自动控制原理习题课答案市公开课一等奖百校联赛获奖课件.pptx

第二章习题课第二章习题课(2-1a)uoi2=R2CuiuoR1R22-1(a)试建立图所表示电路动态微分方试建立图所表示电路动态微分方程。程。解：解：输入量为输入量为ui，输出量为，输出量为uo。ui=u1+uou1=i1R1ic=Cducdt=dtd(ui-uo)i1=i2-icu1=R1+uouo-Cd(ui-uo)dtR2R2ui=uoR1-C R1R2+C R1R2+uoR2duidtdtduouoR1+C R1R2+uoR2=R2ui+C R1R2duoduidtdtCucR1R2uii1i2uoicC第1页第二章习题课第二章习题课(2-1b)2-1(b)试建立图所表示电路动态微分方试建立图所表示电路动态微分方程。程。uouiR1LR2Ci1=iL+icuL=LdiLdtuoiL=i2=R2uL=LR2duodtic=+CducdtCLR2d2uodt2duodt+uoR2CLR2d2uodt2duodti1=+Cuoi2=R2输入量为输入量为ui，输出量为，输出量为uo。ui=u1+uou1=i1R1ic=Cducdt=dtd(ui-uo)第2页习题课一习题课一 (2-2)求以下函数拉氏变换求以下函数拉氏变换。(1)f(t)=sin4t+cos4t解解:Lsinwt=ww2+s2sw2+s2Lsin4t+cos4t=4s2+16ss2+16 =s+4s2+16+Lcoswt=第3页(2)f(t)=t3+e4t3!解解:Lt3+e4t=+=+3!s3+11s-4s41s-4(3)f(t)=tneat解解:Ltneat=n!(s-a)n+1(4)f(t)=(t-1)2e2t解解:L(t-1)2e2t=e-(s-2)2(s-2)3第4页2-3-1 函数拉氏变换。函数拉氏变换。F(s)=s+1(s+1)(s+3)解解：A1=(s+2)s+1(s+1)(s+3)s=-2=-1(s+1)(s+3)A2=(s+3)s+1s=-3=2F(s)=-2s+31s+2f(t)=2e-3t-e-2t第5页F(s)=s(s+1)2(s+2)2-3-2 函数拉氏变换。函数拉氏变换。解解:f(t)=est +lim ests(s+1)2s=-2ddsss+2s -1=-2e-2t+lim(est+est)s -1 sts+22(s+2)2=-2e-2t-te-t+2e-t=(2-t)e-t-2e-2t第6页F(s)=2s2-5s+1s(s2+1)2-3-3 函数拉氏变换。函数拉氏变换。解解:F(s)(s2+1)s=+j=A1s+A2s=+jA1=1,A2=-5A3=F(s)s =1s=0 f(t)=1+cost-5sintF(s)=+1ss2+1s-5s2+1第7页2-3-4 函数拉氏变换。函数拉氏变换。(4)F(s)=s+2s(s+1)2(s+3)解解:f(t)=est +ests+2(s+1)2(s+3)s=0s+2s(s+1)2s=-3+lim s -1d est s+2s(s+3)ds=+e-3t+lim +23112s -1(-s2-4s-6)est(s2+3)2(s+2)tests2+3s=+e-3t-e-t-e-t2311234t2第8页(2-4-1)求以下微分方程。求以下微分方程。d2y(t)dt2+5 +6y(t)=6，初始条件：初始条件：dy(t)dty(0)=y(0)=2。解解:s2Y(s)-sY(0)-Y(0)+5sY(s)-5Y(0)+6Y(s)=1sA1=sY(s)s=0 y(t)=1+5e-2t-4e-3tA2=(s+2)Y(s)s=-2A3=(s+3)Y(s)s=-3A1=1,A2=5,A3=-4 Y(s)=6+2s2+12ss(s2+5s+6)第9页 (2-4-2)求以下微分方程。求以下微分方程。d3y(t)dt3 +4 +29 =29,d2y(t)dt2dy(t)dt初始条件初始条件:y(0)=0 ,y(0)=17 ,y(0)=-122 解解:第10页2-5-a 试画题试画题2-1图所表示电路动态结构图图所表示电路动态结构图,并并求传递函数。求传递函数。CucR1R2uii1i2uoicC解解:ui=R1i1+uo ，i2=ic+i1UI(s)=R1I1(s)+UO(s)ducic=CdtI2(s)=IC(s)+I1(s)IC(s)=CsUC(s)即即:=I1(s)UI(s)-UO(s)R1UI(s)-UO(s)Cs=IC(s)第11页UO(s)UI(s)=1R1(sC)R21+1R1(sC)R2=R2+R1R2sCR1+R2+R1R2sC1R1sCR2UI(s)-UO(s)IC(s)I1(s)I2(s)1R1sC R2()UI(s)-UO(s)第12页2-5-b 试画出题试画出题2-1图所表示电路图所表示电路动态结构图动态结构图,并求并求传递函数。传递函数。uouiR1LR2C解：解：ui=R1I1+ucuc=uo+uLuL=LdiLdtiL=uoR2i1=iL+icic=CducdtUi(s)=R1I1(s)+UC(s)UC(s)=UO(s)+UL(s)UL(s)=sLIL(s)I1(s)=IL(s)+IC(s)第13页1R1CssLR2I1UOUiIC-UC=UO+ULILULI2(s)=UO(s)R2IC(s)=CsUC(s)I1(s)=UO(s)R2I1(s)=UI(s)+UC(S)R1即：即：IL(s)=I1(s)-IC(s)IC(s)=UC(s)Cs第14页解解:电路等效电路等效为为:2-6-a 用运算放大器组成有源电网络如图所用运算放大器组成有源电网络如图所表示表示,试采取复数阻抗法写出它们传递函数。试采取复数阻抗法写出它们传递函数。UO=R3SCR2R21UIR1UOR3SCR2R21SC1=第15页R1+R3+R2R3CS=R1(R2SC+1)R2R3=(+)R1(R2SC+1)R1R1R2=(+R3)(R2SC+1)1=R21R3R2SCR1C(S)=UO(S)UI(S)CR1R2R3uiuoCR1R2R3uiuo第16页CR1R2R3uiuoR4R52-6-b 用运算放大器组成有源电网络如力用运算放大器组成有源电网络如力所表示所表示,试采取复数阻抗法写出它们传递试采取复数阻抗法写出它们传递函数。函数。第17页=R5R4+R5UO(R3SC+1)R2R3SC+R2+R3UOUI=(R2R3SC+R2+R3)(R4+R5)R1(R3SC+1)R5=(R4+R5)(R2+R3)(SC+1)R2R3R2+R3R1R5(R3SC+1)UIR1=R5R4+R5UOR2R3SCSCR3SC1R5R4+R5UOR2R3R3SC 1第18页c(t)t0TK(t)(t)2-8 设有一个初始条件为零系统，系统设有一个初始条件为零系统，系统输入、输出曲线如图，求输入、输出曲线如图，求G(s)。c(t)t0TK(t)(t)c(t)=KTt-(t-T)KT C(s)=K(1-e )Ts2-TSC(s)=G(S)第二章习题课第二章习题课(2-8)解解:第19页2-9 若系统在单位阶跃输入作用时，已若系统在单位阶跃输入作用时，已知初始条件为零条件下系统输出响应，知初始条件为零条件下系统输出响应，求系统传递函数和脉冲响应。求系统传递函数和脉冲响应。r(t)=I(t)c(t)=1-e +e-2t-t解解:R(s)=1sG(S)=C(s)/R(s)1s+21s-C(s)=1s+1+=s(s+1)(s+2)(s2+4s+2)=(s+1)(s+2)(s2+4s+2)C(s)=(s+1)(s+2)(s2+4s+2)脉冲响应脉冲响应:2s+2=1+1s+1-c(t)=(t t)+2e +e-2t-t第二章习题课第二章习题课(2-)第20页2-10 已知系统微分方程组拉氏变换式，已知系统微分方程组拉氏变换式，试画出系统动态结构图并求传递函数。试画出系统动态结构图并求传递函数。解解:X1(s)=R(s)G1(s)-G1(s)G7(s)-G8(s)C(s)X2(s)=G2(s)X1(s)-G6(s)X3(s)X3(s)=G3(s)X2(s)-C(s)G5(s)C(s)=G4(s)X3(s)G1G2G3G5-C(s)-R(s)G4G6G8G7X1(s)=R(s)-C(s)G7(s)-G8(s)G1(s)C(s)G7(s)-G8(s)G6(s)X3(s)X1(s)X2(s)C(s)G5(s)X3(s)G1G2G3G5-C(s)-R(s)G4G2G6G8G7G1G2G5-C(s)-R(s)G7-G81+G3G2G6G3G4-C(s)R(s)G7-G81+G3G2G6+G3G4G5G1G2G3G41+G3G2G6+G3G4G5+G1G2G3G4(G7-G8)G1G2G3G4R(s)C(s)=第二章习题课第二章习题课(2-10)第21页解解:2-11(a)G1(s)G2(s)G3(s)H1(s)_+R(s)C(s)H2(s)G1(s)G2(s)H1(s)_+R(s)C(s)H2(s)G3(s)求系统传求系统传递函数递函数1+G2H1G2 G1+G31+G1H21+G2H1G2 1+G2H1G2=1+G2H1+G1G2H2G2 R(s)C(s)=1+G2H1+G1G2H2G2G1+G2G3G1(s)G2(s)G3(s)H1(s)_+R(s)C(s)G 1(s)H2(s)第二章习题课第二章习题课(2-11a)第22页2-11(a)G1(s)G2(s)G3(s)H1(s)_+R(s)C(s)H2(s)求系统传求系统传递函数递函数解解:L1L1=-G2H1L2L2=-G1G2H1P1=G1G2P2=G3G21=12=1R(s)C(s)=nk=1Pkk=1+G2H1+G1G2H21+G2H1+G1G2H2G2G1+G2G3=第二章习题课第二章习题课(2-11a)第23页解解:2-11(b)G1(s)G2(s)G3(s)G4(s)_+R(s)C(s)H(s)求系统传求系统传递函数递函数G1(s)G2(s)G3(s)G4H_+R(s)C(s)H(s)1+G4G1HG1 G2(s)G3(s)_+R(s)C(s)H(s)1+G4HG1G1 G2G3_+R(s)C(s)1+G4HG1G1 HG1 1+G4HG1G1+G3(1+HG1G4)1+G4HG1G2(1+HG1G4)1+G4G1H+G1G2HR(s)C(s)=1+G1G2H+G1G4HG1G2+G2G3+G1G2G3G4 H第二章习题课第二章习题课(2-11b)第24页解解:2-11(b)G1(s)G2(s)G3(s)G4(s)_+R(s)C(s)H(s)求系统传求系统传递函数递函数R(s)C(s)=1+G1G2H+G1G4HG1G2+G2G3+G1G2G3G4 HL1L1=-G1G2HL1=-G1G4HL2P1=G1G21=1P2=G3G2=1+G4G2H+G1G2H2=1+G1G4H第二章习题课第二章习题课(2-11b)第25页H1_+G1+C(s)R(s)G3G22-11c 求系统闭环传递函数求系统闭环传递函数。解解:H1_+G1+C(s)R(s)G3G2H1R(s)C(s)1+G1G2+G1H1G3H1G1G2(1 G3H1)=_G1C(s)R(s)G2H1+G21-G3H11第二章习题课第二章习题课(2-11c)第26页H_G1+C(s)R(s)G22-11d 求系统闭环传递函数求系统闭环传递函数。解解:(1)_G1+C(s)R(s)G2HG21+G2H1(G1+G2)R(s)C(s)=(2)L1L1=-G2HP1=G11=1P2=G22=1第二章习题课第二章习题课(2-11d)第27页-_G1+C(s)R(s)G2G3G42-11e 求系统闭环传递函数求系统闭环传递函数。解解:(1)_C(s)R(s)G1+G2G3-G4C(s)=R(s)1+(G1+G2)(G3-G4)(G1+G2)1+G1G3+G2G3G1G4-G2G4=(G1+G2)第二章习题课第二章习题课(2-11e)L1L2L3L4L2=G1G4L3=-G2G3L4=G2G4(2)L1=-G1G3P1=G11=1P2=G22=11+G1G3+G2G3G1G4-G2G4=(G1+G2)C(s)R(s)第28页_G1+C(s)R(s)G22-11f 求系统闭环传递函数求系统闭环传递函数。_C(s)R(s)G11-G2G2C(s)=R(s)1+1-G2G1G1G21+G1G2G2G1(1 G2)=第二章习题课第二章习题课(2-11f)解解:(1)(2)L1L1=-G1G2L2L2=G2P1=G11=1-G2=1+G1G2-G2C(s)R(s)1+G1G2G2G1(1 G2)=第29页2-12(a)R(s)G1(s)G2(s)H2(s)_+C(s)H3(s)H1(s)_+D(s)解解:求求:D(s)C(s)R(s)C(s)D(s)=01-G2H2G2 G(s)=1-G2H2G1G2 C(s)=R(s)1+1-G2H2G1G2H31-G2H2G1G2 1-G2H2+G1G2H3G2G1=R(s)=0结构图变结构图变 换成：换成：G2(s)H2(s)_+C(s)G1H3G1H1_D(s)1-G2H2G2 1-G1H1C(s)=D(s)1+1-G2H2G21-G2H2G2 G1H3(1-G1H1)1-G2H2+G1G2H3G2(1-G1H1)=第二章习题课第二章习题课(2-12a)第30页2-12(b)求求:D(s)C(s)R(s)C(s)R(s)Gn+D(s)解解:D(s)=0G(s)=1+G1G2HG1G2 G1G2H_C(s)C(s)=R(s)1+1+G1G2HG1G2 1+G1G2HG1G2 1+G1G2H+G1G2G1G2=R(s)=0Gn+D(s)结构图变结构图变 换成：换成：G1G2H-C(s)Gn+D(s)G1G2H-C(s)Gn/G1+D(s)1+G1G2HG1G2-C(s)+D(s)1+G1G2HG2Gn 1+G1G2HG2G1系统传递函数系统传递函数:)C(s)=D(s)1+1(1+1+G1G2HG1G2 1+G1G2HGnG2 1+G1G2+G1G2H=1+GnG2+G1G2H第二章习题课第二章习题课(2-12b)第31页2-13(a)求求:R(s)E(s)R(s)C(s)C(s)E(s)G1G2G3_+R(s)解解:L1L1=-G2L2L2=-G1G2G3P1=G2G3P2=G1G2G3R(s)C(s)=1+G2+G1G2G3G2G3+G1G2G31=12=1E(s)结构图变结构图变 换成：换成：G1G2+-E(s)G3-R(s)G1+-E(s)R(s)1+G2G3G2-E(s)-R(s)1+G2G2G3G1G2G31+G2系统传递函数系统传递函数:)E(s)=R(s)1+1(1-G1G2G31+G2 1+G2G2G31+G2+G1G2G3=1+G2-G2G3第二章习题课第二章习题课(2-13a)第32页R(s)G4(s)+C(s)E(s)G1(s)G2(s)-+G3(s)第二章习题课第二章习题课(2-14)D(s)X(s)2-14 求求:R(s)C(s)解解:D(s)=0结构图结构图变换为变换为 R(s)G4(s)+C(s)G1(s)G2(s)-+G3(s)G3(s)(G1+G2)(G3+G4)1+(G1+G2)G3G1+G2C(s)R(s)=1+G3(G1+G2)(G1+G2)(G3+G4)第33页D(s)第二章习题课第二章习题课(2-14)R(s)+-E(s)G3G2G1E(s)R(s)=1+G3(G1+G2)1R(s)G4(s)+C(s)E(s)G1(s)G2(s)-+G3(s)X(s)求求:R(s)E(s)2-14解解:D(s)=0结构图变换为结构图变换为 G3(G1+G2)第34页D(s)C(s)D(s)R(s)C(s)G4(s)+E(s)G1(s)G2(s)-+G3(s)X(s)求求:2-14解解:R(s)=0D(s)C(s)=1E(s)X(s)=G2(s)E(s)X(s)第二章习题课第二章习题课(2-14)第35页C1(s)R1(s)第二章习题课第二章习题课(2-15)求求:2-15+G1G2G3C1(s)R1(s)+-H2H1G4G5-G6C2(s)R2(s)解解:结构图结构图变换为变换为+G1G2G3C1(s)R1(s)-H2H1G4G5-1+G4G4G5H1H21+G4G4G5H1H21+G1G1G21+G4+G1G4G5H1H2-G1G2-G1G2G4G1G2G3(1+G4)=C1(s)R1(s)1+G4+G1G4G5H1H2G1G2(1+G4)=第36页C2(s)R2(s)G3C1(s)R1(s)+G1G2-H2H1G4G5G6-C2(s)R2(s)求求:2-14解解:结构图结构图变换为变换为+G4G5G6C2(s)R2(s)-H1H2G2G1-第二章习题课第二章习题课(2-15)1+G4G4G5G1H1H21-G1G21+G4+G1G4G5H1H2-G1G2-G1G2G4G4G5G6(1-G1G2)=1+1+G4G6G4G5G1H1H21-G2G21+G4G4G5C2(s)R2(s)第37页C2(s)G4G5G6-+G1G2-H2H1R1(s)G3C1(s)R2(s)求求:2-14解解:结构图变换为结构图变换为 G4G5G6-+-G1G2H2H1R1(s)C2(s)第二章习题课第二章习题课(2-15)C2(s)R1(s)1+G4H2G4G5G11-G1G21+G4+G1G4G5H1H2-G1G2-G1G2G4G1G4G5G6H2=1+G6H1C2(s)R1(s)G11-G1G21+G4H2G4G5G11-G1G21+G4H2G4G5第38页C2(s)G6R1(s)G4G5-+G1G2-H2H1G3C1(s)R2(s)求求:2-14解解:结构图变换为结构图变换为 第二章习题课第二章习题课(2-15)G1G2G3+G5G4-H1R2(s)C1(s)H2-C1(s)R2(s)G1G2G3+G5G4-H1R2(s)C1(s)H2-G21+G4G4G51-G1G2-G1H11+G4+G1G4G5H1H2-G1G2-G1G2G4-G1G2G3G4G5H1=1+1+G4G4G5G1H11-G2G21+G4G4G5C1(s)R2(s)H2-G1H11-G2G2G2G3第39页G3C1(s)R1(s)+G1G2+-H2H1G4G5-G6C2(s)R2(s)C1(s)R1(s)求求2-15第二章习题课第二章习题课(2-15)解解:L1=G1G2L3=-G4L2=-G1G4G5H1H2P1=G1G2G3=1-G1G2+G1G4G35H1H2+G4-G1G2G41=1+G41+G4+G1G4G5H1H2-G1G2-G1G2G4G1G2G3(1+G4)=C1(s)R1(s)第40页G3C1(s)R1(s)+G1G2+-H2H1G4G5-G6C2(s)R2(s)C2(s)R2(s)求求2-15解解:L1=G1G2L3=-G4L2=-G1G4G5H1H2P1=G4G5G6=1-G1G2+G1G4G5H1H2+G4-G1G2G41=1-G1G21+G4+G1G4G5H1H2-G1G2-G1G2G4G4G5G6(1-G1G2)=C2(s)R2(s)第二章习题课第二章习题课(2-15)第41页G3C1(s)R1(s)+G1G2+-H2H1G4G5-G6C2(s)R2(s)C1(s)R2(s)求求2-15解解:L1=G1G2L3=-G4L2=-G1G4G5H1H2=1-G1G2+G1G4G5H1H2+G4-G1G2G41=1P1=-G1G2G3G4G5H11+G4+G1G4G5H1H2-G1G2-G1G2G4-G1G2G3G4G5H1=C1(s)R2(s)第二章习题课第二章习题课(2-15)第42页G3C1(s)R1(s)+G1G2+-H2H1G4G5-G6C2(s)R2(s)C2(s)R1(s)求求2-15解解:L1=G1G2L3=-G4L2=-G1G4G5H1H2=1-G1G2+G1G4G5H1H2+G4-G1G2G41=1P1=G1G4G5G6H21+G4+G1G4G5H1H2-G1G2-G1G2G4G1G4G5G6H2=C2(s)R1(s)第二章习题课第二章习题课(2-15)返回返回第43页