浙大845自動控制15原理chapter5s stability criterion

1、CHAPTER 5Control-System Characteristics(Ch.6)By Hui Wanghwang87951970-403(O)；2007-11-6Chapter 5-11Review Ch.4Review of chapter 4 (System Representation)9Overall transfer function9Simulation diagrams9Signal flow graph9From transfer function to statespace m2007-11-6Chapter 5-12Review Ch.3Key words of

2、chapter 5Ø System StabilityØ Rouths stability criterionØ Relative stabilityØ System typesØ Steady-state errorØ Steady-state error coefficients2007-11-6Chapter 5-13Outline of this chapterü Introductionü Rouths stability criterionü Mathematical and physical

3、 formü Feedback system typesü Steady-state error coefficientsü Use of steady-state error coefficientsü Nonu-feedback systemü Summary2007-11-6Chapter 5-14IntroductionIntroduction9System stability92007-11-6Chapter 5-15IntroductionIntroductionØ Open- and closed-loop transf

4、er functions have certainbasic characteristics that permit transient and steady-state analyses of the feedback-controlled system.Ø Five factors of prime importance in feedback-controlsystems areØ StabilityØ The existence and magnitude of the steady-state errorØ Controllability Ba

5、sed on space-state mØ ObservabilityØ Parameter sensitivity2007-11-6Chapter 5-16Determined by systems characteristic equation, many methods can be used.IntroductionIntroductionØ The Stability of a LTI system is determined from the systemscharacteristic equation.Ø Rouths stability

6、criterion provides a means for determiningstability without evaluating the roots of the equation.Ø The steady-state error are obtained from the open-loop transferfunction for u-feedback systems(or equivalent u-feedbacksystems), yielding the figures of merit(性能準(zhǔn)則） and a readymeans for classifing

7、 systems.2007-11-6Chapter 5-17IntroductionIntroduction½The issue of ensuring the stability of a closed-loop feedbacksystem is central to control system design. Knowing that anunstable closed-loop system is generally of no practical value, weseek methods to help us analyze and design stable syst

8、ems.½A stable system should exhibit a bounded output if thecorresponding input is bounded. This is known as bounded-input,bounded-output(BIBO) stability.½The stability of a feedback system is directly related to thelocation of the roots of the characteristic equation of the systemtransfer

9、function.2007-11-6Chapter 5-18IntroductionIntroduction½ The RouthHurwitz method is introduced as a useful tool forassessing system stability. The technique allows us to compute thenumber of roots of the characteristic equation in the right half-planewithout actually computing the values of the

10、roots.½Thus we can determine stability without the added computationalburden of determining characteristic roots locations. This gives us adesign method for determining values of certain system parametersthat will lead to closed-loop stability.½ For stable systems we will introduce the not

11、ion of relative stability,which allows us to characterize the degree of stability. Degree ofstability is associated with how far left they are.2007-11-6Chapter 5-19IntroductionThe Concept of StabilityThe concept of stability canbe illustrated by a cone placedon a plane horizontal surface.A necessary

12、 andsufficient condition for afeedback system to bestable is that all the polesof the system transferfunction have negativereal parts.A system is considered marginally stable if only certain boundedinputs will result in a bounded output.2007-11-6Chapter 5-110IntroductionThe Concept of StabilityThe following are physical examples of a stable,unstable and critically stable systemUnstableStableNatureal orCritically stable2007-11-6Chapter 5-111IntroductionThe Concept of Stability穩(wěn)定性是系統(tǒng)最重要的問題，也是對系統(tǒng)最起碼的要