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超调量允许误差10.90.50.1trtpts图3-2表示性能指标td,

6、tr,tp,mp和ts的单位阶跃响应曲线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） 电路图rcr(s)c(s)（c）等效方块

7、图r(s)c(s)（b）方块图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图3-4指数响应曲线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时，时，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)控制可以增大系统的阻尼，使控制可以增大系统的阻尼，使阶跃响应的超调量下降，调节时间缩短，且阶跃响应的超

16、调量下降，调节时间缩短，且不影响系统稳态误差及系统的自然频率。不影响系统稳态误差及系统的自然频率。performance of pd control2222)2()(nntnnskss2nttknis constantdifferential feedback control 测速反馈会降低系统的开环增益，从而加大测速反馈会降低系统的开环增益，从而加大系统在斜坡输入时的稳态误差，但不影响系系统在斜坡输入时的稳态误差，但不影响系统的自然频率，并可增大系统的阻尼比统的自然频率，并可增大系统的阻尼比, 从而从而改善系统的动态性能。改善系统的动态性能。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)( (离虚轴越远的点，其响应分量衰减越快。离虚轴越远的点，其响应分量衰减越快。) )4.6 high-order system analysis 如果所有的闭环极点中，距虚轴最近的极点周围没如果所有的闭环极点中，距虚轴最近的极点周围没有闭环零点，而其它闭环极点又远离