Presentation on theme: "The Performance of Feedback Control Systems"— Presentation transcript:
1 The Performance of Feedback Control Systems Ch4The Performance of Feedback Control Systems
2 Main content Test input signals Response of a first-order system Performance of a second-order systemEffects of a third pole and a zero on system responseRoot location and the transient response
3 Main content continue Steady-state error analysis Performance indices The simplification of linear systemsExamples and simulationSummary
4 Introduction Transient response Steady-state response Design specificationsHow to get compromise?A distinct advantage of feedback control system is the ability to adjust the transient and steady-state responseRefer to P224 Figure 5.1
5 4.1 Test input signals Step input Ramp input Parabolic input The standard test input signals commonly used are:Step inputRamp inputParabolic inputSinusoidal inputUnit impulse input
6 Representation of test signals continueRepresentation of test signalsStep:Ramp:Parabolic:sinusoidal:Input time domain frequency domain
7 Unit impulse response continue Unit impulse: System impulse response: System response is the convolution integral of g(t) and r(t):
8 Standard test signal continue The standard test signals are of the general form:And its Laplace transform is:
9 Performance indices (viewpoint from engineering) Transient Performance:Time delay t dRise time t rPeak time t pSettling time t sPercent overshootSteady-state Performance: Steady-state error
10 4.2 Response of a first-order system The model of first-order systemorFor example, temperature or speed control system and water level regulating system.
11 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 )Refer to script
12 Important conclusion (for n-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.Conclusion:System response for the derivative of a certain input signal is equivalent to the derivative of the response for this input signal.
13 4.3 Response and performance of a second-order system Model of 2nd-order systemRoots of characteristic equation (Poles)The response depends on and
14 Unit step response of 2nd-order system If , 2 positive real-part roots,unstableIf , 2 negative real-part roots,underdampedIf ,2 equal negative real roots,critically dampedIf , 2 distinct negative real roots,overdampedIf , 2 complex conjugate roots,undamped
15 Case 1: underdamped Oscillatory response No steady-state error Refer to script 3-10
16 Case 2: critically damped Mono-incremental responseNo OscillationNo steady-state error
17 Case 3: overdamped Mono-incremental response slower than critically dampedNo OscillationNo steady-state error
18 Performance evaluation ( underdamped condition) Performance indices evaluationAn example of performance evaluation1 Time delay2 Rise time3 Peak time4 Percent overshoot5 Settling timeRefer to script 3-15
19 4.4 Effects of a third pole and a zero on 2nd-order system response Effect of a third poleEffect of a third zeroDominant poles
20 4.5 Root location and transient response Characteristic roots (modes)Effects of Zeros on responseRefer to Figure 5.17 (P240)
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