Design of Linear Multivariable Feedback Control Systems: The Wiener–Hopf Approach using Transforms and Spectral Factorization

This book contains a derivation of the subset of stabilizing controllers for analog and digital linear time-invariant multivariable feedback control systems that insure stable system errors and stable controller outputs for persistent deterministic reference inputs that are trackable and for persistent deterministic disturbance inputs that are rejectable. For this subset of stabilizing controllers, the Wiener-Hopf methodology is then employed to obtain the optimal controller for which a quadratic performance measure is minimized.  This is done for the completely general standard configuration and methods that enable the trading off of optimality for an improved stability margin and/or reduced sensitivity to plant model uncertainty are described. New and novel results on the optimal design of decoupled (non-interacting) systems are also presented.

The results are applied in two examples: the one- and three-degree-of-freedom configurations. These demonstrate that the standard configuration is one encompassing all possible feedback configurations. Each chapter is completed by a group of worked examples, which reveal additional insights and extensions of the theory presented in the chapter. Three of the examples illustrate the application of the theory to two physical cases: the depth and pitch control of a submarine and the control of a Rosenbrock process. In the latter case, designs with and without decoupling are compared.

This book provides researchers and graduate students working in feedback control with a valuable reference for Wiener-Hopf theory of multivariable design. Basic knowledge of linear systems and matrix theory is required.

Joseph J. Bongiorno, Jr. received the bachelor’s, master’s, and doctoral degrees in 1956, 1958, and 1960, respectively, from “Brooklyn Poly” now known as NYU Tandon School of Engineering. He began teaching at the Polytechnic in 1957 as an instructor and remained on the faculty until he retired in 1996. He has continued professional activities since then as Emeritus Professor.

His teaching and research interests have been in control theory, and he has published papers on adaptive systems, stability of linear time-varying systems, dynamical observers, and frequency-domain analytical design techniques for multivariable systems. His research activities have been supported in part through grants from NASA, NSF, and ARO. Professor Bongiorno was a Consultant at Unisys (formerly Sperry) for nearly thirty years where he worked on problems related to inertial navigation of nuclear submarines. He was elected as a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 1985 for contributions to the theory of control system design. He is also a co-recipient of the 1977 IEEE Control System Society Award for the Best Automatic Control Transactions paper.

Kiheon Park received the B.S. and M.S. degrees in Electrical Engineering from Seoul National University, Korea, in 1978 and 1980, respectively, and the Ph.D. degree in System Engineering from Polytechnic University, NY, in 1987. From 1980 to 1983, he served in the Korean Navy as a full-time instructor at the Naval Academy. He was the recipient of a Korea Electric Association Scholarship from 1983 to 1986. From 1988 to 1990, he worked for the Electronic and Telecommunication Research Institute (ETRI), Daejeon, Korea, where he was involved in a factory automation project. Since March 1990, he has been with the School of Information and Communication Engineering at Sungkyunkwan University, Suwon, Korea, where he is currently a Professor. His research interests include optimal design of linear multivariable control systems, decoupling controller design, numerical calculation of Wiener-Hopf controllers and networked control systems.