6 CHAPTER 1.INTRODUCTION Influence of disturbances IMC Set Point Controller Process Output Mode Estimate of process uncertainty Feedback Signal Fig.1.2-1.Internal Model Control Structure. Chapters 5,9 and 13 and in particular the proofs in these chapters are mathe- matically more demanding and can be skipped at first reading.The chapters on sampled-data systems(7 through 9 and 15)assume that the corresponding mate- rial on continuous systems has been studied first.Also the study of the chapters on MIMO systems requires the prior understanding of the SISO concepts.In principle,the SISO material follows as a special case from the MIMO material. For tutorial reasons it is treated separately. With the exception of this first chapter all references are collected at the chap- ter end for continuity.Most chapters contain one or several summary sections, usually located immediately before the reference section.This summary section allows the reader to review the main concepts.Often,mastering this summary section is sufficient for the application of the basic techniques covered in the chap- ter.The equation numbers in the summary section refer to the equation numbers in the main body of the text. The end of proofs and examples is marked with the symbol 1年、、-.-147年
1.5.SOME HINTS FOR THE READER 7 Influence of disturbances Set Point Controller Process Output Fig.1.2-2.Classic Feedback Structure
Part I CONTINUOUS SINGLE-INPUT SINGLE-OUTPUT SYSTEMS
Chapter 2 FUNDAMENTALS OF SISO FEEDBACK CONTROL After a review of some basic definitions,the controller design problem will be for- mulated in general terms.All controller design procedures are based on models of one form or another.These models are necessarily inaccurate.It is of great practical importance that the controller performs well even when the dynamic behavior of the real process differs from that described by its model.In order to accomplish this objective,not only must a process model and the performance specifications be provided for the design,but also some indication of the model accuracy should be made.The attribute "robust"will be used for a property which holds not only for the model but also in the presence of model uncer- tainty.Mathematical conditions for robust stability and robust performance will e器g 2.1 Definitions The block diagram of a typical classic feedback loop is shown in Eig.2.1-1A. Here c denbres the.controller and p the plant transfer function.The transfer function pa describes the effect of the disturbance d'on the process output y. The measurement device transfer function is symbolized by pm.Measurement noise n corrupts the measured variable ym.The controller determines the process nput (manipulated variable)u on the basis of the error e.The objective of the eedback loop is to keep the output y close to the reference(setpoint)r. Commonly we will use the simplified block diagram in Fig.2.1-1B.Here d lenotes the effect of the disturbance on the output.Exact knowledge of the utput y is assumed (pm =1,n=0). 叔观a In general,the transfer functions will be allowed to be rationalor irrational -i.e.,they may include time delays.In order to be physically realizable,the ansfer functions have to be proper and causal 61闭保8
12 CHAPTER 2.FUNDAMENTALS OF SISO FEEDBACK CONTROL Pm B Figure 2.1-1.General (A)and simplified(B)block diagram of feedback control system. Definition 2.1-1.A system g(s)is proper if lim,og(s)is finite.A proper system is strictly proper if lim,(s)=0 and semi-proper if lim(s)> 0.All systems which are not proper are improper. 58 A system g(s)is improper if the order of the numerator polynomial exceeds the order of the denominator polynomial and proper otherwise.An improper system cannot be realized physically because it contains pure differentiators. Definition 2.1-2.A system requiring prediction (ets)is noncausal!A sustem which does not require prediction is cavsal, 特来 Some care has to be used in determining if a system is causal or not.A time delay in the denominator of a transfer function does not necessarily imply lack of causality.For example, g()==e9 1 4(s) 2es9-1=2-e-s0 is causal because the present output y is determined solely by past values of y and the present value of u: )=2e-ys)+u(s》 iGenerally an improper system is also referred to as noncausal.In this book we will reserve noncausal to denote prediction