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7R20. Non-linear Control for Underactuated Mechanical Systems. - I Fantoni and R Lozano (UMR CNRS 6599, Univ de Technologie de Compiegne, BP 20529, Compiegne, 60205, France). Springer-Verlag London Ltd, Surrey, UK. 2002. 295 pp. ISBN 1-85233-423-1. $109.00.

Reviewed by SC Sinha (Dept of Mech Eng, Auburn Univ, 202 Ross Hall, Auburn AL 36849-5341).

This is an application-oriented book that is intended for engineers, graduate students, and researchers who are interested in the design of nonlinear controllers for underactuated mechanical systems. Underactuated systems are defined as systems with lesser number of independent control actuators than the degrees of freedom to be controlled. Readers with a background in intermediate level dynamics and control should have no trouble following the material.

After an introduction in Chapter 1, some definitions and background material are presented in Chapter 2. These include Lyapunov stability concepts, Krasovskii-LaSalle invariance principle, passivity criteria, and controllability condition. The next nine chapters deal with the development of control algorithms for a number of underactuated mechanical systems, most of which have served as academic benchmarks. In Chapter 1, an energy-based nonlinear controller is developed for the classical problem of cart-inverted pendulum. Simulations and experimental results are also included. Similar analysis is presented in Chapter 4 that deals with a convey-crane system. Using the passivity property, an energy-based control law is proposed for a pendubot system in Chapter 5.

In Chapter 6, modeling, analysis, and control of the Furuta pendulum (named after K Furuta of Tokyo Institute of Technology) is discussed. The reaction wheel pendulum is presented in Chapter 7. Chapters 8 and 9 are devoted to the design of control algorithms for planar robots. In Chapter 8, the authors present analysis and control of two as well as three link planar robots with flexible joints while in Chapter 9, the problem of a planar robot with two prismatic and one revolute (PPR) joints is considered. It is to be observed that the PPR system has four degrees of freedom and only three control inputs. The control strategy, once again, is based on an energy approach and passivity properties of the system. The ball-beam control is described in Chapter 10, and in this case, the control force is assumed to be acting on the ball rather than the beam. The controller for a simple hovercraft model is designed in Chapter 11.

Chapter 12 deals with the control problem associated with a planar vertical take-off and landing (PVTOL) aircraft. A Lyapunov function using the forwarding technique is used to obtain the control law. The last three chapters are devoted to the modeling and control of helicopters. In Chapter 13, after some general considerations, a simplified model called the helicopter-platform model is analyzed. This model has three degrees of freedom with two control inputs. The nonlinear control strategy guarantees an asymptotic tracking of the desired trajectories. A Lagrangian formulation of the helicopter dynamics is presented in Chapter 14 and a Lyapunov approach is used to design a tracking controller. The same problem is discussed in Chapter 15 via the Newtonian approach. In this case, the control algorithm was developed using the backstepping and Lyapunov techniques.

In summary, Non-linear Control for Underactuated Mechanical Systems is an excellent source for the development of control strategies for an important class of problems, viz, the underactuated mechanical systems. The book is clearly written, and the ideas are conveyed well by the authors. This book is a must for engineering graduate students, researchers, teachers, as well as practicing engineers. It is strongly recommended for individuals and libraries.