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1、第二章习题课(2-1)i=i1+i2i2=Cdu1dtuoi1=R2u1-uo=LR2duodtR1i=(ui-u1)(b)C-+-uiuoR1R2i1ii2Lu1=R1ui-u1uo+CR2du1dtu1=uo+LR2duodtduodtR1R2Lduodt+CLR2d2uodt2=-uiR1uoR1uoR2+C)uoR1R2Lduodt)CLR2d2uodt2=+(uiR11R11R2+(C+解：第1页/共46页2-2 求下列函数的拉氏变换。(1)f(t)=sin4t+cos4t Lsint=2+s2=s+4s2+16Lsin4t+cos4t=4s2+16ss2+16+s2+s2 Lcos
2、t=第二章习题课(2-2)解：(2)f(t)=t3+e4t解：Lt3+e4t=3!s41s-4+6s+24+s4s4(s+4)=第2页/共46页(3)f(t)=tneatLtneat=n!(s-a)n+1(4)f(t)=1(t-)e2tL1(t-)e2t=e-s1s-2第二章习题课(2-2)解：解：第3页/共46页2-3 求下列函数的拉氏反变换。A1=(s+2)s+1(s+2)(s+3)s=-2=-1=2f(t)=2e-3t-e-2t(1)F(s)=s+1(s+2)(s+3)第二章习题课(2-3)解：A2=(s+3)s+1(s+2)(s+3)s=-3F(s)=2s+31s+2-=A1s+2s+
3、3+A2第4页/共46页(2)F(s)=s(s+1)2(s+2)f(t)=-2e-2t-te-t+2e-t第二章习题课(2-3)解：=A2s+1s+2+A3+A1(s+1)2A1=(s+1)2s(s+1)2(s+2)s=-1A3=(s+2)s(s+1)2(s+2)s=-2ddsss+2A2=s=-1=-1=2=-2第5页/共46页(3)F(s)=2s2-5s+1s(s2+1)F(s)(s2+1)s=+j=A1s+A2s=+j A2=-5A3=F(s)s s=0 f(t)=1+cost-5sint第二章习题课(2-3)解：=s+A3s2+1A1s+A2=1 s 2s2-5s+1=A1s+A2 s
4、=js=j j-2-5j+1=jA1+A2 -5j-1=-A1+jA2 A1=1F(s)=1ss2+1s-5s2+1+第6页/共46页(4)F(s)=s+2s(s+1)2(s+3)第二章习题课(2-3)解：=+s+1A1s+3A2(s+1)2+sA3+A4-12A1=23A3=112A4=A2=ds=-1 ds(s+2)s(s+3)-34=-34A2=+-43+f(t)=e-t32e-3t2-te-t121=s=-1 s(s+3)2s(s+3)-(s+2)(2s+3)第7页/共46页2-4 求解下列微分方程。y(0)=y(0)=2 A1=1y(t)=1+5e-2t-4e-3tA2=5 A3=-
5、4Y(s)=6+2s2+12ss(s2+5s+6)第二章习题课(2-4)+6y(t)=6+5d2y(t)dt2dy(t)dt(1)解：s2Y(s)-sy(0)-y(0)+5sY(s)-5y(0)+6Y(s)=6ss2Y(s)-2s-2+5sY(s)-10+6Y(s)=6s=A1s+2s+3+A3s+A2第8页/共46页+y(t)=t2dy(t)dt(2)y(0)=0 第二章习题课(2-4)第9页/共46页 2-5 试画题图所示电路的动态结构图，第二章习题课(2-5)并求传递函数。(1)ii2+-uruc+-R2R1ci1解：I2(s)I1(s)+Uc(s)Ur(s)_Cs1R1+R2Uc(s)
6、I(s)Ur(s)Uc(s)=1R1(1+(+sC)R21R1+sC)R2=R2+R1R2sCR1+R2+R1R2sC第10页/共46页第二章习题课(2-5)(2)C-+-urucR1R2Lu1i2i1iI(s)Ur(s)_1R1U1(s)解：I1(s)-I2(s)L1=-R2/LsL2=-/LCs2L3=-1/sCR1L31=1L1 L3=R2/LCR1s21CsU1(s)Uc(s)-1LsR2I1(s)Uc(s)L1L2P 1=R2/LCR1s2=R1CLs2+(R1R2C+L)s+R1+R2Ur(s)Uc(s)R2第11页/共46页第二章习题课(2-6)2-6 试采用复阻抗写出传递函数。
7、R1ucCR2ur-+R3第12页/共46页第二章习题课(2-7)2-7 试证明两系统为相似系统。i-+-uiuoR1R2i1i2c1c2xix0yk1k2f1f2第13页/共46页c(t)t0TK(t)2-8 设有一个初始条件为零的系统，系统的输入、输出曲线如图，求G(s)。c(t)t0TK(t)c(t)=KTt-(t-T)KT C(s)=K(1-e )Ts2-TSC(s)=G(s)第二章习题课(2-8)解:第14页/共46页2-9 若系统在单位阶跃输入作用时，已知初始条件为零的条件下系统的输出响应，求系统的传递函数和脉冲响应。r(t)=I(t)c(t)=1-e +e-2t-t解:R(s)=
8、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:2s+2=1+1s+1-第二章习题课(2-9)c(t)=(t)+2e-2t-e-t 第15页/共46页2-10 已知系统的拉氏变换式，试画出系统的动态结构图并求传递函数。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)G1G2G3
9、G5-C(s)-R(s)G4G6G8G7=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)G4G2G6G8G7第二章习题课(2-10)第16页/共46页G1G2G5-C(s)-R(s)G7-G81+G3G2G6G3G4G1G2G3G5-C(s)-R(s)G4G6G8G7-C(s)R(s)G7-G81+G3G2G6+G3G4G5G1G2G3G41+G3G2G6+G3G4G5+G1G2G3G4(G7-G8)G1G2G3G4R(s)C(s)=第二章习题课(2-10)
10、第17页/共46页解: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)求系统的传递函数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(2-11)(a)第18页/共46页(a)G1(s)G2(s)G3(s)H1(s)_+R(s)C(s)H2(s)求系统的传递函数解:L1L1=-G2H1L2L
11、2=-G1G2H2P1=G1G2P2=G3G21=12=1R(s)C(s)=nk=1Pkk=1+G2H1+G1G2H21+G2H1+G1G2H2G2G1+G2G3=第二章习题课(2-11)第19页/共46页解:G1(s)G2(s)G3(s)G4(s)_+R(s)C(s)H(s)求系统的传递函数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+G1
12、G2HR(s)C(s)=1+G1G2H+G1G4HG1G2+G2G3+G1G2G3G4 H第二章习题课(2-11)(b)第20页/共46页解:(b)G1(s)G2(s)G3(s)G4(s)_+R(s)C(s)H(s)求系统的传递函数R(s)C(s)=1+G1G2H+G1G4HG1G2+G2G3+G1G2G3G4 HL1L1=-G1G2HL2=-G1G4HL2P1=G1G21=1P2=G3G2=1+G1G4H+G1G2H2=1+G1G4H第二章习题课(2-11)第21页/共46页H1_+G1+C(s)R(s)G3G2(c)解:H1_+G1+C(s)R(s)G3G2H1R(s)C(s)1+G1G2
13、+G1H1G3H1G1G2(1 G3H1)=_G1C(s)R(s)G2H1+G21-G3H11第二章习题课(2-11)第22页/共46页H_G1+C(s)R(s)G2(d)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(2-11)1+G2H1(G1+G2)R(s)C(s)=第23页/共46页-_G1+C(s)R(s)G2G3G4(e)解:(1)_C(s)R(s)G1+G2G3-G4C(s)=R(s)1+(G1+G2)(G3-G4)(G1+G2)第二章习题课(2-11e)L1L2L3L4
14、L2=G1G4L3=-G2G3L4=G2G4(2)L1=-G1G3P1=G11=1P2=G22=11+G1G3+G2G3G1G4-G2G4=(G1+G2)C(s)R(s)第24页/共46页_G1+C(s)R(s)G2(f)_C(s)R(s)G11-G2G2C(s)=R(s)1+1-G2G1G1G21+G1G2G2G1(1 G2)=第二章习题课(2-11f)解:(1)(2)L1L1=-G1G2L2L2=G2P1=G11=1-G2=1+G1G2-G2C(s)R(s)1+G1G2G2G1(1 G2)=第25页/共46页(a)R(s)G1(s)G2(s)H2(s)_+C(s)H3(s)H1(s)_+D
15、(s)D(s)C(s)R(s)C(s)L1L1=G2H2L2L2=-G1G2H31=1P1=G1G21-G2H2+G1G2H3G2G1=R(s)C(s)L1=G2H2L2=-G1G2H3P1=G21=1P2=-G1G2H12=11-G2H2+G1G2H3G2(1-G1H1)=D(s)C(s)第二章习题课(2-12)第26页/共46页R(s)G1(s)G2(s)H2(s)_+C(s)H3(s)H1(s)_+D(s)解: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+
16、G1G2H3G2G1=R(s)=0结构图变 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(2-12)(a)第27页/共46页(b)求:D(s)C(s)R(s)C(s)Gn+D(s)解:R(s)G1G2H_C(s)L1=-G1G2L2=-G1G2H1=1P1=G1G21+G1G2H+G1G2G1G2=R(s)C(s)P1=GnG21=1P2=12=1+G1G2HD(s)C(s)1+G1G2+G1G2H=1+G
17、nG2+G1G2H第二章习题课(2-12)第28页/共46页求:D(s)C(s)R(s)C(s)Gn+D(s)解:D(s)=0G(s)=1+G1G2HG1G2 R(s)G1G2H_C(s)C(s)=R(s)1+1+G1G2HG1G2 1+G1G2HG1G2 1+G1G2H+G1G2G1G2=R(s)=0Gn+D(s)结构图变 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系统的传递函数:)C(s)=D(s)1+1(1+1+G1G2HG1G2 1+G1G2HGnG2 1+G1
18、G2+G1G2H=1+GnG2+G1G2H第二章习题课(2-12)(b)第29页/共46页(a)求:R(s)E(s)R(s)C(s)C(s)E(s)G1G2G3_+R(s)解:L1L1=-G2L2L2=-G1G2G3P1=G2G3P2=G1G2G3R(s)C(s)=1+G2+G1G2G3G2G3+G1G2G31=12=1E(s)第二章习题课(2-13)P1=-G2G32=1+G21=1P2=1R(s)C(s)=1+G2+G1G2G3-G2G3+1+G2第30页/共46页求:R(s)E(s)R(s)C(s)C(s)E(s)G1G2G3_+R(s)第二章习题课(2-13)结构图变 换成：G1G2+
19、-E(s)G3-R(s)G1+-E(s)R(s)1+G2G3G2-E(s)-R(s)1+G2G2G3G1G2G31+G2系统的传递函数:)E(s)=R(s)1+1(1-G1G2G31+G2 1+G2G2G31+G2+G1G2G3=1+G2-G2G3(a)第31页/共46页(b)求:R(s)E(s)R(s)C(s)第二章习题课(2-13)C(s)E(s)G1G2-+R(s)G3G4G5解:L1=-G3G4L2=-G2G3G51=1P1=G1G5P1=G1G51=1P2=12=1+G3G4P2=G2G3G52=11+G2G3G5+G3G4=R(s)C(s)G1G2G5+G1G51+G2G3G5+G
20、3G4=R(s)E(s)G1G5+(1+G1G5)第32页/共46页R(s)G4(s)+C(s)E(s)G1(s)G2(s)-+G3(s)D(s)X(s)2-14C(s)R(s)=1+G3(G1+G2)(G1+G2)(G3+G4)解:L1=-G1G3L2=-G2G31=1P1=G1G3P2=G2G32=1P3=G1G43=1P4=G2G44=1E(s)R(s)=1+G3(G1+G2)11=1P1=1D(s)C(s)=1=G2(s)E(s)X(s)第二章习题课(2-14)第33页/共46页R(s)G4(s)+C(s)E(s)G1(s)G2(s)-+G3(s)第二章习题课(2-14)D(s)X(s
21、)解:D(s)=0结构图变换为 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)求:R(s)C(s)2-14第34页/共46页D(s)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:R(s)E(s)2-14解:D(s)=0结构图变换为 G3(G1+G2)第35页/共46页D(s)C(s)D(s)R(s)C(s)G4
22、(s)+E(s)G1(s)G2(s)-+G3(s)X(s)求:2-14解:R(s)=0D(s)C(s)=1E(s)X(s)=G2(s)E(s)X(s)第二章习题课(2-14)第36页/共46页第二章习题课(2-15)+G1G2G3C1(s)R1(s)+-H2H1G4G5-G6C2(s)R2(s)解:结构图变换为+G1G2G3C1(s)R1(s)-H2H1G4G5-1+G4G4G5H1H21+G4G4G5H1H21+G1G1G21+G4+G1G4G5H1H2-G1G2-G1G2G4G1G2G3(1+G4)=C1(s)R1(s)1+G4+G1G4G5H1H2G1G2(1+G4)=C1(s)R1(s
23、)求:2-15第37页/共46页G3C1(s)R1(s)+G1G2-H2H1G4G5G6-C2(s)R2(s)解:结构图变换为+G4G5G6C2(s)R2(s)-H1H2G2G1-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)求:2-14C2(s)R2(s)第38页/共46页C2(s)G4G5G6-+G1G2-H2H1R1(s)G3C1(s)R2(s)解:结构图变换为 G4G5G6-+-G1G2H2H1R1(s
24、)C2(s)第二章习题课(2-15)1+G4H2G4G5G11-G1G21+G4+G1G4G5H1H2-G1G2-G1G2G4G1G4G5G6H2=1+G6H1C2(s)R1(s)G11-G1G21+G4H2G4G5G11-G1G21+G4H2G4G5求:2-14C2(s)R1(s)第39页/共46页C2(s)G6R1(s)G4G5-+G1G2-H2H1G3C1(s)R2(s)求:2-14解:结构图变换为 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-G1
25、H11+G4+G1G4G5H1H2-G1G2-G1G2G4-G1G2G3G4G5H1=1+1+G4G4G5G1H11-G2G21+G4G4G5C1(s)R2(s)H2-G1H11-G2G2G2G3第40页/共46页G3C1(s)R1(s)+G1G2+-H2H1G4G5-G6C2(s)R2(s)C1(s)R1(s)求2-15第二章习题课(2-15)解:L1=G1G2L3=-G4L2=-G1G4G5H1H2P1=G1G2G3=1-G1G2+G1G4G35H1H2+G4-G1G2G41=1+G41+G4+G1G4G5H1H2-G1G2-G1G2G4G1G2G3(1+G4)=C1(s)R1(s)第41
26、页/共46页G3C1(s)R1(s)+G1G2+-H2H1G4G5-G6C2(s)R2(s)C2(s)R2(s)求2-15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(2-15)第42页/共46页G3C1(s)R1(s)+G1G2+-H2H1G4G5-G6C2(s)R2(s)C1(s)R2(s)求2-15解:L1=G1G2L3=-G4L2=-G1G4G5H1H2=1-G1G2+
27、G1G4G5H1H2+G4-G1G2G41=1P1=-G1G2G3G4G5H11+G4+G1G4G5H1H2-G1G2-G1G2G4-G1G2G3G4G5H1=C1(s)R2(s)第二章习题课(2-15)第43页/共46页G3C1(s)R1(s)+G1G2+-H2H1G4G5-G6C2(s)R2(s)C2(s)R1(s)求2-15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(2-15)返回第44页/共46页第二章习题课(2-16)G1G2G3H1G4H2_C(s)+R(s)D(s)第45页/共46页感谢您的观看！第46页/共46页