This monograph investigates the stability and performance of control systems subject to actuator saturation. It presents new results obtained by both improving the treatment of the saturation function and constructing new Lyapunov functions. In particular, two improved treatments of the saturation function are described that exploit the intricate structural properties of its traditional convex hull representation. The authors apply these treatments to the estimation of the domain of attraction and the finite-gain L2 performance by using the quadratic Lyapunov function and the composite quadratic Lyapunov function. Additionally, an algebraic computation method is given for the exact determination of the maximal contractively invariant ellipsoid, a level set of a quadratic Lyapunov function. The authors conclude with a look at some of the problems that can be solved by the methods developed and described throughout the book. Numerous step-by-step descriptions, examples, and simulations are provided to illustrate the effectiveness of their results. Stability and Performance of Control Systems with Actuator Saturation will be an invaluable reference for graduate students, researchers, and practitioners in control engineering and applied mathematics.

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.

This monograph details basic concepts and tools fundamental for the analysis and synthesis of linear systems subject to actuator saturation and developments in recent research. The authors use a state-space approach and focus on stability analysis and the synthesis of stabilizing control laws in both local and global contexts. Different methods of modeling the saturation and behavior of the nonlinear closed-loop system are given special attention. Various kinds of Lyapunov functions are considered to present different stability conditions. Results arising from uncertain systems and treating performance in the presence of saturation are given. The text proposes methods and algorithms, based on the use of linear programming and linear matrix inequalities, for computing estimates of the basin of attraction and for designing control systems accounting for the control bounds and the possibility of saturation. They can be easily implemented with mathematical software packages.

Compiling the most significant advances from nearly a decade of research, this reference compares and evaluates a wide variety of techniques for the design, analysis, and implementation of control methodologies for systems with actuator saturation. The book presents efficient computational algorithms and new control paradigms for application in the

Saturation nonlinearities are ubiquitous in engineering systems: every physical actuator or sensor is subject to saturation owing to its maximum and minimum limits. Input saturation is an operating condition that is well known to the control community for its “side effects”, which cause conventional controllers to lose their closed-loop performance as well as control authority in stabilization. Therefore, the practical application of control theory cannot avoid taking into account saturation nonlinearities in actuators, explicitly dealing with constraints in control design.

This book provides a wide variety of state-space--based numerical algorithms for the synthesis of feedback algorithms for linear systems with input saturation. Specifically, it addresses and solves the anti-windup problem, presenting the objectives and terminology of the problem, the mathematical tools behind anti-windup algorithms, and more than twenty algorithms for anti-windup synthesis, illustrated with examples. Luca Zaccarian and Andrew Teel's modern method--combining a state-space approach with algorithms generated by solving linear matrix inequalities--treats MIMO and SISO systems with equal ease. The book, aimed at control engineers as well as graduate students, ranges from very simple anti-windup construction to sophisticated anti-windup algorithms for nonlinear systems. Describes the fundamental objectives and principles behind anti-windup synthesis for control systems with actuator saturation Takes a modern, state-space approach to synthesis that applies to both SISO and MIMO systems Presents algorithms as linear matrix inequalities that can be readily solved with widely available software Explains mathematical concepts that motivate synthesis algorithms Uses nonlinear performance curves to quantify performance relative to disturbances of varying magnitudes Includes anti-windup algorithms for a class of Euler-Lagrange nonlinear systems Traces the history of anti-windup research through an extensive annotated bibliography

This book presents basic research on delta operator systems (DOS) with actuator saturation. It proposes null controllable regions of delta operator systems, introduces the enlarging of the domain of attraction and analyzes the performance of DOSs subject to actuator saturation. It also discusses the domain of attraction on different systems in delta domain, and investigates the applications in complicated systems using delta operator approaches.