反馈控制系统的性能.pptxVIP

反馈控制系统的性能第1页/共52页 Define and measure the performance of control systemsStabilityTransient response：the response that disappears with timeSteady-state response: the response that exists for a long time following an input signal initiationDesign specifications: for a specified input commandTime response indicesDesired steady-state accuracyEffective compromise5.1 Introduction第2页/共52页 Step inputRamp inputParabolic input5.2 Test Input Signals第3页/共52页 Unit impulse The unit impulse function δ(t) has the following properties: The impulse input is useful when we consider the convolution integral for the output y(t) in terms of an input r(t), which is written asThe general form of standard test signals:5.2 Test Input Signals第4页/共52页 If the input is a unit impulse function, we have The integral has a value only at τ = 0; therefore, the impulse response of the system G(s).The impulse response test signal can often be used for a dynamic system by subjecting the system to a large-amplitude, narrow width pulse of area A.The standard test signals are of the general form and the Laplace transform 5.2 Test Input Signals第5页/共52页 5.2 Test Input Signals第6页/共52页 With a unit step input5.3 Performance of a Second-order System第7页/共52页 The response as a function of ζ and time is alsoshown in Figure 5.5(b) for a step input. As ζ decreases, the closed-loop roots approach the imaginary axis, and the response becomes increas-ingly oscillatory. 5.3 Performance of a Second-order System第8页/共52页 With an impulse function input R(s)=15.3 Performance of a Second-order System第9页/共52页 The swiftness of the response is measured by the rise time Tr and the peak time Tp. For under-damped systems with an overshoot, the 0-100% rise time Tr is a useful index. If the system is over-damped, then the peak time is not defined, and the 10-90% rise time Tr1 is normally used.The actual response matching the step input is measured by the percent overshoot and settling time