The book pro- vides concise discussions of relevant theoretical aspects of the
ASVC prob- lem and detailed application samples that can assist those
interested ...
BOOKSHELF
Active Sound and Vibration Control: Theory and Applications, by Osman Tokhi and Sandor Veres, Editors, Peter Peregrinus, 2002, 448 pp., ISBN: 0 85296 038 7, US$95.00. Reviewed by Kevin Fishbach. This volume is a comprehensive compilation of the state of active sound and vibration control (ASVC) up to the year 2001. The book provides concise discussions of relevant theoretical aspects of the ASVC problem and detailed application samples that can assist those interested in the design of sound attenuating systems. The book covers a wide breadth of subjects that will appeal to controls engineers, and is well documented by extensive references. The book is divided into three sections. Section I (chapters 1, 2, and 3) presents the history of ASVC, introduces analytical tools for characterizing sound fields, and discusses several control approaches for the ASVC problem. Section II (chapters 4 through 9) discusses additional control methodologies for this problem. Section III (chapters 10–15) discusses applications in different areas of ASVC. Chapter 1 presents a history of ASVC with many examples. Chapter 2 focuses on the attenuation of a single source in a 3-D free field using a frequency-domain SISO-feedforward controller and presents performance and stability measures for analyzing the sound field. Chapter 3 introduces the filtered-reference least mean square (LMS) adaptive algorithm and applies it to a duct noise control problem using a feedforward controller. The chapter also discusses feedback control and internal model control. Chapter 4 introduces an adaptive finite impulse response (FIR) feedforward controller for overcoming the difficulties of the filtered-x LMS algorithm in the multiple-input case. Chapter 5 tackles the problem of sound field contamination by multiple disturbance frequencies through
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the design of multiple controllers tuned to the individual frequencies. This discussion is based on the filtered-x LMS algorithm. Chapter 6 introduces a model-free time-domain iterative controller and presents schemes for tuning feedforward and feedback controllers and frequency selective filters. Chapter 7 presents procedures for generating modelbased H∞ controllers for vibration control on active mounts and glass plates. Chapter 8 shows how neural networks based on the multilayered perceptron (MLP) and radial basis
function (RBF) approaches can be used in control design. Chapter 9 presents genetic algorithms and their use in the determination of control source location and control filter weight optimization. Chapter 10 evaluates the sound field around a model of the human head under adaptive control. This chapter suffers from poor organization of figures to the extent that some of the figures referenced actually don’t exist in the text. Chapter 11 introduces the modeling and feedback control of microvibrations using a state space model derived using the Lagrange-Rayleigh-Ritz approach and a control law based on the linear qua-
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dratic regulator. Chapter 12 deals with the control of flexible manipulators. Open-loop control is explored with wave-shaping strategies such as lowpass filtered, band-stop filtered, and Gaussian-shaped torque inputs. Feedback control is explored using adaptive variable structure control, adaptive joint-based colocated control, and adaptive inverse-dynamic active control. Controller performance is evaluated using objective measures such as end-point acceleration. Chapter 13 introduces the subject of noise cancellation in locomotive engines. The chapter identifies, and ranks, the sound field components inside a locomotive engine and develops a technique for attenuating the sound fields perceived by the conductor. The control methodology referred to as a successive optimization procedure. This oversight leaves the reader without a clear idea of the control methodology used in the simulations. Chapter 14 is an excellent, but short, introduction to the subject of road booming noise control in automotive applications. The chapter presents the different components of road booming noise and proceeds to a comparison between FIR filtering and infinite impulse response (IIR) filtering in the constrained multiple filtered-x LMS algorithm. Unfortunately, the chapter is short, and the reader is left with a desire for a deeper exposition of one of the most common ASVC problems. Chapter 15 deals with the subject of processor hardware for ASVC calculations. Transputers, RISC processors, and DSP devices, in parallel and sequential-processing arrangements, are used to process a beam simulation and self-tuning ASVC algorithm. The performance of the different arrangements is assessed, and the results are explained based on factors such as the processor’s ability to perform matrix calculations. This book provides a useful review of theoretical approaches and applications in the field of active sound and vibration control. Any
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reservations about the presentation are counterbalanced by the thorough theoretical expositions and the wealth of practical examples given. The book is geared toward engineers interested in noise reduction but would be useful for any engineer interested in learning how a broad variety of control methods can be applied to solve a particular problem. Stability of Time-Delay Systems by Keqin Gu, Vladimir L. Kharitonov, and Jie Chen, Birkhäuser, 2003, 353 pp., ISBN 0-8176-4212-9, $79.95. Reviewed by Vladimir Rasvan and Dan Popescu. The destabilizing effects of time delays are well known to control engineers. In fact, robustness against time delay has been an important and challenging problem from the earliest days of classical control. The last 10–15 years have witnessed a renewed interest in time delay control systems because of new problems, new models, and new techniques. The advent of linear matrix inequalities and other computationally feasible methods has stimulated research in mature areas such as linear system stability and stabilization. The Routh-Hurwitz problem of locating the roots of a characteristic polynomial in the stability zone, which is either the open left-half plane or the interior of the unit disk, can be tackled by frequency or matrix methods, the latter being related to quadratic Lyapunov functions. The book covers these topics in the context of linear time delay systems, where the characteristic equations are quasi-polynomials and the Lyapunov functions are LyapunovKrasovskii functionals. The authors of this book are well known to those who are active in the field of time delay systems. Chen has developed frequency-sweeping tests for root location of quasi-polynomials; Gu has introduced spatial-discretization techniques for LyapunovKrasovskii functionals; and Kharitonov has investigated quadratic Lyapunov-
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Krasovskii functionals for stability domain estimation. This book is a product of these specialists’ research in the field of linear time delay systems and contains the essence of their contributions. The book consists of two main parts: the Frequency Domain Approach, dealing with classical stability, frequency sweeping, and constant matrix tests; and the Time Domain Approach, dealing with Lyapunov-Krasovskii functionals and their discretized versions. The cases of single delay, commensurate delays, and incommensurate delays are discussed separately.
A third part, called the Input-Output Approach, deals with input/output stability, a topic familiar to control engineers. These problems involve small gain analysis of feedback loops and robustness to uncertainty introduced by finite-dimensional delay approximation. This book has many useful features that complement the prior literature. For the frequency-domain approach to the characteristic equation, the book completes the line of books by Pinney (1958), Bellman and Cooke (1963), and Stepan (1989) with respect to the case of several delays.
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For the time-domain approach, the book is a successor to Krasovskii (1959), Halanay (1963), Hale (1971, 1977, 1993), and Kolmanovskii and Nosov (1981); the technique of constructing Lyapunov-Krasovskii functionals is developed in more detail. In addition, the reader can find useful information about software implementation and computational complexity. Last, but not least, the authors are experts in the field, and they relate their own experience. The book can be useful to engineers, applied mathematicians, and graduate students. Foundations of Deterministic and Stochastic Control, by Jon H. Davis, Birkhauser, 2002, 440 pp., ISBN 08176-4257-9, US$77.95. Reviewed by Pavlos K. Giannakopoulos. This book serves as an introductory text on deterministic and stochastic control and estimation. The author’s approach emphasizes inner product space methods and the use of WienerHopf methods for infinite-time linear regulation and stationary filtering. The book is divided into 14 chapters. The first chapter is a brief introduction to state-space models, including linear time-varying and time-invariant models as well as the concepts of observability, controllability, and reachability. Chapter 2 is devoted to the derivation of the optimal linear regulator. The problem is treated as a minimum norm problem in an inner product space. Algebraic Riccati equation properties are briefly discussed, and the chapter ends by considering the linear optimal tracking problem. Chapter 3 introduces Lyapunov stability and asymptotic stability theorems. Invariance theory is briefly presented and the stability of input-output systems is considered. Chapter 4 turns to random variables and processes, with emphasis on the study of Gaussian variables. Chapter 5 is devoted to the problem of state estimation. The projection theorem is used to derive the
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discrete-time Kalman filter. Some elementary results on the boundedness of the error covariance, and the stability of optimal filters for time-invariant stochastic systems, are given. Chapter 6 is a short introduction to stochastic integrals and stochastic differential equations. Based on the definitions presented, the continuous-time Kalman-Bucy filter is derived. Chapter 7 presents the discrete- and continuous-time stochastic regulator problem with both full- and partial-state observation. The problem is treated as a stochastic dynamic programming problem, which yields the separation theorem under Gaussian assumptions.
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Chapter 8 discusses full-state and reduced-order observers. Chapter 9 considers the filtering and estimation problem for the general case in which the system model is described by nonlinear equations and offers a short presentation on finite-state machines, finite Markov processes, and hidden Markov models. Chapter 10 deals with the Wiener-Hopf equation for the continuous and discrete-time linear filtering problem. The filtering problem is solved by means of spectral factorization techniques using Gohberg-Krein results. The basic relations for the frequency domain version of the linear regulator are also discussed. Finally, the optimal feedback gain is computed without the solution of the algebraic Riccati equation. Chapter 11 deals with the linear regulator problem for open-loop unstable distributed systems using the Wiener-Hopf method. The regulator problem is formulated as a minimum norm problem in a manner similar to that of the open-loop stable system, resulting in a generalized Wiener-Hopf equation. The optimal feedback gain for the closed-loop system is then computed by means of spectral factorization, without the need to solve the Riccati equations. The chapter ends by applying the results to a distributed system model. In Chapter 12 the Kalman-Bucy filter for distributed stationary systems is derived using frequency domain methods. The derivation of the optimal filter using the above methods is short, and avoids the solution of distributed Riccati equations. The algebraic Riccati equation is used as a heuristic guide for deriving the optimal gain of the filter. The expression for the gain of the filter is proved to be optimal, and yields a stable filter realization.
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Chapter 13 uses a Newton iteration to solve the Riccati equation. This chapter includes the derivation of both the continuous- and the discrete-time forms of the algorithm; the convergence of these two algorithms is also established. The last chapter tackles the numerical solution to the Wiener-Hopf equations by means of spectral factorization techniques and gives the derivation of a recursive algorithm based on Newton’s algorithm for solving the Riccati equation. The last section of the chapter discusses the convergence of the resulting algorithm, and illustrates the algorithm on a sample problem. The book could have benefited from a more extended discussion of the control topics, including a more detailed analysis of the properties of the optimal regulator, which would have given the text added breadth. Overall, the text is well suited to graduate students, researchers, and practicing engineers involved in control.
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