9R10. Lyapunov-Based Control of Mechanical Systems. - MS de Queiroz (Dept of Mech Eng, Louisiana State Univ, Baton Rouge LA 70803-6413), DM Dawson, SP Nagarkatti, and Fumin Zhang (Dept of Elec and Comput Eng, Clemson Univ, Clemson SC 29634-0915). Birkhauser Boston, Cambridge MA. 2000. 316 pp. ISBN 0-8176-4086-X. $69.95.
Reviewed by J Bentsman (Dept of Mech and Indust Eng, MC-244, Univ of Illinois, 1206 W Green St, 140 Mech Eng Bldg, Urbana IL 61801).
This book is unique in taking a rigorous approach to controller synthesis for mechanical systems incorporating both flexible and rigid components and making it mathematically accessible to graduate students with relatively modest background. This approach is characterized by generating Lyapunov functions for the entire system using full distributed parameter description of the flexible part in terms of the partial differential equations (PDEs). The strong point of the book is also the presentation of the implementation results where the authors demonstrate the feasibility and the effectiveness of the algorithms proposed. The book is suitable for a graduate course in nonlinear control, with the material on infinite dimensional systems introduced at the outset. The book is also of considerable interest to researchers in control theory, since, in addition to the original theoretical results followed by the detailed proofs, it provides physical examples of the systems, accompanied by their detailed mathematical models, to which the infinite dimensional control technique can be successfully applied.
The book consists of seven chapters followed by four appendices and a relatively detailed index. A number of pertinent figures are incorporated into the text, as well. Chapter 1 briefly introduces the concept of Lyapunov-based control, and rigid and flexible mechanical systems description in terms of ordinary differential equations (ODEs) and PDEs, respectively. It also briefly discusses real-time controller implementation. Chapter 2 addresses the problem of controller design for systems with friction. Here several design issues, such as parametric uncertainty and state inaccessibility are considered in the single-input-single-output (SISO) case, setting the stage for the multi-input-multi-output (MIMO) case considered in Chapters 3 and 4. Chapter 3 presents adaptive tracking controller design for a full state feedback. Motivated by the inaccuracy of the velocity measurements in mechanical systems, Chapter 4 extends the results of Chapter 3 to output feedback. Chapters 5 through 7 consider controller design for mechanical systems with both rigid and flexible components that produce combined ODE/PDE-based control laws. These chapters consider the case of known parameter values, giving rise to model-based control laws, as well as the challenging case of known equation structure, but unknown parameter values, giving rise to the infinite-dimensional adaptive control laws. Chapter 5 gives controller design methods for boundary control of string-type systems, while Chapter 6 gives boundary control laws for flexible beams. Chapter 7 presents controller design for several mechanical systems, including an axially moving string system, a robotic manipulator with flexible link, and a flexible rotor system.
All chapters (2 through 7) present experimental evaluation of the algorithms proposed. Each chapter has an extensive list of references. Appendices provide some of the relevant mathematical facts, derivation of the bounds on the variables in the control laws, and C real-time program codes of the control laws.
Lyapunov-Based Control of Mechanical Systems is a very valuable addition to the literature on control of mechanical systems, nonlinear control methods, adaptive control, and control of the infinite dimensional systems. It is strongly recommended for purchase both by libraries and individual researchers.