自动控制原理课件：CH3_1_Time Domain Analysis for First-order Systems

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1、 CH3 Time Domain AnalysisThis chapter aims to develop:Mathematical Models - System Analysis - System DesignSystem Analysis Methods:Time Domain AnalysisComplex Domain Analysis (Root Locus Method)Frequency Domain Analysis1 In this chapter：Performance Index for System ResponseTime Domain Analysis for 1

2、 -order SystemsTime Domain Analysis for 2 -order SystemsTime Domain Analysis for higher-order SystemsLinear System Stability AnalysisstndLinear System Steady State Analysis2 3-1 Performance Index for System Response1、Typical Input（1）why choose typical inputs？（2）what types of typical inputs？3）which t

3、o choose？（2、Dynamic & Steady State Processesdynamic/transient process monotonceonvergenecoscilatorcyonvergenecsteady stateperiodicaolscilationdivergence3 3-1 Performance Index for System Response3、Dynamic & Steady State PerformanceDynamic Performance Indices：t（1）Delay Timedt（2）Rising Time3）Peak Time

4、 tpr（Steady State Performance Index：Steady state error4）Regulation Time t ( 5 %, 2 %)sh(t ) - h( ) 100 %5）Overshoot s % =p4 3-2 Time Domain Analysis for 1st-order SystemsIn this chapter：Mathematical ModelsUnit Step ResponseUnit Impulse ResponseUnit Ramp ResponseUnit Acceleration Response5 1. Mathema

5、tical Modelsi(s)C(s) 1R(s) Ts +1F(s) = =,Rr(t)c(t)CT = RCTime ConstantClose-loop pole: - 1TOpen-loop pole：0 R(s)-C(s)11 I(s)CsR1st-order system without zero6 2. Unit Step Response2r(t) =1(t)1Tr(t)1R(s) =s11 1Ts + s1 - e- t t /T( 0)h t = L-1()css =1=- -t/Tc(t) 1 e04T2T3T=1Tth (T) =63.2%h(2T)=86.5%h(3

6、T)=95%Dynamic performance indices:td = 0.69Ttr = 2.2Tts = 3Tdh(t)1=dtTh(4T)=98.2%7 3. Unit Pulse Response32Tr(t) = d (t)R(s) =11T1 Ts 1+=-1k(t) Lk(t)c(t) =1 e-t/TT11=e (t 0)-t /TTdc(t)|t=0 = - 10T2T3T4TdtT 2tImpulseTesting8 4. Unit Ramp Response3Tr(t) = tR(s) = 12.050/T2Tc(t)1 1 c(t) L=-11.135/TTs 1

7、 s +Tc(t) (t T) Te= (t T) Te (t 0)- + -t /T0.386/TSteady steate error :T0T2T3T4T-Tt9 5. Unit Acceleration Response1()22R(s) = 13s1 1 c t = L-1()3= 1tt ),( 0)2-Tt +T 2 (1- e-t /T210 1st-order System Input ResponseInputOutput Response-e-t/T , (t 0)11(t)1d(t)-t /Te ，(t 0)Tt - T + Te - t / T t , ( 0)t1t 2122- +t Tt T (1 e ), (t 0)2-t /T2conclusion：r = r c = c2&121Exercise：3-1,3-311