Tsai M.-C., Gu D.-W. Robust and Optimal Control: A Two-port Framework Approach

Springer, 2014. — 346 p.
This book presents an alternative approach to find a robust controller via optimization. This approach is based on the chain scattering decomposition (CSD), initiated by Professor Hidenori Kimura [4] and references therein who also named this as chain scattering description. CSD uses the configuration of two-port circuits which is a fundamental ingredient of electrical engineering and is familiar to all electrical engineers and students with basic electrical engineering knowledge. It is shown in the book that (sub)optimal H1, H2 as well as stabilizing controllers can be synthesized following the CSD approach. The book starts from the well-know linear fractional transformation (LFT), in which a control design problem can easily be formulated, and then converts LFT into CSD format. From the CSD formulation, the desired controller can be directly derived by using the framework proposed in the book in an intuitive and convenient way. The results are complete and valid for general system settings. The derivation of solution formulae is straightforward and uses no mathematics beyond linear algebra. It is hoped that readers may obtain insight from this robust and optimal controller synthesis approach, rather being bewildered in a mathematics maze.
The prerequisites for reading this book are classical control and state variable control courses at undergraduate level as well as elementary knowledge of linear algebra and electrical circuits. This book is intended to be used as a textbook for an introductory graduate course or for senior undergraduate course. It is also our intention to prepare this book for control engineers training courses on robust and optimal control systems design for linear time-invariant systems. With the above consideration in mind, we use plenty of simple yet illustrative worked examples throughout the book to help readers to understand the concepts and to see how the theory develops. Where appropriate, MatLAB codes for the examples are also included for readers to verify the results and to try on their own problems. Most chapters are followed with exercises for readers to digest the contents covered in the chapter. To further demonstrate the proposed approaches, in the last chapter, an application case study is presented which shows wider usage of the framework.