Control Design For Nonlinear Systems Research Articles

Iterative learning control design of nonlinear multiple time-delay systems

Most available results on iterative learning control address trajectory tracking problem for systems without multiple time-delay. This paper is concerned with iterative learning control design for nonlinear systems with multiple delays, in which external disturbances and output measurement noises are involved. We obtain some new and interesting criteria to guarantee the convergence of the tracking error in the sense of the λ − norm. It will be shown that the convergence of the system outputs to the desired trajectory is ensured in the absence of disturbances and output measurement noises. In the presence of disturbance and measurement noises, we estimate the upper bound of the tracking error. In order to confirm the validity of the present results, numerical simulation is also presented.

Optimal Control Design for Nonlinear Systems with Disturbances

This paper considers the optimal control design problem for nonlinear systems with composite disturbances. First, the original system is transformed into an augmented system without disturbances. Then with respect to the quadratic performance indexes of infinite horizon, we design an optimal controller for the augmented plant without disturbances. Thus the disturbances can unfold of the signal through the Taylor series for the form of polynomial function of time, and obtain optimal controller design approach to eliminate the general disturbance. Finally, a practical example is given to illustrate the effectiveness of the theory.

Fuzzy Model Reference Adaptive Controller Design for Multivariable Nonlinear System

This paper describes the fuzzy model reference adaptive controller design for nonlinear system based on TSK model. The stability of closed-loop system can be assured by Lyapunov function and the adaptive law is developed. The parameters of the controller can be regulated by the adaptive rules and the control scheme is applied on the automatic gauge control system and spherical motor system as two examples. The analysis of dynamic performance for ordinary PID controller and fuzzy adaptive controller is performed in detail with simulation software. Simulation results verify the systems with strong adaptive ability and can adapt to the changes and disturbances of the controlled object. This study provides a theoretical guide for the configuration design, optimization and control research of multivariable nonlinear systems.

Frequency domain based nonlinear feed forward control design for friction compensation

A frequency domain based method for controller design for nonlinear systems is presented. In a case study, this method is applied to optimally design a feed forward friction compensator for an industrial motion stage in a transmission electron microscope. It is shown that the frequency domain approach yields a tool to fast and easily design friction control in practice with high detection sensitivity and orthogonal tuning of the controller parameters, while providing a well defined notion of optimal performance.

Design of nonlinear PID control systems using boosting algorithm

AbstractThere are many nonlinear systems among process control systems. However, it is difficult to handle nonlinear properties with a linear controller. Thus, various methods have been studied in this field. On the other hand, a scheme called boosting has been proposed in the machine learning field. This scheme can obtain highly accurate conditions by combining less‐accurate conditions. Boosting can obtain better results than a neural network with fewer learning data. In this paper, we propose a method for the design of nonlinear PID control systems using the boosting algorithm. The original boosting is capable of dealing only with two‐valued variables, and thus we extend the algorithm for function approximation using it. Finally, simulation examples are presented in order to demonstrate the effectiveness of the proposed scheme. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(9): 52–58, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ecj.10310

Analytic LQR Design for Spacecraft Control System Based on Quaternion Model

In this paper, linear-quadratic regulator (LQR) method is proposed for the design of nonlinear spacecraft control systems. The proposed design is based on the linearized spacecraft model that involves only three components of the quaternion. By using a simple and special structure of the linearized reduced quaternion model, an analytical solution for the controller. It is shown that the analytical solution of the state feedback matrix is an explicit function of the cost matrices Q and R. The analytic solution makes it convenient in design practice to tune the feedback matrix and the cost matrices Q and R to balance the requirements between response performance and fuel consumption. It is shown that the designed controller globally stabilizes the nonlinear spacecraft system, whereas it locally optimizes the spacecraft performance. A design example is provided to show the effectiveness of the design method.

Call for Papers: International Journal of Robust and Nonlinear Control Performance of Nonlinear Control Systems

The International Journal of Robust and Nonlinear Control is inviting papers for a special issue on ‘Performance of Nonlinear Control Systems’ (for a description of the scope, see below). Authors are kindly requested to submit their papers by October 1st 2011 following the link Online Submission on the journals homepage: wileyonlinelibrary.com/journal/rnc. Authors must select Nathan van de Wouw or Marcel Heertjes as the Submitting Editor. Each submission must be clearly identified as a submission for this special issue by entering Performance of Nonlinear Control Systems in the Special Issue Title Field. The manuscripts should be prepared in accordance with the publication format described in ‘For Authors’ on the journal homepage. Scope: The topic of this special issue is the performance analysis and performance-oriented design of nonlinear control systems. Nonlinear control has received wide attention in the systems and control literature and examples of the practical application of nonlinear control in practice are widely available. Still, the majority of the (theoretical) advances made are related to the design of stabilizing nonlinear controllers for (nonlinear) plants, indeed no easy task in general, while not accounting for performancerelated issues. Moreover, in many industries, still the application of linear control techniques prevails. One of the main reasons is the fact that performance is key in practical applications, be it in the form of transient performance criteria, such as rise time and overshoot, or in the form of sensitivity to perturbations, such as measurement noise and external disturbances. On the one hand, linear control techniques have been so successful since a profound (frequencydomain) framework for performance analysis exists. On the other hand, linear control is subject to fundamental (performance) limitations, a famous example of which is the Bode sensitivity integral. Nonlinear control may overcome such limitations. To harvest the full potential of nonlinear control in practice, the further development of powerful performance analysis tools for nonlinear control systems and matching performance-based design techniques for nonlinear controllers are needed, hence this special issue. Resuming, topics of particular interest are, but not limited to: • Performance limitations in linear control systems and how nonlinear control may be employed to overcome such limitations. • Tools for performance analysis of nonlinear control systems. • Performance-based synthesis techniques of nonlinear controllers. • (Industrial) application of high-performance nonlinear controllers.

Nonlinear underwater robot controller design with adaptive disturbance prediction and smoother

A new hybrid adaptive control algorithm is proposed for the nonlinear system controller design of underwater robot. Compared with the previous works in the controller design of underwater robot, the main advantages of this work are: (1) A new disturbance prediction and compensation model is proposed; (2) A new adaptive fuzzy smoother is proposed for the control input; (3) A time-varying flow disturbance is considered for the control design which is always neglected in many previous works and several practical experiments under different environment were implemented to verify the control performance. The Lyapunov stability theory proves the stability and convergence of this new control system. Simulation and experiment results demonstrate the performance and the effectiveness of this new algorithm.

Exponential stability analysis and controller design of fuzzy systems with time-delay

Abstract Takagi–Sugeno (T–S) fuzzy models can provide an effective representation of complex nonlinear systems with a series of linear input/output submodels in terms of fuzzy sets and fuzzy reasoning. In this paper, the T–S fuzzy model approach is extended to the stability analysis and controller design for nonlinear systems with time delays. An improved stability condition is proposed by introducing adjustable parameters into the Lyapunov–Krasovskii functional. Stabilization approach for fuzzy state feedback is also presented. Sufficient conditions for the existence of fuzzy feedback gain are derived through the numerical solution of a set of obtained linear matrix inequalities (LMIs). Compared with the existing methods in the literature, the proposed approach has less conservatism and both the sizes of delay and its derivative are involved in the criterion. The dynamical performance of the system can be adjusted by changing the adjustable parameters. Finally, two examples are given to show the effectiveness of the proposed approach.

A Dual Comparison Principle for the Analysis and Design of Discrete-Time Dynamical Systems

AbstractIn this article, two new comparison principles for studying positive invariance and stability of linear and nonlinear discrete-time systems are presented. First, a general comparison principle enabling one to determine necessary and sufficient conditions of positive invariance of sets described by their “border surfaces” is developed. Then, a dual comparison principle describing the dynamics of the “vertices” of these sets is established. Both results can be used for the stability analysis and the control design of nonlinear systems.

Model-Reference Discretized PID Control and Robust Stabilization for Continuous Plants

AbstractThis paper deals with a designing problem of discrete-time and discrete-value (discretized) control systems based on a model-reference feedback structure. The model used in this study is assumed to be a second-order lag system that is expressed by a bilinear transformation. That type of discretized (nonlinear) control systems is presented and analyzed. The model reference feedback using a second-order continuous-value (linear) system is equivalently transformed into a traditional PID control. The robust stability analysis and design of such nonlinear control systems is examined in a frequency domain. Numerical examples for model-reference type discretized control are provided to verify the design method.

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.

Operator-based non-linear control system design for unstable plants with input saturation

Operator-based robust right coprime factorisation approach is an interesting approach for non-linear control. It provides an effective framework for non-linear unstable system. In practice, the input constraint always exists, which induces that the real control input is different from the controller output, thus the input constraint may destabilise the system. However, control system design for non-linear plants with input saturation has seldom been studied due to the difficulties in dealing with non-linearity. Also in operator-based robust right coprime factorisation method, input saturation is not considered. In this paper, a new control system design for non-linear unstable plants with input saturation is proposed. Based on the robust right coprime factorisation, an operator-based switching controller is designed, which avoids the unstable region. Moreover, based on the proposed design scheme, the output tracking performance is also realised, and the effectiveness of the proposed method is verified by simulation.

Variable structure based robust backstepping controller design for nonlinear systems

This study presents robust control architecture in the sense of variable structure control via a backstepping design. By using systematic backstepping design techniques, closed-loop behavior of an n-order nonlinear system can be transformed into a stability and convergence problem of a fast switched 2nd order system. There are two main parts contained within the proposed control algorithm; one is a nominal control effort generated according to the Lyapunov stability criterion during recursive backstepping processes, and the other belongs to a smooth robust control law designed to eliminate the effects of unknown lumped perturbations. Finally, a Genesio system is used as an illustrated example to demonstrate the robustness of the control algorithm. The feasibility and properties of the proposed method are given by numerical simulations.

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.

A MATLAB toolkit for composite nonlinear feedback control — improving transient response in tracking control

We present in this article a MATLAB toolkit with a user-friendly graphical interface for composite nonlinear feedback control system design. The toolkit can be utilized to design a fast and smooth tracking controller for a class of linear systems and nonlinear systems with actuator and other nonlinearities as well as with external disturbances. The parameters of the controller can be tuned easily on the user panel or autotuned by the toolkit. The toolkit is capable of displaying both time-domain and frequency-domain responses on its main panel and generating three different types of control laws, namely, the state feedback, the full-order measurement feedback and the reduced-order measurement feedback controllers. The usage and design procedure of the toolkit are illustrated by practical examples on a rotational/translational actuator (RTAC) system and a hard disk drive servo system. The toolkit can be utilized to design servo systems that deal with point-and-shoot fast targeting.

Robust stabilisation of polynomial systems with uncertain parameters

The last few years witnessed an increasing interest in the problem of control design of nonlinear systems. A special and very interesting class of nonlinear systems is those with polynomial vector fields. Moreover, the models of real physical systems usually contain uncertainties typically due to bad knowledge of the values of the parameters. This article presents a systematic computational procedure for the design of controllers for polynomial systems with uncertain parameters, combining some results of real algebraic geometry, polynomial certificates and recent numerical methods for verification of the positivity of polynomials. The applicability of the proposed approach is tested by numerical simulations including nonlinear oscillators with polynomial restoring forces with uncertain parameters.

Passive fuzzy controller design for nonlinear systems with multiplicative noises

Abstract This paper proposes a passive fuzzy controller design methodology for nonlinear system with multiplicative noises. Applying the Ito's formula and the sense of mean square, the sufficient conditions are developed to analyze the stability and to design the controller for stochastic nonlinear systems which are represented by the Takagi–Sugeno (T–S) fuzzy models. The sufficient conditions derived in this paper belong to the Linear Matrix Inequality (LMI) forms which can be solved by the convex optimal programming algorithm. Besides, the passivity theory is applied to discuss the effect of external disturbance on system. Finally, some numerical simulation examples are provided to demonstrate the applications of the proposed fuzzy controller design technique.

PID controller design of nonlinear systems using an improved particle swarm optimization approach

In this paper, an improved particle swarm optimization is presented to search for the optimal PID controller gains for a class of nonlinear systems. The proposed algorithm is to modify the velocity formula of the general PSO systems in order for improving the searching efficiency. In the improved PSO-based nonlinear PID control system design, three PID control gains, i.e., the proportional gain K p , integral gain K i , and derivative gain K d are required to form a parameter vector which is called a particle. It is the basic component of PSO systems and many such particles further constitute a population. To derive the optimal PID gains for nonlinear systems, two principle equations, the modified velocity updating and position updating equations, are employed to move the positions of all particles in the population. In the meanwhile, an objective function defined for PID controller optimization problems may be minimized. To validate the control performance of the proposed method, a typical nonlinear system control, the inverted pendulum tracking control, is illustrated. The results testify that the improved PSO algorithm can perform well in the nonlinear PID control system design.

Controller design for nonlinear systems with time delay using model algorithm control (MAC)

This paper presents a digital model algorithm control (MAC) for nonlinear time-delayed systems. The MAC controller is designed based on the sampled-data representation of the dynamic system. A new discretization method using the Taylor series and zero order hold assumption is proposed to discretize the continuous nonlinear time-delayed system. The proposed discretization method can provide accurate time discretization results and convert the discrete-time system into a general nonlinear system, so that the MAC method can be employed. Several simulations are conducted to verify the performance of the proposed method.