Synthesis of actuator limited multivariable control systems

One particular difficulty encountered in modern control systems is the control of systems with actuator constraints. Although there exists a wealth of theory for the design of 1inear control systems, from simple PI/PID control to multi-objective optimal control, many methods do not account for input constraints. Neglecting input constraints can lead to significant controller performance degradation and possible instability in otherwise stable systems.; Over the past 50 years, several methods have been proposed for retrofitting classical linear control techniques to accommodate input constraints which are collectively referred to as anti-windup control. The primary motivation for anti-windup techniques was its simplicity and its two-step design procedure. The control engineer can first design the linear controller and then design the anti-windup compensator. However, early techniques lacked a firm theoretical basis in nonlinear stability and performance analysis. The past decade has seen more systematic approaches to the anti-windup problem primarily due to significant improvements in nonlinear stability analysis tools. Foremost, the development of interior point algorithms and improved computing power have made convex optimization over linear matrix inequalities a practical method for optimal controller analysis and synthesis. As a direct result, significant advances in the stability analysis of anti-windup systems have been made using techniques such as absolute stability theory and piecewise quadratic stability analysis.; Despite these significant advances in the stability analysis of anti-windup systems, relatively little progress has been made towards the synthesis of anti-windup controllers, especially with regard to performance. Moreover, basic design choices such as the proper framework, the correct performance objectives, and how to handle multi-variable systems are just a few issues still open at the beginning of this thesis.; Therefore, the objective of this thesis is to develop anti-windup synthesis techniques which provide a theoretical basis for stability and performance while remaining computationally tractable. The first part of this thesis is devoted to the synthesis of traditional static anti-windup controllers using recent advances in stability analysis. The latter part of this thesis will focus on the traditional anti-windup framework and design procedure.