《控制工程(周川)a.ppt》由会员分享，可在线阅读，更多相关《控制工程(周川)a.ppt（43页珍藏版）》请在三一办公上搜索。
1、The Performance of Feedback Control Systems,Ch4,Main content,Test input signalsResponse of a first-order systemPerformance of a second-order systemEffects of a third pole and a zero on system responseRoot location and the transient response,Main content,Steady-state error analysisPerformance indices
2、The simplification of linear systemsExamples and simulationSummary,continue,Introduction,Transient responseSteady-state responseDesign specificationsHow to get compromise?,A distinct advantage of feedback control system is the ability to adjust the transient and steady-state responseRefer to P244 Fi
3、gure 5.1,Two performance measures versus Parameter p,4.1 Test input signals,Step inputRamp inputParabolic inputSinusoidal inputUnit impulse input,The standard test input signals commonly used are:,Representation of test signals,Step:Ramp:Parabolic:Sinusoidal:,continue,Input time domain frequency dom
4、ain,Step,Ramp,Parabolic,Unit impulse response,continue,Unit impulse:,System impulse response:,System response is the convolution integral of g(t)and r(t):,Standard test signal,continue,The standard test signals are of the general form:,And its Laplace transform is:,Performance indices(viewpoint from
5、 engineering),Time delay t dRise time t r Peak time t pSettling time t sPercent overshoot,Transient Performance:,Steady-state Performance:Steady-state error,Step response of a control system,4.2 Response of a first-order system,The model of first-order system,or,For example,temperature or speed cont
6、rol system and water level regulating system.,Response 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),Unit step response,Dynamic Performance:,Un
7、it step response,Unit impulse response,Unit ramp response,Unit parabolic response,Important conclusion(for nth-order LTI system),From above analysis,we can see that impulse response of a system is the 1st-order derivative of step response or 2nd-order derivative of ramp response of the system.Conclu
8、sion: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 systemRoots of characteristic equation(Poles),The response depends on and,Roots of charact
9、eristic equation,Unit step response of 2nd-order system,If,2 positive real-part roots,unstable If,2 negative real-part roots,underdampedIf,2 equal negative real roots,critically dampedIf,2 distinct negative real roots,overdamped If,2 complex conjugate roots,undamped,Case 1:underdamped,Oscillatory re
10、sponseNo steady-state error,Case 2:critically damped,Mono-incremental responseNo Oscillation No steady-state error,Case 3:overdamped,Mono-incremental responseslower than critically dampedNo Oscillation No steady-state error,Step response for different damping ratio,Performance evaluation(underdamped
11、 condition),Performance indices evaluationAn example of performance evaluation,1 Time delay2 Rise time3 Peak time4 Percent overshoot5 Settling time,Refer to script 3-15,Swiftness,Closeness,Performance evaluation,4.4 Effects of a third pole and a zero on 2nd-order system response,Effect of a third po
12、leEffect of a third zero Dominant poles,is constant,PD control,PD control can increase damping ratio and reduce the P.O and settling time,and keep the natural frequency constant.PD(比例-微分)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，且不影响系统稳态误差及系统的自然频率。,Performance of PD control,is constant,Differential feedback co
13、ntrol,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，但不影响系统的自然频率，并可增大系统的阻尼比,从而改善系统的动态性能。,Performance of Differential feedback control,4.5 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,When，,(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有闭环零点，而其它闭环极点又远离虚轴，那么距虚轴最近的闭环极点所对应的响应分量，在系统的时间响应过程中起主导作用，这样的闭环极点就称为闭环主导极点。,一对闭环零极点，若它们之间的距离较与其它零极点的距离相比，非常小，则它们的作用可以相互抵消。,偶极子,主导极点,Assignment,E5.2E5.3E5.4E5.8P5.4,
