自動(dòng)控制原理+課后答案

1、.(t)Cu (t) Cu容 ，11ccuuu+(t)+(t)C+ 111uuuRRuuuuu+iiuooio(a)(c)圖 t)Cucu t) u t)u t)ciodu t) u t) u t)CcdtcRoR12 t)11 t) u t)C( u t) CR RoiiRo121C 、 uC(t),u (t)1212cu t) u t)u t)1iou t)u t) u t)u t)du t)Cic2oc2c2dtRR2du t)u t)u t) RC1dtoc21d2u t) t) u t)d2u t) t) u t) C1(2C C ) CCoooRiiiR22121221 uR(t)

2、u (t),u (t)2R21c2u (t) u (t)u (t)）1iR2u (t) u (t)u (t)c2oR2 t) t) ut)CC）1c2R2R2.u t)u t) t)C）ioc2R1 t) t) u t)u t)R2oioRC1 t) t) t) u t)CCCioR2R2R2d2u t)1( )du t u t( )d2u t( )1du t u t( ) ( )R C2( R CoodtoRCiiRC dtiRCdt2RC12dt2111 U Uc+C11RRC+CUi+U oUiU oUiU oU 2圖 U (s) U (s) (s)）CoRRC12U (s) U (s)

3、U (s)Cio1U (s)RR RR1o1221 1 R RU (s)RR R Ri121212U (s) U (s)U (s)）C1ioU (s)U (s) U (s)U (s)C sU (s)iC2oC2RR2C2.RC sU (s) U (s)U (s)1C1oC21sU (s)2R2CC s222s11 s2o1CC s1 s1U (s)R (2 )1 C C22s2 si1212212U (s) U (s)U (s)）C1iR2U (s) U (s)U (s)C2oR2U (s) (s) (s)）R2C1C2R2U (s)U (s) (s)ioR2C11U (s)RR C2s RR

4、222o112 11U (s)RR C2s(R 2R 122 R R RR i1121212(s)/R(s) C(s)/N(s)和 。 C）C(s)/R(s)圖 令N(s)0.GG121122圖GG121122圖GG12C(s)R(s)1GH 1G HGG1112222GGGH G H )GG H1H1211221231GH 1G H3112GG121G H G H G H G H GG H11221122123C(s)/N(s)R(s)0N(S)C(S)+圖 將 3H.C(S)+G2+223圖HG 和11-1/G H11C(S)N(S)G-G H211+22H /H31圖1GG H121+1

5、2231圖GG H121C(s)N(s)11G H)22GG H HGH111213111G H H22GH 1GG H1GH11211G H GG H1122123G GG H21211G H GG H22123C(s)/R(s) 2H.C(S)R(S)G1H1圖23C(S)R(S)31G H33圖 將 1H2C(S)R(S)31G H331G H323圖 131G H G H22331G H123圖.GG G213C(s)1G H G H2GG G2331G HR(s)1H31233G G1G H G H1223323GG G2131GH G H G H GH G H122331133 C

6、(s)/R(s)和C(s)/N(s)。111圖N(s) 0，求系統(tǒng)傳遞函數(shù)C(s)/R(s)(s)R C(s)p GG112L GH L G HL GG H，3111222123與L 2L1L GH G H1122 1(L L L ) L 1G H G H GG H GG H H12311221231212. 11C(s) pGG1112R(s)1GH G H GG H GG H H11221231212R(s) 0，求系統(tǒng)傳遞函數(shù)C(s)/N(s)N(s)C(s)p G ， p GG H122121L G H ，L GG H1222123 1(L L ) 1G H GG H1222123 1

7、 1，12C(s) 1G GG H2 p 2121R(s) 1G H GG Hiii1221231111圖C(s)/R(s)(s)R C(s)p GG G1123.L GH ，L G H ，L G H111222333與L L31L GG H H1313 1(L L L ) L 1G H G H G H GG H H1231122331313 11C(s) pGG G21113R(s)1GH G H G H GG H H1122331313 h(t)1012.5e1.2t t53.1 ) t 。 % tpsh(t)1012.5e1.2t t53.1 )1.25e1.2t sin(1.6t53.

8、1 )1ht)1e 1 t)n2t1n2 n1 1 2 1 2n 0.6 2n% e 2100% e100% 9.5% 0.61.25.1.96s t t20.8 1 p2n2sn0.4s1 G(s)s(sG(s)0.4s12sa(s)n1G(s) s s1 a s s222dnn 2, 0.5,z 2.5an2zndht)1re sin( 1 ) t t2dnnd2 2z22 rdnnz 132d 1 1 22 arctan( )arctan1.686ndd zdnd12 arctan1.047 d3dd 3.155 td 1 p2nd%1 16.2%dtp 2nr e2d113 ln(z

9、)lnz )22222nnnd t sdnK G(s)(s2)(s4)(s26s.s12s 69s 198sK 0432s4s3s21s0169200+K1219852.5 200+K7995-12K200+K666.25s1K52.5s 0由s2 s2i4.062rad/s K(0.5ss(ss2s G(s) KD(s) s 3s 4s (2K)s2K 0432s4s31342+K10-Ks22K3(10-K)(2+K)6K3110-K3s02K10K03(10K)(2K)/36K(10K)/302K 0.0 K 1.705K G(s) et) rt)ct)，s 2 a ssK,T abK

10、0圖 KK /T(s) 1KTTs2s Ks2 sTK111,2, 0.5 , K 即TTTTnnnD(s) Ts2 s K,令s s2D(s) T(s2)2 s2 K Ts2 (4T sT 1/T 2 0s2s1s0T T 2 T 2T T T 1/T 2 00T 1/4或T T T 1/T 200T 1/4,4 K Rt) tI e1/K. s KK(s) (K s G0sK s K 021KK )s Ts1KKTs2E(s) R(s)C(s) R(sG(s)00s2Ts2sKsTs s K)211令e sE(s) 0 K 1/K00s02sKK0sss0K 0）G(s)ssst)t r(

11、t) 2tt和 2 r） G(s)sss sss K10。111(t),t, t0, ,K221rt)t 時(shí)的穩(wěn)態(tài)誤差為 e 2 0.2 ，該系統(tǒng)在輸入為 r(t) 2tt2 時(shí)的穩(wěn)態(tài)誤差為ss2K1e 202ss2K K(s G(s)s(ss 4s16)2K 0z， ，1 p 0 p 1 p 2 j2 31123,4 實(shí)軸上根軌跡區(qū)間為(,23m3， 60 ,60， naa.11111d d 1 d2 j2 3 d 2 j2 3d1 d 0.45d12j0-11圖 K(s2s4)1.4s2G(s) ,K 0s(s4)(s6)(s2K0,4,6 j和1 ( s記(s)s(s4)(s6)(s 1

12、.4s1)s 11.4s 39s 43.6s 24s25432B(s)s 2s42由 A(s)B(s)(s)B(s)(5s 45.6s 117s 87.2s24)(s 2s4)4322(s 11.4s 39s 43.6s 24s)(2s2)54323s 30.8s 127.4s 338.4s 531.2s 348.8s065432用試探法或程序算得區(qū)間(2.3557.f (s) s 11.4s 39s (43.6k)s (242K)s4K 05432 4 0KK42 令s 2 0 K 43 K42 0 642 1.2115, 2.1545, 3.7537123圖 1.2115 ，1s(s4)(

13、s6)(s 1.4s2K |s22s4sj 2.1545 3.753764.74,K 163.43K 和2323 KK15.54 64.74 K 163.43或 h(t)11.8e 4 0.8e 9 t t.1R(s)s1 H(s) s s4 s9 s(s4)(sH(s)系統(tǒng)的閉環(huán)傳遞函數(shù)為G(s)R(s) (s4)(s G(s)將sG()( KsG(s)H(s), ,T 0K ；2( s T T 和K K j G()H()() 222K j0 0G(j0 )H(j0 ), ) 當(dāng)當(dāng)0 ( 0 2K( jG(j)H(j)0,() Tj2K K T T ( )2G()H() ( ( 2 T2 2

14、2T當(dāng)當(dāng)T. 1G(s)H(s)s(ss2)1G)H)() (11 0( 0 ) ( 0 )G j H j, )若若 ) 11( ) ( )G j H j0,()() (121 0( 0 ) ( 0 )G j H j, ) 若若 ) 21( ) ( )G j H j0,()() (232701 0G j H j( 0 ) ( 0 ), ) 若 ) 3.1G j H j( ) ( )0,()若() (3436010G(j0 )H(j0 ), )若 ) 41G j H j( ) ( )0,()若() (4圖 KG(s)s(s 5s 10K 。cKG()( 5 j j j則221(12)12G()

15、)12002 2)522 G() )2002.圖 2 G(j ) 0G(j ) 1 )1(12)1 12又122002 /sc 50(s2)G(s)H(s)211 10ss 。c50(s50(sG(s)H(s)s s (ss2G()H()(G(j)H(j) 50(4 ) (1 )1(100 )1122222220ln G(j)H(j) 20ln(50(4 ) (1 )1(100 )11)222222 20ln 5010ln(4 49rad /s ) 10ln(1 ) 10ln(100 ) 0 222c.10當(dāng) ；1 2；當(dāng)2 100 ；當(dāng)10當(dāng)；圖 T T 和(jT當(dāng)0N0P P2N 0T即Z

16、sN 1當(dāng)T0P P2N 2 2個(gè)極點(diǎn)，T s即Z 1N 0P 0 P2N 0 1s即Z N1P0當(dāng) P2N 2s 2即Z 3s sK 02.sss321TK1T-KTKTs0K KT 0則當(dāng)當(dāng) TK KT 0 sr(ss2)10srsr 2s 1021r當(dāng)r1s3s21134210s012當(dāng)rsss4321320123201s0-3,4r2當(dāng)r KG(s)； K,T0ss2TK10KT K，T .圖 0N0(j。P ( ( 2KK T T 2G()( j j T ( ( T 24222a、T 2( K T 2K20T T 24222422222 ( K T 3 2 K21T T 242224

17、222320 K 、K10b( K T T ( 220T T T T 24222242221T110 T 1) ( 1)K T 2T11 11T 1) T 1)24222T 2 T 1)2T T2T190T c( K T ( K T 220T T T T 2422224222.1T1K T 1) ( 1)K T 2T11 11T 1) T 1)24222T 2 T 1)2T T2TT 110 K ,0 T TK 1 ；K1 j0圖 40dB/dec /， 22（ 20 / dB dec1. 2dB dec20 /2 5dB dec20 / 21K s)KT s)G(s) 1111s2T sT

18、s)s2ss)2323KKL ( ) 20ln20lnK ln 20lnK 40lna,L ) 10Ka2s)故所測系統(tǒng)傳遞函數(shù)為G(s)20.5 0.2 )sss 0.8sG(s)s1KKe G() 1j KG() ,) 12(jKG() ) 122.45,K 2.45212.65 0K2.650 K 2.65故K. 5s e s2G(s)(s4 e 2 j G()(42G(j ) ,) 122(j2G(j ) 122 1 2 1.618, 0.61812) 1.37即又10 1.37 0 1.37 G(s)ss045 ，截止頻率不低于50 。L ( ) 40, 14c.圖1 55()610

19、lgaL( ) a T 取Lacmmm1aTs 10.036s(s)aG1Ts 10.009sc( )4L 55, ) 47.2cc KG(s)s(s450；1 rade；15ss7.5rad s 截止頻率。c1 1 K 15 K 15e得k 15G(s)由G(j ) 13.81s(scc 90 arctan 14.710 0c 7.5L G j ( 取mc1由 a La14T am.0.504s10.036s1G(s) 0.504s1(s) G(s)Gs(s 0.036s1c 90 arctan arctan0.504 arctan0.036 67.7 450ccc 4KG(s)s(s2)5

20、00 h10dBK 20s 1。limG (s)2K10。 KKKvps0() G( j j p6.325rad /sc17.5501Ts(s),a10G (j ) 1 G1aTscc.圖.500 55 17.55 33 5 38 由。m (1 sin )/(1 sin ) 0.24 mm )G (j ) 1/ a mcm益穿越頻率等于( ) ( )，G j G j mpcm20lg |G (G ()20lg |G ()|20lg |G ()|pcccpccc20lg |G (j)| 10lg 0pc20lg |G ( )10lg6.20dBpc9.04rad /s9.04 可以算出cm111

21、 T T TTm10.0226sG (s)s4.4294.16710.0542ss18.453c KG(s)ss)200 ) 50K，0 cK 200.0(s)s s44.7c90 arctan4.47 12.6計(jì)算相角裕度為G (s)Ts1c 50 12.6 37.4 038 arctanT arctan44.7T 38取， c0.0175T(s)0.0175s1Gc200(0.0175sssG(s)(0.0175sss 90 arctan0.1 arctan0.0175 50.6 50cc G(s)11s s s 11 ；0 30 20 。( ) 3615.5 L 得ccc.圖 10T 1/0.1 60L( ) 。bbb2016dB，故可得c )G (G()a / / /j j j jca 20, 30令 90 arctan20/ arctan20/60 arctan126 / arctan20/63aa8.9a0.112ss)G (s)s0.016s)c33.7 30