IEEE Control Systems Magazine

IEEE Control Systems Magazine 119 Quantitative Feedback Design of Linear and Nonlinear Control Systems, by Oded Yaniv, Kluwer Academic, 1999, 369 pp., $140.00, ISBN 0-7923-8529-2; Quantitative Feedback Theory: Fundamentals and Applications, by Constantine H. Houpis and Steven J. Rasmussen, 1999, Marcel Dekker, 408 pp., $150.00, ISBN 0-8247-7872-3. Reviewed by Gerald Hearns. After years without a suitable textbook on quantitative feedback theory (QFT), two have now appeared virtually simultaneously! QFT is a control design technique in the frequency domain that can design controllers for robust performance and stability for use with systems with parametric uncertainty. The main advantages of the technique are its capacity to design controllers with minimum dynamic order and bandwidth and that have nonconservative performance, while being transparent enough to give insight into the trade-offs involved in robust controller design. Both books under review pay homage to the father of QFT, Isaac Horowitz, with whom all the authors have had the benefit of working. The fundamental difference between the two books is that Houpis and Rasmussen keep the mathematics to a minimum, whereas Yaniv provides a much more rigorous mathematical presentation. The first two chapters of Houpis and Rasmussen introduce feedback systems and QFT, citing the numerous successful applications of QFT and including the apparently obligatory section in such texts on “Why Feedback?” Chapter 3 presents the fundamentals of QFT for multi-input, single-output (MISO) continuous systems. The procedures for specifying plant uncertainty, closed-loop performance, bounds for the Nichols chart, and loop shaping are described in a systematic manner. The procedures used to calculate the bounds that specify the required open-loop gain and phase for robust performance are the traditional graphical manipulation on the Nichols chart. Although this provides great insight into the fundamentals of QFT, no mention is made of the algebraic techniques for calculating bounds that are used in computer packages. It is unlikely that anyone nowadays would manually calculate QFT bounds using a Nichols chart when design packages are available. The material from Chapter 3 is extended to discrete systems in Chapter 4. Chapters 5-7 cover the multivariable application of QFT, which involves using MISO-equivalent plants and then designing each loop individually. Two design methods are presented, the second of which tackles the criticism often leveled at multivariable QFT that the controllers are overdesigned. Chapter 8 explains multivariable systems with external disturbances, although it would have been better if the material on disturbance rejection had been integrated with the tracking control design in the previous chapters. Chapter 9 is a personal presentation on how to bridge the gap between theory and practice. Chapter 10 tells the story of the successful design and implementation of a QFT controller for an unmanned research vehicle. Included with the book is the TOTAL-PC CAD package, which is a DOS-based design package with QFT functions. In the second text, it is worth recalling that Oded Yaniv is one of the authors of the MATLAB QFT Toolbox. Thus, it is no surprise that all the examples in this book have been generated using this toolbox; readers are also encouraged to use the toolbox with the script files available at the author’s Web site. The text is divided into two parts dealing with linear and nonlinear systems, respectively. Chapters 1 and 2 introduce linear systems and, in particular, explore the frequency domain, the Nichols chart, and loop shaping. Chapter 3 covers the synthesis of controllers for MISO linear plants (whereas Houpis and Rasmussen talk about design, Yaniv talks about synthesis). The calculation of QFT bounds by both graphical and algebraic methods is described, and the extension to discrete systems is also briefly discussed. Chapter 4 discusses the synthesis of controllers for multivariable linear plants. Every type of problem is covered in a thorough manner: one DOF, two DOF, disturbances at input, disturbances at output, and so on. Although most multivariable QFT designs produce diagonal controllers, there is an interesting section on the design of nondiagonal controllers for QFT. Another innovative section covers the stating of QFT problems using the linear fractional transform notation used in H∞ controller design, such that inferBOOKSHELF