Chapter 1 INTRODUCTION 良已茶 The main ideas covered in this book are motivated and put in historical perspec- tive.A new controller parametrization is outlined and the concept of "robustness" is explained.The scope of the book is defined and hints for its study are provided. 提7 1.1 The Evolution of Control Theory 子 Feedback control mechanisms have been used for millenia.The first applications of the feedback principle(Mayr,1970)can be traced back to ancient Greece:the water clock of Ktesibios (ca.300 B.C.)employed a float regulator.The first automatic feedback controller used in an industrial process was James Watt's flyball governor invented in 1769 for controlling the speed of a steam engine.As these centrifugal_governors were refined,they developed some serious problems, then referred to as "hunting"and now known as "instability."This in turn prompted the first mathematical analysis of a feedback system via differential equations by Maxwell(1868).During the same period Vyshnegradskii (1877) formulated a mathematical theory of regulators. The invention of the negative feedback amplifier at Bell Laboratories by Black prior to World War II marks another milestone in the use of feedback.The 板 observed stability problems ("singing")were explained through the frequency domain analysis techniques by Bode and Nyquist (Nyquist.1932;Bode,1964: Black,1977). Throughout the 1940s and 1950s feedback design by trial and error was pre- dominant and even today this approach plays a major role.Typically,perfor- mance specifications are defined initially and then the controller design is modified iteratively until the best compfomise between the frequently conficting objectives is reached.Every design step is followed by an analysis step and the iterations are guided by experience and rules of thumb.In the late 1950s Newton,Gould, and Kaiser (1957)showed that if the control objectives are formulated in terms of the integral square error (ISE)the "optimal"feedback controller can be found 烈
1机心 CHAPTER 1.INTRODUCTION ".nalytically"-i.e.,directly and without trial and error.This approach,which sbased on the Wiener-Hopf factorization technique,was subsequently greatly eralized,in particular by Kalman. The deficiendy of these "synthesis"techniques is that.typical practical per- rmance objectives are usually much more complex than ISE Frequently the igner wishes totraints on the closed-loop system response char- .teristics like overshoot,rise time,and decay ratio.Also a certain "robustness" gainst changes in the dynamic characteristics of the plant to be controlled is sirable.Often it is possible to achieve these attributes indirectly by frequency- weighting the ISE and by adding to the objective apnalty for excessive move- ments of the manipulated variable.For that purpose the weights and penalties lave to be chosen again iteratively by trial and error.Thus,for a practical design the advantages of such an "optimal control synthesis"procedure over an ad hoc nofool parameters and atest via simulation can become quite mall. The ISE or,in the more general context,the H2-optimal control formulation ominated the literature for about 20 years.In the late seventies three major and in some sense related discoveries started a new era of feedback control theory. .Youla and coworkers (1976)showed that it is possible to parametrize all sta- bilizing controllers for a particular system in a very effective manner:when searching for a controller with specific properties one can simply and without loss search over the space of all stable transfer functions.The parametriza- tion guarantees that the resulting feedback controller automatically yields a closed-loop stable system.Thus,the search for a good controller is greatly simplified. 假定 Zames (1981)postulated that measuring performance in terms of the o-, norm rather than the traditional 2-norm (ISE)might be much closer to the practical needs.This ushered in the era of H optimal control. 别南 Doyle argued that model uncertainty is often described very effectively in terms of norm-bounded perturbations.For these perturbations and the Ho performance objective he developed a powerful tool (the structured singular value)for testing "robust stability"(i.e.,stability in the presence of model uncertainty)and "robust performance"(i.e..performance in the presence of model uncertainty).This is probably the primary motivation for the modern -norm objective In parallel to these developments in mathematics and electrical engineering a new type of algorithm exemplified by Model Algorithmic Control(Richalet et al., 笔晚州 5好
1.2.CONTROLLER PARAMETRIZATION:THE IMC STRUCTURE 3 , 1978)and Dynamic Matrix Control (Cutler and Ramaker,1979)was invented in the process industries and applied successfully to complex process control prob- lems.Though these algorithms had a heuristic basis Garcia and Morari(1982) discovered that some of the modern robust control characteristics,had been in- corporated in them in an ad hoc fashion.Thus,the time was ripe put these irical algorithms on a firmer and to have them benefit from the rich new theory.The objective of this book is to do that while retaining the features which make these algorithms easy to understand and easy to adjust on-line.At times this required mathematical generality to be sacrificed. 1.2 Controller Parametrization:The IMC Structure Consider the block diagram shown in Fig.1.2-1 where the control system is shaded:it includes the two blocks labeled controller and model.The control system has as its inputs the setpoint and process output (measurement)and as its output the manipulated variable (process input).Let us discuss qualitatively the advantages of such a structure over the classic feedback structure shown in Fig.1.2-2. The effect of the parallel path with the model is to subtract the effect of the manipulated variables from the process output.If we assume for the moment that the model is a perfect representation of the process.then the feedback signal is equal to the influence of disturbances and is not affected by the action of the manipulated variables.Thus,the system is effectively open-loop and the usual stability problems associated with feedback have disappeared.The overall system is stable simply if and only if both the process and the IMC controller are stable. Moreover,the I\IC controller plays the role of a feedforward controller and can be designed as such.But the I.IC controller does not suffer from the disad- vantages of feedforward controllers:it can cancel the influence of (unmeasured) disturbances because the feedback signal is equal to this influence and modifies the controller setpoint accordingly. | 位. If the model does not mimic the dynamic behavior of the process perfectly then the fecdback signal expresses both the infiuence of (unmeasured)disturbances and the effect of this model error.The model error gives rise to feedback in the true sense and leads to possible stability problems.This forces the designer to "detune"the ideal feedforward controller for "robustness." The controller form described here is a special case of the Youla- parametrization mentioned above.It is inherent in all "model predictive"control schemes,in particular Model Algorithmic Control and Dynamic Matrix Control
4 CHAPTER 1.INTRODUCTION 1.3 Robustness Regardless of what design technique is used,controllers are always designed based on(necessarily incomplete)information about the dynamic behavior of the pro- cess.This information(i.e.,the"model")can have the form of a system of coupled partial differential equations or be simply the process gain and the settling time experienced by the plant operator.The accuracy of this information varies but is never perfect.Moreover,the.behavior of the plant itself changes with time (feedstock changes,catalyst activity changes,etc.)and these changes are rarely captured in the models.It is most desirable that the controller be insensitive to this kind of model uncertainty,i.e.,the controller should be robust. Though the design objective robustness seems most practical and reasonable it is essentially absent from the control literature from about 1960 to 1980.This is probably one of the reasons why the design techniques developed in this time period have had negligible effect on the industrial control practice.Since the late 1970s robustness has become a major objective of control research.This book will demonstrate the importance of robustness considerations for process control and will propose design techniques which include robustness as one of the objectives. 1.4 Scope of Book The book has several goals: to alert the reader to the key role model uncertainty and robustness play in the design and successful operation of feedback control systems. to outline the basic ideas behind the most recent theoretical advances for addressing robustness systematically in feedback design. to describe simple and effective analysis and design techniques for robust feedback controllers. The different parts of the book aim at different groups of readers: the first-year graduate student who wants to broaden his/her horizon,gain some basic insights into feedback control,and get a taste of the direction of the new theory. the beginning researcher in the area of robust control who wishes to master the transition from the undergraduate process control course to the mono- ghs by Vidyasagar (195)and Francis (197)as well as the curentre search papers in this area
1.5.SOME HINTS FOR THE READER the industrial practitioner who needs easily applicable and proven controller 5 tuning techniques and who is interested in learning about the basic dos and don'ts of multivariable control. Depending on the reader's objectives and background some chapters might be of more interest than others.Chapters 2 through 4 discuss the basic trade-offs in single-input single-output(SISO)feedback control systems and how they can be addressed in the Internal Model Control framework.These chapters are essential for understanding the rest of the book.Chapter 5 generalizes the results to unstable systems and can be skipped by the application-oriented reader.Chapter 6 proposes some very effective PID tuning rules and discusses more general SISO control structures like Smith predictor,cascade and feedforward,control systems. Chapters 7 through 9 deal with sampled-data systems and mimic Chapters 1 through 6.In the derivations particular emphasis is placed on the behavior of the continuous output-e.g.,provisions against intersample rippling are built into the controllers. 限把 液 Chapters 10 and 11 cover basic aspects of robustness of multi-input multi- output (MIMO)systems.These concepts are the key to understanding the un- usual phenomena observed in the conro of MIMO systeThe MIMO design technique proposed in Chapter 12 is complex and tentativeUndoubtedly,more effective techniques will become available in the future.Chapter 13 discusses the system properties which limit the achievable performance of MIMO systems.A knowledge of these properties helps when screening designs according to their op- erability characteristics.Chapter 14 deals with the design of controllers for MIMO systems with a restricted information structure-e.g.,multiloop controllers. Chapter 15 extends the discussion of Chapters 10 through 12 to sampled-data systems.The book concludes with the detailed report on an application to a high-purity distillation column(Chapter 16). 1.5 Some Hints for the Reader The book assumes that the reader has mastered the material covered in a typical undergraduate control text like the one authored by Stephanopoulos(1984)or Franklin et al.(1986).Furthermore some knowledge of linear algebra(e.g., Strang,1980)and complex variables(e.g.,Churchill Brown,1984)is required. Finally,some familiarity with linear operator theory (e.g.,Desoer&Vidyasagar, 1975;chapters 1 through 6 of Ramkrishna&Amundson,1985)is advantageous, but not necessary