Control Systems with Actuator Saturation

Saturation nonlinearities are ubiquitous in engineering systems. In control systems, every physical actuator or sensor is subject to saturation owing to its maximum and minimum limits. A digital filter is subject to saturation if it is implemented in a finite word length format. Saturation nonlinearities are also purposely introduced into engineering systems such as control sys tems and neural network systems. Regardless of how saturation arises, the analysis and design of a system that contains saturation nonlinearities is an important problem. Not only is this problem theoretically challenging, but it is also practically imperative. This book intends to study control systems with actuator saturation in a systematic way. It will also present some related results on systems with state saturation or sensor saturation. Roughly speaking, there are two strategies for dealing with actuator sat uration. The first strategy is to neglect the saturation in the first stage of the control design process, and then to add some problem-specific schemes to deal with the adverse effects caused by saturation. These schemes, known as anti-windup schemes, are typically introduced using ad hoc modifications and extensive simulations. The basic idea behind these schemes is to intro duce additional feedbacks in such a way that the actuator stays properly within its limits. Most of these schemes lead to improved performance but poorly understood stability properties.

"The book is very well written. The topics chosen are all fundamental control problems and are treated in depth. All the results presented in the book appear to be the authors' own recent research findings and, without doubt, represent a significant contribution to the important research topic of analysis and design for control systems with actuator saturation. The results included in the book, along with an extensive bibliography will prove to be an important resource for researchers in this area as well as researchers interested in entering this area.The book will prove equally valuable to practicing engineers. The results included in the book are applicable to general systems including strictly unstable ones. All optimization problems involved are convex and can readily and reliably be solved with the Matlab LMI Toolbox. Moreover, all the results are illustrated with fully worked out examples and simulation. In conclusion, the book will be a valuable addition to the libraries of both control theory researchers and control engineering practitioners." International Journal of Robust and Nonlinear Control

"The book reads very well. The results, along with an extensive bibliography will prove to be an important resource for researchers in this area as well as researchers interested in entering this area. It is also noted that many results developed in the book may have applications in the study of a class of recurrent artificial neural networks." IEEE Transactions on Automatic Control

Contenu
Preface.- 1 Introduction.- 1.1 Linear Systems with Actuator Saturation.- 1.2 Notation, Acronyms, and Terminology.- 2 Null ControllabilityContinuous-Time Systems.- 2.1 Introduction.- 2.2 Preliminaries and Definitions.- 2.3 General Description of Null Controllable Region.- 2.4 Systems with Only Real Eigenvalues.- 2.5 Systems with Complex Eigenvalues.- 2.6 Some Remarks on the Description of C(T).- 2.7 Asymptotically Null Controllable Region.- 2.8 Conclusions.- 3 Null ControllabilityDiscrete-Time Systems.- 3.1 Introduction.- 3.2 Preliminaries and Definitions.- 3.3 General Description of Null Controllable Region.- 3.4 Systems with Only Real Eigenvalues.- 3.5 Systems with Complex Eigenvalues.- 3.6 An Example.- 3.7 Asymptotically Null Controllable Region.- 3.8 Conclusions.- 4 Stabilization on Null Controllable Region -Continuous-Time Systems.- 4.1 Introduction.- 4.2 Domain of Attraction-Planar System under Saturated Linear Feedback.- 4.3 Semi-Global Stabilization-Planar Systems.- 4.4 Semi-Global Stabilization-Higher Order Systems.- 4.5 Conclusions.- 5 Stabilization on Null Controllable Region-Discrete-Time Systems.- 5.1 Introduction.- 5.2 Global Stabilization at Set of Equilibria-Planar Systems.- 5.3 Global Stabilization-Planar Systems.- 5.4 Semi-Global Stabilization-Planar Systems.- 5.5 Semi-Global Stabilization-Higher Order Systems.- 5.6 Conclusions.- 6 Practical Stabilization on Null Controllable Region.- 6.1 Introduction.- 6.2 Problem Statement and Main Results.- 6.3 Proof of Main Results.- 6.4 An Example.- 6.5 Conclusions.- 6.A Proof of Lemma 6 3 1.- 6.B Proof of Lemma 6 3 2.- 7 Estimation of the Domain of Attraction under Saturated Linear Feedback.- 7.1 Introduction.- 7.2 A Measure of Set Size.- 7.3 Some Facts about Convex Hulls.- 7.4 Continuous-Time Systems underState Feedback.- 7.5 Discrete-Time Systems under State Feedback.- 7.6 Extension to Output Feedback.- 7.7 Conclusions.- 8 On Enlarging the Domain of Attraction.- 8.1 Introduction.- 8.2 Continuous-Time Systems.- 8.3 Discrete-Time Systems.- 8.4 Conclusions.- 9 Semi-Global Stabilization with Guaranteed Regional Performance.- 9.1 Introduction.- 9.2 Expansion of the Domain of Attraction.- 9.3 Semi-GlobalizationDiscrete-Time Systems.- 9.4 Semi-Globalization Continuous-Time Systems.- 9.5 An Example.- 9.6 Conclusions.- 10 Disturbance Rejection with Stability.- 10.1 Introduction.- 10.2 Continuous-Time Systems.- 10.3 Discrete-Time Systems.- 10.4 Conclusions.- 11 On Maximizing the Convergence Rate.- 11.1 Introduction.- 11.2 Continuous-Time Systems.- 11.3 Discrete-Time Systems.- 11.4 Conclusions.- 12 Output RegulationContinuous-Time Systems.- 12.1 Introduction.- 12.2 Preliminaries and Problem Statement.- 12.3 The Regulatable Region.- 12.4 State Feedback Controllers.- 12.5 Error Feedback Controllers.- 12.6 An Example.- 12.7 Conclusions.- 13 Output RegulationDiscrete-Time Systems.- 13.1 Introduction.- 13.2 Preliminaries and Problem Statement.- 13.3 The Regulatable Region.- 13.4 State Feedback Controllers.- 13.5 Error Feedback Controllers.- 13.6 Conclusions.- 14 Linear Systems with Non-Actuator Saturation.- 14.1 Introduction.- 14.2 Planar Linear Systems under State Saturation-Continuous-Time Systems.- 14.3 Planar Linear Systems under State Saturation-Discrete-Time Systems.- 14.4 Semi-Global Stabilization of Linear Systems Subject to Sensor Saturation.- 14.5 Conclusions.