自动控制理论基础左为恒周林主编机械工业出版社习题解

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1、第2章习题解C12.1(a)求图示RC电路的++传递函数G(s)。R2R1UiUoC2--(1RCs)(1RCs)1122G(s)(a)RCs(1RCs)(1RCs)121122I1Cs1I1UoUrR2Cs2-1RI212.2(a)是一反相比例运算电路，其R2RUi-G(s)2R1U0R+1(a)R32.3试用复数阻抗法画出图E2.3所示电路的动态结构图，并求传递函数。Uo(s)、Uc(s)G(s)G(s)Ur(s)Ur(s)uLR1uco++urCR2uuco--图E2.3题2-3RLC电路R1uucLo++IILR1ICurCR2uu

2、co---UI1U1R1IC1UCorRRCsLsI2-11-LU(s)Ro2G(s)U(s)(RCs1)(LsR)Rr121R1uucoLR1++++ILurCR2uuocurCucR2----1Ur1I(R2Ls)UcCsR11-(R2Ls)CsU(s)LsRc2G(s)2U(s)RLCs(RRCL)sRRr112122-6试画出图E2.5所示系统的动态结构图，并求传递函数Uc(s)。Ur(s)R1C1C2R4urR0-R3-R2-ucR+0++图E2.5题2-6图R1C1C2R4urR0-R3-R2-ucR+0++UrR1R

3、4Uc1R0(R1Cs1)R2C2sR3-U(s)RRc14G(s)U(s)RRRCs(RCs1)RRr02321142.7系统动态结构图如图E2.6所示。试求传递函数C1(s)、C2(s)、C1(s)、C2(s)。R1(s)R1(s)R2(s)R2(s)R1C1G1G2G4C2R2G3图E2.6题2.7图R1C1G1C(s)G11G2R(s)1GGGGG411234C2R2G3C(s)GGG2123R(s)1GGGG图E2.6题2.7图11234C1(s)G1G3G4C2(s)G3R2(s)1G1G2G3G4R2(s)1G1G2G3

4、G42.8系统结构图如图E2.7所示。求传递函数C(s)/R(s)和C(s)/N(s)。若要消除干扰对输出的影响（即C(s)/N(s)=0），问G(s)=?nGn(s)N(s)K4R(s)+-C(s)K2K3K1sTs+1图E2.7题2.8图Gn(s)N(s)K4R(s)+-C(s)K2K3K1sTs+1图E2.7题2.8图C(s)KKK123解：1）令N(s)=0,则R(s)s(Ts1)KKK123C(s)KKKGKKS123n342）令R(s)=0,则N(s)s(Ts1)KKK123Gn(s)N(s)K4R(s)+-C(s)K2K3K1sTs+1框

5、N(s)-KC(s)3图K4Ts1简化-如KK下12s+R(s)=0GnN(s)-KC(s)3K4Ts1-KK12s+GnN(s)-KC(s)K34Ts1-1KK12K4s+GnN(s)-KC(s)K34Ts1-1KK12K4s+GnN(s)-KKC(s)34Ts1KK12-1Ks4+GnN(s)-KKC(s)34Ts1KK12-1Ks4+GnN(s)-KKC(s)34Ts1KK12-1Ks4+KK12GnKs4N(s)-KKC(s)34Ts1KK12-1Ks4+KK12GnKs4N(s)KKC(s)34-Ts1+KKKK1212-1GnK4sKs

6、4N(s)KKC(s)34-Ts1+KKKK1212-1GnK4sKs4C(s)KKKGKKs123n34N(s)s(Ts1)KKK123要消除干扰对输出的影响，令C(s)/N(s)=0Ks4则G(s)nKK122.9简化图E2.8中各系统结构图，并求出传递函数C(s)/R(s)。R(s)C(s)R(s)+C(s)++GG11++G2G2+G3G3（a）G4（b）R(s)+C(s)G1+G（c）2+图E2.8习题2-9图R(s)C(s)++G1+RCG+GG122-+G3G-G34G4（a）C(s)GG12G(s)R(s)1(GG)(GG

7、)1234R(s)+C(s)R+CG1G1-+G2+G2-G3G2G3（b）R+CG1C(s)GG-+12G(s)G2GGR(s)1GG2323R(s)+C(s)G1+（c）G2+C(s)G(1G)12G(s)R(s)1GGG212RCG1-G21G22.10系统结构如图E2.9所示，试求出系统的传递函数。++G1G2R(s)+C(s)H++G3G4图E2.9题2.10系统结构图++G1G2R(s)+C(s)H++G3G4H-GG12RCGG34-HH-GG12RCGG34-HGH2-G1G2RCG3G4-GH4GH2-G1G2RCG3G