Control systems theory and applications for linear repetitive processes.
The concept of a repetitive process was first introduced by Eric Rogers and David Owens In the early 1970's as a result of work in the University of Sheffield on the modeling and control of long-wall coal cutting and metal rolling operations. This interesting monograph summarizes results of the collaborations between the Universities of Southampton, Zielona Gora, Sheffield and Wuppertal. The monograph consists of ten chapters. Chapter 1 introduces the unique features and control problems for repetitive processes and their general model in a Banach space. Chapter 2 presents the stability theory for the Banach space together with the results of applying it to the various forms of differential and discrete linear repetitive processes. In chapter 3 two types of Lyapunov equations in the stability of discrete linear repetitive processes are investigated. The role of Lyapunov equations in the stability related analysis of differential linear repetitive processes are investigated in chapter 4. The stability robustness of discrete unit memory linear repetitive processes and their differential counterparts are analyzed in chapter 5. For the differential case an LMI approach is applied. In chapter 6 the controllability, observability, poles and zeros of discrete and differential linear repetitive processes are investigated. The \(2d\) discrete linear systems are described by the Roesser or Fornasini-Marchezini state-space models. A behavioral approach is used to define poles and zeros for the processes. The control of differential and discrete linear processes is investigated in chapter 7. The control laws used both current and previous passes and the LMI approach is applied. In chapter 8 the control law design algorithms for models with uncertainties are computed using LMIs and are based on \(H_\infty\), \(H_2\) and mixed \(H_\infty/H_2\) techniques. The application of repetitive processes theory to interactive learning control is analyzed in chapter 9. The norm optimal approach is developed. Chapter 10 summarizes the current state of the art and discusses areas for possible future research.
scientific article; zbMATH DE number 5133618
scientific article