自动控制理论作业解答

1、课堂作业：作业 1i2Ci1urucR1R2C解：根据定律(i1 i2 )dt ur R i 1C1 1uc R i (i i )dt 12 2C12R1 i1 i2 dt R2 i21C拉氏变换(s) R I (s) I (s) I (s)U 1 r11sC12U (s) R I (s) I (s) I (s) 1 c2212sCR I (s) 1 I (s) R I (s)11222sCU (s)RR C 2s2 (R R )Cs 1 c 1 212U (s)R R C 2s2 (2R R )Cs 1r1 212作业 2R(s)C(s)GG34H2G4R(s)C(s)G1G2G4H1G3G

2、4 11 GG H3 43G2G3G4 21 G G H G G H2 323 43H3G3H1H3G2G1H2C(s) G1G2G3G4R(s)1 G2G3 H2 G3G4 H3 G1G2G3G4 H1作业 3G3R(s)C(s)G2G4相加点后移G3R(s)C(s)GG12G4 H H方框图化简G3R(s)C(s)G1G1 GG H21 4相加点前移G3R(s)C(s)G11 GG H1 4方框图化简(s) G1G2 G2G3 G1G2G3G4 H1 G1G2 H G1G4 H1 G1G4 HG2G1H HHG1课后作业：3-7 题RfRinuIUinuUout解： i i 0 I Rin

3、 (u u )(1)UinU(2)式代入到(1) I R (u u )(2)outf由(2)式1(uI u ) U(3)outRf(3)式代入到(1) Rin (u (uu ) Uu )UinoutRf107u u Uouts 1U ( Rin 1) s 1URin Uinoutout107RRffRfU out ) s 1 RUin(R Rinfin1073-8 题uuUoutUin解：理想运放： i i 0 ， u uUin u u非理想运放 Uout i i 0 u u UinUout107u u Uouts 1s 1 107Uout UinUoutU out1s 1 1Uin1073-

4、13 题R(s)C(s)G4G6G7 G8引出点前移R(s)C(s)G1G2G4G6 G4G7 G8G3G4 11 G G G3 4 5G2G3G4 21 G G G G G G 3 4 52 3 6G1G2G3G4C(s) R(s)1 G3G4G5 G2G3G6 G1G2G3G4G7 G1G2G3G4G83-15 题解：拉氏变换G3G5G2G1G3G5 X1(s) R(s) s C(s) k1 N (s) X(s) k X (s)201 X 3 (s) X 2 (s) N (s) X 5 (s)Ts X 4 (s) X 3 (s) X(s) X (s) C(s)54s C(s) C(s) X

5、 5 (s)N (s)R(s)C(s)1s 1 s相加点前移，引出点前移N (s)R(s)C(s)1s 1s 1 si.设 N (s) 0 ，计算C(s) R(s)R(s)C(s)1k0s 1s 1 s1 (s) 1s 21Ts2 (2T 1)s 1 (s) 2k0C(s)R(s)Ts (2T k 1)s 120ii.设 R(s) 0 ，计算C(s) N (s)1Tsk01Tsk0 k1 1k01Tsk1C (s)1N (s)s 1s 11 (s) 1s 2k0k1 1C(s)N (s)Ts (2T k 1)s 1203-20 题Z (s)R(s)C(s)G2G4解：信号流图Z (s) H2

6、(s) 1G2 (s) G3 (s) G4 (s) G1 (s) 11R(s) C(s) H1 (s) L1 G2 H1 ， L2 G4 H3 ， L3 G3G4 H2 1 L1 L2 L3 L1L2 L3 L4P1 G1G2G3G4 H2 ， 1 1Z (s) G1G2G3G4 H2R(s)1 G2GG3G4 H1H23-22 题解：H1H3G3G1H2 sk0k0 k1 11Ts11s0.5(s 1)19C (s)R (s)11111190.5(s 1)R (s)C (s)221求取C1 (s)R (s)1)1L 9 ， L9 ， L 811s0.5(s 1)20.5(s 1)1 1 L1 L2 L3 L1L299P ， 1 L 1， P 81 ， 1s0.5(s 1)120.5(s 1)22162 99s 34281(s)(s)182118s 34282求取C1 (s)R2)(s)2P1 9 ， 1 1P9s(s 1)2C (s) 1 11R1 (s)82s3 182s2 118s 342求取C2 (s)R (s)3)1P1 9 ， 1 1P9s(s 1)2