9R12. Nonlinear Control Based on Physical Models. Lecture Notes in Control and Information Sciences, Vol 260. - A Kugi (Dept of Auto Control and Control Syst Tech, Inst for Auto Control and Elec Drives, Johannes Kepler Univ, Altenbergerstr 69, Linz, 4040, Austria). Springer-Verlag London Ltd, Surrey, UK. 2001. 172 pp. Softcover. ISBN 1-85233-329-4. $62.80.

Reviewed by MA Cutchins (Dept of Aerospace Eng, Auburn Univ, 211 Aerospace Eng Bldg, Auburn AL 36849-5338).

This timely book is important because most physical systems are nonlinear (NL) in nature, and control success is linked to the need for progress in a number of areas in order to achieve practical nonlinear control. These areas are: 1) Practical applications and their requirement for more demanding performance than theoretical applications alone, 2) Increasing computer power for both numeric and symbolic computation, 3) Real-time execution of the complicated NL control laws.

The book emphasizes electromagnetic, mechanical, and hydraulic systems that can be described well analytically. Most of these applications fall under the following categories:

  • • PCH-port-controlled Hamiltonian systems

  • • PCHD-port-controlled Hamiltonian systems with dissipation

  • • PBC-passivity-based control systems

  • • PWM-(pulse-width-modulation)-controlled systems

  • • HGC-hydraulic gap control systems

There are some examples of PD controllers. Typical of the author’s approach on these different systems are the postulation of explicit system definitions followed by theorems and propositions and solutions to several of the simplest cases. The approach progresses in complexity, usually culminating in experimental cases with graphic results. For example, in the chapter on electromagnetic systems, the applications are a simple electric circuit, a three-phase power system, a dc-to-dc converter with four switches, concluding with both theory and experimental results for a C´uk converter.

In the chapter on mechanical systems, a very appropriate topic for today is the author’s approach to actuator and sensor design of piezoelectric structures. Beams with various loading and support motions are utilized as examples.

In the chapter on hydraulic-drive systems, the success of linear controllers in practical applications is summarized, and the use of controllers that take into account the NL nature of the systems is addressed. This culminates in a four-high mill stand model, a pump-displacement-controlled rotational piston actuator, and the swash-plate mechanism of a variable-displacement pump.

The book has excellent figures, 147 references, a brief index, and while mathematically complex, reads well. An excellent feature is the use of nomenclature tables for the more complex models. This reviewer recommends Nonlinear Control Based on Physical Models as primarily a reference book intended for control engineers, professors, and libraries. The author succeeds in his goals, elaborating the link between modeling and NL control, and demonstrating how the physics behind the mathematical models can contribute to the success of certain control strategies.