控制工程周川ac5

1、the performance of feedback control systemsch4main content test input signals response of a first-order system performance of a second-order system effects of a third pole and a zero on system response root location and the transient responsemain content steady-state error analysis performance indic

2、es the simplification of linear systems examples and simulation summary continueintroduction transient response steady-state response design specifications how to get compromise?a distinct advantage of feedback control system is the ability to adjust the transient and steady-state responserefer to p

3、244 figure 5.1 two performance measures versus parameter p4.1 test input signals step input ramp input parabolic input sinusoidal input unit impulse inputthe standard test input signals commonly used are:representation of test signals step: ramp: parabolic: sinusoidal:continue22322sin102110,10),( 1s

4、atasttsttstt input time domain frequency domainsteprampparabolicunit impulse responsecontinueotherwisett,022,1)(unit impulse:)()(1sgltgsystem impulse response:tsrsgldrtgty)()()()()(1system response is the convolution integral of g(t) and r(t): standard test signalcontinuethe standard test signals ar

5、e of the general form:nttr)(and its laplace transform is:1!)(nsnsrperformance indices(viewpoint from engineering) time delay t d rise time t r peak time t p settling time t s percent overshoot %transient performance:steady-state performance: steady-state error0tmp超調(diào)量允許誤差10.90.50.1trtpts圖3-2表示性能指標td,

6、tr,tp,mp和ts的單位階躍響應(yīng)曲線tdh(t)0.02或0.05)(h)(h)(h)(hstep response of a control system4.2 response of a first-order system)()()(trtctctthe model of first-order systemor11)()()(tssrscstfor example, temperature or speed control system and water level regulating system. i(t)+r(t)c(t)+（a） 電路圖rcr(s)c(s)（c）等效方塊

7、圖r(s)c(s)（b）方塊圖i(s)(trudtdurccc)()()(trtctct11)()()(tssrscsresponse of first-order system unit step response (no steady-state error) unit impulse response ( transfer function) unit ramp response (constant steady-state error) unit parabolic response ( infinite steady-state error ) refer to script 3.1

8、-3.8圖3-4指數(shù)響應(yīng)曲線1063.2%86.5%95%98.2%99.3%t2t3t4t5t0.632tc(t)=1-ec(t)0tttetc1)(111111)()()(tssstssrsscunit step responsedynamic performance:ttd69. 0ttr20. 2）%5(3 ttsexistentnonandptunit step response11)(tssc01)(tettcttunit impulse responsetststsstssrssc11111)()()(222tttttettetttc11)1 ()()1 ()()()(1ttet

9、tctrteunit ramp responsetteetss)(lim)0()1 (21)(122tetttttctt)1 ()()()(12ttettttctrtetststststsdscsbsastssrssc1111)11()()()(2223233unit parabolic responseimportant conclusion(for nth-order lti system) from above analysis, we can see that impulse response of a system is the 1st-order derivative of ste

10、p response or 2nd-order derivative of ramp response of the system. conclusion: system response for the derivative of a certain input signal is equivalent to the derivative of the response for this input signal. 4.3 response and performance of a second-order system model of 2nd-order system roots of

11、characteristic equation (poles)2222)()()(sssrsyst122, 1nnsthe response depends on and n2222)()(nnnsssrsc110101011122, 1nnsroots of characteristic equationunit step response of 2nd-order system if , 2 positive real-part roots,unstable if , 2 negative real-part roots,underdamped if ,2 equal negative r

12、eal roots,critically damped if , 2 distinct negative real roots,overdamped if , 2 complex conjugate roots,undamped010110case 1: underdamped oscillatory response no steady-state errorsssscnnn12)(222)sin(11)(2tetcdtnarccos12ndcase 2: critically damped mono-incremental response no oscillation no steady

13、-state errorssscnn1)()(22ttnnnetetc1)(case 3: overdamped mono-incremental response slower than critically damped no oscillation no steady-state errorsssscnnn12)(22221321)(ttttecectc)1,1(2211tsts0)(limteetssstep response for different damping ratioperformance evaluation( underdamped condition) perfor

14、mance indices evaluation an example of performance evaluation1 time delay2 rise time3 peak time4 percent overshoot5 settling timerefer to script 3-15 ndt7 . 01drtdpt%100%21/ensnstt5 . 4%25 . 3%5時，時，swiftnessclosenessperformance evaluation4.4 effects of a third pole and a zero on 2nd-order system res

15、ponse effect of a third pole effect of a third zero dominant poles2222)2() 1()(nndndnstssts2nddtnis constantpd control pd control can increase damping ratio and reduce the p.o and settling time, and keep the natural frequency constant. pd(比例比例-微分微分)控制可以增大系統(tǒng)的阻尼，使控制可以增大系統(tǒng)的阻尼，使階躍響應(yīng)的超調(diào)量下降，調(diào)節(jié)時間縮短，且階躍響應(yīng)的超

16、調(diào)量下降，調(diào)節(jié)時間縮短，且不影響系統(tǒng)穩(wěn)態(tài)誤差及系統(tǒng)的自然頻率。不影響系統(tǒng)穩(wěn)態(tài)誤差及系統(tǒng)的自然頻率。performance of pd control2222)2()(nntnnskss2nttknis constantdifferential feedback control 測速反饋會降低系統(tǒng)的開環(huán)增益，從而加大測速反饋會降低系統(tǒng)的開環(huán)增益，從而加大系統(tǒng)在斜坡輸入時的穩(wěn)態(tài)誤差，但不影響系系統(tǒng)在斜坡輸入時的穩(wěn)態(tài)誤差，但不影響系統(tǒng)的自然頻率，并可增大系統(tǒng)的阻尼比統(tǒng)的自然頻率，并可增大系統(tǒng)的阻尼比, 從而從而改善系統(tǒng)的動態(tài)性能。改善系統(tǒng)的動態(tài)性能。performance of differenti

17、al feedback control4.5 root location and transient response characteristic roots (modes) effects of zeros on response refer to figure 5.17 (p260)impulse response for various root locations in s-plane)()()()()()(11srsszsksrsscnjjmiiwhen ，ssr1)(njjjssasasc10)(njtsjjeaatc10)( (離虛軸越遠的點，其響應(yīng)分量衰減越快。離虛軸越遠的點，其響應(yīng)分量衰減越快。) )4.6 high-order system analysis 如果所有的閉環(huán)極點中，距虛軸最近的極點周圍沒如果所有的閉環(huán)極點中，距虛軸最近的極點周圍沒有閉環(huán)零點，而其它閉環(huán)極點又遠離