Conclusions

Mechanics and Control of Robots provides a `how-toaintroduction to robotics. Unfortunately, there are severalproblems with the text. Some of the writing is cumbersomeand hard to follow, and several fundamental items, such ashomogeneous transformations, robot dynamics and con-trol, are not adequately explained. Should subsequentversions of this book be published, Chapter 1, `Introduc-tiona requires signi"cant revisions and Chapter 4, `Dy-namics and Controla should be revised and expandedconsiderably. In its current form,Mechanics and Control ofRobots may fall short as a primary text but the manyexamples provide a good supplement to a robotics course.

References

Craig, J. (1986). Introduction to robotics. Reading, MA: Addison-Wesley,1986.

0005-1098/01/$ - see front matter � 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 5 - 1 0 9 8 ( 0 1 ) 0 0 0 4 2 - 5

Murray, R. M., Zexiang Li, & Shankar Sastry, S. (1994). A Mathe-matical introduction to robotic manipulation. Reading, MA: CRCPress, 1994.

Noah CowanDepartment of EECS: Systems Division,

University of Michigan, 1101 Beal Avenue,Ann Arbor, MI 48109-2110, USA

URL: http://www.eecs.umich.edu/&ncowan/E-mail address: ncowan@eecs.umich.edu

About the reviewer

Noah J. Cowan received his B.S. degree in EE from the Ohio StateUniversity in 1995 and his M.S. in EE from the University of Michiganin 1997. He is currently pursuing his Ph.D. in EECS at the University ofMichigan, expected in May 2001. His dissertation research is on visionguided robot control.

The art of control engineeringK. Dutton, S. Thompson and B. Barraclough; Addison-Wesley, Longman, 1997, ISBN: 0-201-17545-2

The book under review is essentially an undergraduatetextbook on Control Systems Engineering. It di!ers fromthe typical undergraduate text in that the range of topicsdiscussed is extensive and spans almost the entire subject.In this sense it could potentially, also be useful for self-study by an engineer interested in a quick introduction toadvanced topics such as Adaptive, Multivariable, Non-linear, Robust and Optimal Control and even in a grad-uate course that is practically oriented. The authors statein the Preface that the book is directed at the ControlEngineering curriculum in European universities. ThePreface lays out strategies for carving out, from thecontents of the book, "ve di!erent types of controlscourses emphasizing classical control, nonlinear controlsystems, digital control, time-domain methods or fre-quency-domain methods, respectively. It is also pointedout that many of the topics can be studied progressivelyat three levels of depth, corresponding possibly, to threeyears of an undergraduate Control Engineering curriculum.For the purposes of this review the contents of the

book may roughly be clustered into three groups. Chap-ters 1}4 are devoted mainly to classical control theory,Chapters 5}9 deal with state space methods, digital con-trol, on}o! controllers and system identi"cation andChapters 10}14 deal with some advanced control topics,namely, multivariable systems in the frequency domain,Adaptive Control, Optimal Control, Robust Control andNonlinear Systems. Each chapter has a a good supplyof worked out example problems and a set of exercise

problems. There are seven appendices dealing withmatrix algebra, Laplace transforms, Matlab, Simu-link, z transforms, Kalman Filter derivation and analgorithm for on line least-squares estimation, respective-ly. These along with references and an index make up813 pages.Let us give a more detailed rundown of the contents.

Classical control is covered in the "rst four chapters.Chapter 1 is introductory and begins with descriptiveexamples of familiar control systems such as oven tem-perature control, household central heating and cooling,the inverted pendulum and a rocket. The washingmachine is cited as an example of open-loop control.A `strolla through the "eld of control allows the authorsto introduce the language and terminology of controlsystems, point out important issues related to analysis,synthesis and design, such as linearity and nonlinearity,adequate modelling, coupling in multivariable systems,stability and performance tradeo!s and control usingPID, lag, lead and digital controllers. The role of statespace methods are discussed and it is rightfully pointedout that the terms classical and modern control are notonly outdated but misleading since the so-called classicalmethods are the ones mainly used to design most real-world control systems today. The PID controller is de-scribed in some detail as it is the most common controllerin use across many industries. The `uglya fact that modelmismatch cannot be overcome by online tuning (presum-ably adaptive control) is stressed and thus the import-ance of robust control is established. I think this informaland nonmathematical chapter will be very useful to theserious student of the subject and sets the contents of therest of the book in perspective.

Book reviews / Automatica 37 (2001) 957}967 961

In Chapter 2 di!erential equations describing lumpedparameter models of RLC networks, simple mechanicalsystems, thermal and #ow systems are derived from theconservation laws of physics. Time-domain solutions areobtained using Laplace transforms. The latter also leadsto the de"nition of transfer functions and block diagramalgebra. The loading problem, a pitfall in the use of blockdiagram algebra, is demonstrated through an example.Linearization of nonlinear systems is discussed. Statespace models are brie#y introduced as are di!erenceequations and digital simulations.Chapter 3 brings in some design and performance

issues. Stability tests for transfer function and state spacemodels, the system response to step, ramp and sinusoidaltest inputs, dominant pole analysis, the calculation ofsteady state errors, integral squared error criteria, Bodeplots, the e!ects of right half-plane zeros and time delayson system response, gain and phase margins and stepresponse speci"cations are discussed through examples.The Routh stability test is presented and the Ziegler}Nichols procedure for tuning of PID controllers from theresults of step response and frequency response tests aredescribed. The Nyquist and Inverse Nyquist plots andthe Nichols chart are brie#y introduced as additionaldesign tools. Discrete time models and the discretizationof continuous time state space models are discussed.A fairly detailed discussion is given of methods for identi-"cation of system transfer functions from step and fre-quency response data.Chapter 4 continues the discussion on the design of

single-input}single-output (SISO) systems initiated inChapter 3 with the focus shifting to the Nyquist criterion,which is now proved, and root locus methods for settinggains and investigating the e!ect of parameter variations.The design of PID, lag, lead and lag}lead controllers arediscussed as is the implementation of analog controllersusing op-amps.The next cluster, Chapters 5}9, contains state space

methods (Chapters 5 and 9), on}o! and programmablelogic controllers (PLC's) (Chapter 6), digital control sys-tems (Chapter 7) and system identi"cation (Chapter 8).Most of these topics would be covered in a secondundergraduate course in control.Chapter 5 mainly deals with state variable feedback.

First, the concepts of controllability, observability andstabilizability are introduced. That minimal order realiz-ations are necessarily controllable and observable ismentioned without proof. The notion of state variablefeedback as a technique to control a system is introduced.The fact that controllability allows arbitrary assignmentof eigenvalues by state feedback is used, again, tacitly andwithout proof, to develop some design examples of regu-lator and tracking systems. In the latter case integralcontrol is used in conjunction with state feedback inthe augmented system to stabilize the closed loop andthereby track step inputs with zero steady state error.

Naturally, this requires the augmented system to be con-trollable or at least stabilizable. This assumption is statedbut the authors do not point out that the controllabilityof the augmented system requires that there be at least asmany inputs as outputs and that the plant contain notransmission zeros at the origin. In my opinion this is anexample of a situation where there is essential insight tobe obtained from the mathematics. The rest of the chap-ter deals with discrete time systems, z transforms, digitalequivalents using pole zero matching and Tustin equiva-lents, digital PID control and the e!ects of samplingperiods on accuracy requirements. The step responseequivalent is not mentioned although this is a popularmethod of designing digital controllers.A logical follow up to Chapter 5 is Chapter 9 which

deals with the problem of recovering unmeasurable statesfrom available measurements. Both the deterministic (ob-servers) and stochastic (Kalman "lters) versions of thisproblem are dealt with in Chapter 9. Observers or es-timators are needed to implement state feedback controllaws using only available measurements. Full and re-duced order observers are treated. Here again the lack ofa clearly stated pole assignment result haunts the pre-sentation. For example, the reader does not know whythe reduced order observer can be stabilized at all. Therole of observers in closed-loop systems is discussed andthe `separation principlea is established. The rest of thechapter deals with the Kalman "lter which is an optimal(minimum variance) state estimator for a system corrup-ted by dynamic and measurement noise. The Kalman"lter equations and their optimality properties are dis-cussed and illustrated here but the detailed derivation is,appropriately, deferred to Appendix 6.Chapter 6 describes on}o! controllers and programm-

able logic controllers (PLC's). A simple discrete eventsystem example is used to develop the `ladder logica usedto program PLC's. There is also some discussion ofhydraulic servos and op-amp implementation of analogcontrollers. I have not seen any other undergraduate textcovering this material and I found it refreshing.`Truea digital control is the subject of Chapter 7. By

this the authors mean the z-transform analysis and de-sign of a continuous time plant controlled by a discretetime system connected to it through sample and holddevices. After developing the z-transform machinery theauthors discuss the design of deadbeat, Kalman andDahlin controllers. The deadbeat controller is de"ned tobe one which zeroes out the error to a step input in onesampling instant; therefore such a design is achievable for"rst order systems only. The Kalman controller is ann-step dead beat controller, whereas the Dahlin control-ler attempts to produce a "rst order exponential responseto a step input. Examples of these designs are included forillustration. As far as deadbeat control goes, I would haveliked to see a clear statement regarding the fact thatdeadbeat control requires all the closed-loop poles to be

962 Book reviews / Automatica 37 (2001) 957}967

located at the origin. I would also have liked a briefdiscussion of intersample behaviour and the problems itcan cause.Chapter 8 gives a detailed treatment of system identi-"cation. The technique of cross correlation testing toobtain the impulse response is described. The use ofpseudo-random binary sequences as inputs to carry outsuch tests are treated and the problem of obtainingfrequency response information from such tests are alsodescribed. The problem of obtaining transfer functionsfrom Bode plots, discussed earlier in Chapter 3, isrevisited, and nonminimum phase and time delaysare brought in. The rational approximation (Padeapproximant) of time delay transfer functions is de-scribed. It is my experience that the Pade approximationis rather dangerous for stability analysis of closed loopsystems with delays. In other words the Pade approxi-mant in the loop may be stable while the actual system isnot. I would have expected to see some warnings regard-ing this but did not. The chapter contains a nice set ofexamples.The third cluster consisting of Chapters 10}14, deal

with advanced topics, typically covered in graduatecourses. Chapter 10 is devoted to frequency responsemethods in multivariable system design. Here the maintool is diagonal dominance, a concept due to Rosen-brock, who developed it in the 1960s and 1970s as anextension of Gershgorin's theorem on eigenvaluesbounds obtainable from matrix elements. When diagonaldominance is achievable, say, by pre- or post-compensa-tion, a multivariable system can essentially be then de-signed as a set of single-loop designs. This chapterdescribes the characteristic locus, which is the trace of aneigenvalue q

�(s) of the forward transfer function as the

Nyquist contour is traced by s. These traces can be usedto give a Nyquist type stability criterion. When diagonaldominance can be achieved, even at a particularfrequency, SISO techniques can be used to attemptmultivariable design. The chapter contains an exten-sive discussion of inverse Nyquist array methodsof design and the so-called Perron Frobenius methodto test for diagonal dominance achievability atparticular frequencies and the associated compensationmethods.Chapter 11 discusses adaptive and self-tuning control.

It begins by describing the concepts of gain schedulingand self tuning. The parameter estimation required in selftuning leads to the on-line least-squares estimation (oridenti"cation) algorithm called Plackett's algorithm,which is derived in Appendix 7. The controller synthesisbased on the identi"ed model is usually a pole placementcontroller. Examples are given of this technique. Thedeep issues of stability of closed-loop adaptive controlsystems are not dealt with. Model reference adaptivecontrol and variable structure systems are brie#ydescribed.

Optimal control is the subject of Chapter 12. Bellman'sPrinciple of Optimality is introduced and used to derivethe dynamic programming algorithm to solve multistagedecision problems. This is then applied to the linearquadratic regulator problem to derive the standard solu-tion. The "nite time optimal tracking problem, and thedi$culties of the in"nite time tracking problem are men-tioned. In the latter case the performance index is in"niteunless an integrator or more generally an `internalmodela in included apriori. Two case studies*a machinetool drive and an antenna positioner are given as illustra-tive examples.In Chapter 12 some ideas of Robust Control are pre-

sented. The usual tradeo!s between the sensitivity andcomplementary sensitivity are discussed for SISO sys-tems. For multivariable systems, worst-case analysismethods for performance in the H

�and H

�norms, their

calculation through Lyapunov equations and singularvalues and the small gain approach to robust stabilityunder unstructured uncertainty are described. The usualtwo port representation of `generalizeda plants is intro-duced, however the now standard DGKF solution of theworst-case optimal controllers are not described. There isno mention of any of the rich results available on robust-ness under real parametric uncertainty.The last chapter, Chapter 14 deals with Nonlinear

Systems in some detail. It begins with a description ofvarious types of nonlinear elements and nonlinearities.These include discussion of limit cycles, saturation, deadzones, chaos, asynchronous quenching, jump resonance,hysteresis, backlash, quantization and friction. Lineariz-ation is then discussed followed by phase plane analysisof second order systems. Next Lyapunov's (second)method is introduced and applied to a number of exam-ples. The describing function is introduced and illus-trated by examples of the calculation of describingfunctions for several nonlinearities. The chapter endswith descriptions of Popov's and Zames's methods forthe stability analysis of nonlinear feedback systems.Feedback linearization and backstepping are not men-tioned despite their popularity as design techniques innonlinear control theory.So where is the `arta promised in the title ? In my

opinion the authors have successfully painted the richand exotic landscape of control engineering with a broadbrush. The range of topics spanned by the book itselfgives a good idea of the diversity of approaches anddesign issues of concern to the control engineer. Indeedthe only topic left out seems to be Intelligent Control.The art is also in the details of the examples, generouslyprovided in each chapter, and constructed to emphasizethe practical engineering aspects, rather than the mathe-matics. The authors state at the outset that their objectiveis to promote control engineering as a discipline andmathematics is used only as and when it is needed to aidin the design calculations. The art is also evident in the

Book reviews / Automatica 37 (2001) 957}967 963

consistent e!ort to extract `intuitiona from the calcu-lations and examples.There is also a downside to the authors' attitude to-

wards mathematics and this shows up as de"ciencies insome crucial places. I would have at least included a clearstatement of the pole assignment theorem. This wouldhave put the chapters on state feedback and observers ona solid footing. The equivalence of minimality of realiz-ations to joint controllability and observability and it'smany subtle consequences should have been worked out;it would have clari"ed many issues of multivariable sys-tem stability and the dangers of phantom cancellations.There are also omissions of fundamental control topics.The tracking and disturbance rejection problem and theassociated results such as the Internal Model Principleare absolutely central to the control "eld but they are notmentioned. The examples of integral control given arenot enough to make up for this gap. In all fairnessthough, this criticism can be made of just about everyundergraduate textbook in circulation. The chapter onRobust Control does not even mention a single resultfrom the "eld of `Parametric Robust Controla despitethe existence of many elegant and practically useful re-sults developed since 1985.

0005-1098/01/$ - see front matter � 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 5 - 1 0 9 8 ( 0 1 ) 0 0 0 4 3 - 7

To summarize this review, I would like to reiterate thatthe authors have produced a unique textbook with topicscovering almost all aspects of control engineering. Thebook would be useful as an undergraduate textbook, andin this regard it is superior to many popular texts cur-rently in the market. A working engineer could "ndthe book useful as a quick, albeit super"cial, introduc-tion to advanced control topics (Chapters 10}14). I donot regard the book suitable for a graduate course inControl at least as it is taught typically in most USuniversities.

Shankar P. BhattacharyyaDepartment of Electrical Engineering,

Texas A&M University,College Station, TX 77843-3128, USAE-mail address: bhatt@ee.tamu.edu

About the reviewerShankar P. Bhattacharyya was born on June 23, 1946 in Rangoon,Burma and educated at the Indian Institute of Technology, Bombayand Rice University, Houston. He is a Professor of ElectricalEngineering at Texas A&M University, College Station, Texas. Hehas authored or coauthored 4 books and over 180 papers onControl Systems. He is also a concert artist, playing Indian Classicalmusic on the Sarode.

Control of movement for the physically disabledD. PopovicH and T. Sinkjaer; Springer, New York, 2000,ISBN: 1-85233-279-4

It is an unfortunate paradox that the advances inmedical therapy and care and the increased life expect-ancy results in an expanding population of physicallydisabled persons. Many physically disabled su!er fromneuronal damage (e.g., stroke or spinal cord injury)that prohibits or disturbs the control of movements;others are amputees that lack a limb or part of a limb.The challenge to assist these patients with arti"cialmotor control and arti"cial limbs is enormous; itrequires a multidisciplinary expertise in medicine andengineering.From a control engineer perspective, the biological

motor control system is amazing. Even the very basicability to produce a stable walking pattern in roughunknown terrain, which is naturally generated by thebiological motor control system, is an extremely di$cultengineering endeavor, as any student who tried to stabil-ize an inverted pendulum can testify (see, e.g., Raibert andSutherland, 1983) for an inspiring attempt to imitatebiological locomotion in robots).The authors, PopovicH and Sinkjaer, are both trained

as engineers and are well known for their research in

this "eld. In this book, they cover an extremelylarge portion of the state of the art technology andtheories in the "eld of motor control for the physicallydisabled.Other books contain more quantitative and qualitat-

ive examples about motor control (e.g., McMahon, 1984;Rosenbaum, 1991; Latash, 1993). However, these booksdo not thoroughly address the issues of rehabilitationtechnology.My main criticism is aesthetic; this book uses a`wide surveya style, which includes rapid transitionsfrom one model to another and from one result to theother. This style occasionally prevents full appreci-ation of each model and result. In addition, there area number of poor quality "gures and several cumber-some sentences especially in the very "rst chapter. Asa result, the book is rather di$cult to read in certainsections.In spite of these shortcomings, the book provides

a comprehensive reference source, and it is certainly thede"nitive reference book in this "eld. I strongly recom-mend it for the biomedical engineering shelves of anymedical and engineering library and for the researchersand students of this "eld.In the rest of this review, I will brie#y describe the "eld

and the content of the book; and then compare it to other

964 Book reviews / Automatica 37 (2001) 957}967