. Moreover, the SWF method and a synchronous detection method are used for further decomposition of components extracted by HHT to improve the accuracy of parametric and non-parametric estimations. Numerical simulations of several nonlinear systems show that the proposed method can provide accurate parametric and non-parametric identifications of different nonlinear dynamical systems.

Mathematical simulation of nonlinear waveguiding systems based on 2D photonic crystals

A mathematical model of nonlinear two-dimensional waveguiding systems based on photonic crystals was constructed using the finite-difference time-domain method (FDTD), the total field/scattered field (TF/SF) method, and the perfectly matched layer method (PML). The constructed numerical algorithm can also be used for investigation of other two-dimensional waveguiding systems. The results of simulating the elements of particular waveguiding systems are presented.

Three-Dimensional Finite Element Simulation of Nonlinear Dynamic Rotor Systems of a Turbocharger

This paper presents the modeling procedure for a high-velocity rotor system (RS) combined with sliding bearings. The equations for motion of the RS parts were derived based on the model of a rotating elastic medium. Lubrication layers have been calculated with the use of the Reynolds equations. The discretization of the RS model has been carried out using three-dimensional contact finite element method and two-dimensional method of finite differences. The integration with respect to time is performed by an absolutely stable step-by-step method. The paper also compares and discusses computed and experimental amplitude-frequency characteristics of the self-oscillating turbocharger’s RS. The values of dynamic loads in parts, as well as reactions, clearances, and losses in bearings, computed based on the presented modeling procedure make the RS designing more accurate and reliable.

Deterministic Excitation Forces for Simulation and Identification of Nonlinear Hysteretic SDOF Systems

This paper investigates how to design deterministic excitation forces in studying nonlinear single-degree-of-freedom systems, especially those with rate and path dependency and strength and stiffness degradation. One frequency-modulated periodic excitation and its amplitude-modulated counterpart are proposed as a solution, and a series of numerical exercises are carried out to show that these forces can be designed for sufficient forcing functions to study the complex nonlinear hysteresis. To rapidly reveal the underlying characteristics of the system and also to further lead to an effective system identification, four evaluation tools are proposed to be utilized together with the proposed excitation forces. These tools include the response curves, force-state map, intercycle drift, and intercycle pattern change, based on which some distinctive “patterns” are obtained to reveal the existence of nonlinearities, types of nonlinearities, existence of memory, and degradation. By using both Bouc-Wen and Bouc-Wen-Baber-Noori models for the system in all the simulations, the writers compare the commonly used forces with the proposed excitation forces to further demonstrate the advantages of the proposed excitation forces and evaluation tools. The writers also explore challenges in terms of implementing the proposed excitation forces. The results of this study are expected to benefit both physical testing and numerical simulation of complex nonlinear hysteretic systems in a time- and cost-effective manner, as well as leading to efficient schemes for system identification.

Black-box identification and simulation of continuous-time nonlinear systems with random processes

This paper proposes a methodology for black-box identification and simulation of continuous-time nonlinear dynamical systems based on random process modeling and kriging. It is assumed that the (finite-dimensional) state vector is observed with noise at regularly or irregularly spaced instants. The proposed identification method consists of two steps. The first step is the estimation of the time derivatives of the state vector. The second step consists in the approximation of the controlled vector field. For the simulation of the system, a new integration scheme is proposed. This integration scheme makes it possible to deal consistently with the error of approximation of the vector field.