matlab控制系统仿真第四章(1)

1、234是控制系统是控制系统分析与设计分析与设计的前提的前提为系统控制为系统控制器设计提供器设计提供重要依据重要依据选择控制装选择控制装置置,构成优性构成优性能的新系统能的新系统5671( )(1)cPDIG sKT sTsPKDTIT0PK 0DT IT 0PK 0DT IT 0PK 0DT IT 0PK 0DT IT 89sse %减小最大偏差量1( )(1)cPDIG sKT sTs100DT IT 1 5PK 1( )(1)cPDIG sKT sTsg1g2g12g3g4g程序运行后，可得不同Kp下调速系统的单位阶跃响应曲线12Kp1234515.329.139.146.853.1ts0

2、.150.1560.1660.1780.191ess0.270.160.110.080.07%130DT 0.030.07IT 1PK 141( )(1)(+1)=cPDIPIIG sKT sTsK TsTsggc15TI0.030.040.050.060.07ts4835.526.820.515.90.3730.2490.1850.1840.184%1612,48,84DT 10.01T 0.01PK 1721( )(1)(1)cPDIPIIDIG sKT sTsK TsTT sTs gcg程序运行后，可得不同TD下调速系统的单位阶跃响应曲线（如图4-35）18%TD1248849.1215

3、.315.6ts2.488.4213.6%1920sse %减小最大偏差量210,DITT m控制规律KpTITDP0.5KmPI0.45KmPID0.59Km1.7/m /m 0.25 /m 220180( )(0.21)(0.51)Gssss23240,DITT m控制规律KpTITDP0.5KmPI0.45KmPID0.59Km1.7/m /m 0.25 /m 250.04mK 3.2/mrad smmK260180( )(0.21)(0.51)Gssss0.024PK 0.98IT 0.25DT 210.024(0.250.981)( )0.024(10.25 )0.98cssGsss

4、s控制规律KpTITDP0.5KmPI0.45KmPID0.59Km1.7/m /m 0.25 /m 270.04mK 3.2/mrad s1( )(1)cPDIG sKT sTs% 59.4%5.7sts0sse 280000( )1sKGseT s控制规律KpTITDPPIPID)/(9 . 0000KT03 .3)/(2 . 1000KT02 .205 .0)/(000KT2918008( )3601sG ses23231511()()()244601511()()()24460ssssesss303118008( )3601sG ses0.3PK 396IT 90DT 控制规律KpTI

5、TDPPIPID)/(9 . 0000KT03 .3)/(2 . 1000KT02 .2)/(000KT0000( )1sKGseT s18008( )3601sG ses3205 .033210.3(900.00253)( )0.3(190 )396cssG ssss 1( )(1)cPDIG sKT sTs18008( )3601sG ses% 29.5%1210sts0sse 34控制规律 KPTITDP PIPID10001(/)0.3333TK100010.9(/)0.082TK100011.35(/)0.27TK200000003.33(/)0.3(/)12.2(/)TTTT200

6、000002.5(/)0.5(/)10.6(/)TTTT000000.37(/)10.2(/)TTT350000( )1sKGseT s18008( )3601sGses0.37PK 430.4IT 60.5DT 2160.5430.40.37(60.50.0023)( )0.37(1)cssssssG361( )(1)cPDIG sKT sTs控制规律 KPTITDP PIPID10001(/)0.3333TK100010.9(/)0.082TK100011.35(/)0.27TK200000003.33(/)0.3(/)12.2(/)TTTT200000002.5(/)0.5(/)10.6

7、(/)TTTT000000.37(/)10.2(/)TTT370000( )1sKGseT s% 51.7%1420sts0sse 382160.5430.40.37(60.50.0023)( )0.37(1)cssssssG18008( )3601sGses0( )e t dt20( )e t dt0( )t e t dt39000000000(/)(/)(/)BPIBBDATKKTTATTT AT400000( )1sKGseT s41表4-7 基于误差积分指标极小化的PID参数整定公式中的A、B取值误差积分指标类型误差积分指标类型控制规律控制规律控制作用控制作用ABIAEPP0.902-

8、0.985ISEPP1.411-0.917ITAEPP0.904-1.084IAEPIP0.984-0.986I0.608-0.707ISEPIP1.305-0.959I0.492-0.739ITAEPIP0.859-0.977I0.674-0.680IAEPIDP1.435-0.921I0.878-0.749D0.4821.137ISEPIDP1.495-0.945I1.101-0.771D0.5601.006ITAEPIDP1.357-0.947I0.842-0.738D0.3810.9952.501( )201sG ses42437.165PK 5.12IT 0.96DT 217.165

9、(0.960.2)( )7.165(10.96 )5.12cssG ssss 000000000(/)(/)(/)BBPIDBATTKTTT ATKAT440000( )1sKGseT s% 43.6%22.8sts0sse45464748( )ccccsZG sKsP4950( )ccccs ZG sKs P1( )s 01180( )cG s51( )cG s1BsO112cDsCEsCcDOP cEOz cPcZ11Im( )Re( )tan()cPsPs12cPsDO 11Im( )Re( )tan()cZsZs12cZs EO 52PPM M2c2( )ccccs ZG sKs P1

10、( )(5)(15)G ss ss%16%0.6sts5354551(5)(15)gs ss561( )(5)(15)G ss ss57585960610.6sts21%100%e3.5(5%)snt n% 62% 16%0.6sts1,2 5.7910.03si 63222( )2nnnsss321112075dgvsss1( )zetag s 641( )s 01180( )cG s1( )(5)(15)G ss ss( )cG s1BsO112cDsCEsCcDOP cEOz cPcZ11Im( )Re( )tan()cPsPs12cPsDO 11Im( )Re( )tan()cZsZs

11、12cZs EO 65PPM M2c266ZP1( )gG s( )ccccs ZG sKs P1( )zetaG s 11Im( )Re( )tan()cPsPs12cPsDO 11Im( )Re( )tan()cZsZs12cZs EO 3.847( )526.7434.84sGc ss67ZP1( )gG s( )ccccs ZG sKs P1( )zetaG s 68693.847( )526.7434.84sGc ss70710.6sts%16%本例校正后的单位阶跃响应曲线如图4-11所示。72%12.8%0.433sts1 0.26( )593.921 0.029csG ss730

12、( )G s1( )1ZccPT sG sKT s7401( )( )0cG s G s1001001111( ) ,( ),( ),1ZccPT sMG sG sMG sKcT s 111( )(1)(1)ccZPG sTsTs 01cM M 0c0M0ZTPT1ss 1sMs0000sinsin()sinscsZcsK MTK M M000sinsin()sincssPsK MTM ZTPTZTPT7502( )(0.251)(0.11)G ssss%30%0.8sts0.1sse 012( )( )(0.251)(0.11)1ZccPT sG s G sKsssT s10.12ssceK

13、765cK 5cK 010400( )(0.251)(0.11)(4)(10)G sssss ss77%74.5%7.62sts78%30%0.8sts21%100%30%e3.50.8(5%)snt n% 222( )2nnnsss%30%0.8sts01( )( )0cG s G s1001001111( ) ,( ),( ),1ZccPT sMG sG sMG sKcT s 111( )(1)(1)ccZPG sTsTs 01cM M 0c0M0ZTPT1ss 1sMs0000sinsin()sinscsZcsK MTK M M000sinsin()sincssPsK MTM ZTPTZ

14、TPT80811( )1ZccPT sG sKT s02( )(0.251)(0.11)G ssss001001( ) ,( )MG sG s1ss 1sMs0.36471( )50.016561csG ss82%30%0.8sts83%23.6%0.682sts840.361( )1*0.0171csG ss851( )(1)1cTsG sTs0( )G s0( )( )( )cG sG s G s01( )( ) 0cG s G s8687111111111( )11csTsTG sTssT001( )MG s1( )ccMGs0011cM MM88002000( )(20)G sKs s

15、% 15%0.4sts0.01sse000200010011( )( )(20)1(0.051)1cKKTsTsGs Gss sTsssTs010.01100sseK8901K 01K 0100( )(0.051)G sss90从图中可以得到系统的最大超调量 ，调整时间ts=0.299s，不能满足性能指标的要求。%48.5%91% 15%0.4sts21%100% 15%e% 0.55nd3.5snt929394因此期望的闭环主导极点可由以下程序求取：kesi=0.55;wn=18.2;p=1 2*kesi*wn wn2,roots(p)执行结果为：06.0416M0M222( )2nnnss

16、s0011cM MM001( )MG s1( )(1)1cTsG sTs1111()( )2040eR sT21( )12.11csG ss9541( )1.08241csGss96本例校正后的根轨迹图如图4-17970.303sts%14.4%98991004.2.1 基于伯德图的相位超前校正11( )(1)1caTsG saa Ts1arcsin1maa1mTa()10lgccLaccm0()() 0cccLL0( )G sc0()cL10100( )(1)KG ss s0.1sserad 4.4/crad s045 10hdB000111( )( )(/ )(1)1(1)1cKaTsKa

17、TsG s G sKKas sa Tss sTs010( )(1)G ss s10.1sseK10K10K 102103018h 3.08c104( )cG s0()cL 4.4/crad s0()6cLdB 10.456110.1141aTssTss1mTa()10lgccLa1050()cL10610.456110.1141aTssTss107查看校正后系统的开环对数频率特性曲线，可得系统性能：相角裕度(P.M.) ，幅值裕度 （G.M.） ， 满足性能指标要求。049.6h 4.43c1080( )G sc0M01( )1ZcPt sG st s0( )( )( )cG sG s G s

18、c109 （4-14） （4-15）（4-14）和（4-15）联立，可解 （4-16）11001()11ZccPct jG jMt j0001 180() 180()1ZccPct jG jt j00001cos( )sin( )ZcMtM （4-17） 000cos( )sin( )PcMt00( )(0.11)(0.0011)KG ssss 176/crad s0 43001( )( )(0.11)(0.0011)1ZcPKt sG s G sssst s0.001sse 1000K 1000K 01000( )(0.11)(0.0011)G ssss01/0.001sseK1111120

19、0.0699.5/crad s113( )cG s0 1 0.019( )1 0.0024csG ss1141 0.019( )1 0.0024csG ss115043.4179/crad s116117( )cG sc0( )G s0()cL1( )(1)1cbTsGsbTs0()c ()ccL()cc 00 180()()ccc 0()6cc c00()()180ccc（4-19）118020lg()0cb L10.1cbT11900( )(0.11)(0.21)KG ssss040 2.3/crad s001( )( )(0.11)(0.21)1cKbTsG s G ssssTs000l

20、im( )( )30vcsKsG s G sK030( )(0.11)(0.21)Gssss120121从图4-24中可以读出相角裕度(P.M.) ， ，不满足性能指标要求。017.29.77/crad s122000000()() 180406180134ccc c0()cL1231242.7/crads3.71( )34.61csGss020lg()0cb L10.1cbT1253.71( )34.61csGss126041.1 2.73/crad s127128( )cG s0( )G s0L11( )(1,)11abcabbaT sT sGsTTTT ss1/bTbc020lg()20

21、lg0cbcLT1290()cL20lgbcTca1aT1sin1sinH20lgbcT20lgbcT1300( )11(1)(1)62vKGssss0180( )11(1)(1)62Gssss180vK 131132从图4-27中可以读出相角裕度(P.M.) ，不能满足性能指标要求。055.1 133( )cG s2b10.5bbT26c3sts1sinrM2(2 1.5(1)2.5(1) )srrcktkMM3.2/crad s 3.5/crad s1340() 26.8cLdB135136 3.5/crad s0.5bT 20lg4.9bcT020lg() 20lg 233.7cbcLT

22、 48.450011800.51( )( )1110.011(1)(1)62acaT ssGs GsT sssss180(1)1(1)(0.011)(1)6aaT ssssT s020lg()20lg0cbcLT137000000001 180arctan 90arctan arctan0.01 arctan690arctan 30.262arctan57.7arctan 30.262arctanacccacacacacacTTTTTT 1aTc0arctan90acT 1.28aT 0061 sin457.695.831/1.281 sin45H1 1.281 0.5( )1 641 0.0

23、1cssG sss1381 1.281 0.5( )1 641 0.01cssG sss1390 46.5 3.25/crad s28.1hdB1403sts1411420.2aR 0.5R0.18mTs0.03aTs0.007 /( /min)tKVr0.05 /iKV A40sK 1431440.002oiTs0.01onTs0.0017sTs220 136 0.20.132min/1460NNaeNUI RCVrn14501/( )( )1114( )( )( )(0.031)(0.0021)(0.0017)isicioisaciciiKKRG sG sT sTsT sG sG s G

24、sss1461471489.51miK 582mi0.454.3PimiKK1.7 /0.009IimiT (1)4.3(0.0091)( )0.009PiIiciIiKT ssGsT ss1491503232( )10.15517.2( )0.000110.03371.15517.20.15517.2200.000110.03371.15517.2aniiIssUsKsssssss151320( )/( )( )1( )2.94(0.15517.2)( )(0.011)(0.000110.03371.15517.2)( )( )taencnonnimcncnnKI sR CG sGsT sU

25、sT ssGssssssGs Gs15215311mnK22.4mn0.454.95PnmnKK1.7 /0.24InmnT 154(1)4.95(0.241)( )0.24PnIncnInKT ssGsT ss155156157158xAxBuyCxuv Kx 4.4.1 极点配置()xABK xBvyCx159det() 0IA BK4.4.1 极点配置160161( )180( )(1)(2)Y sU ss ss162163164xAx Bu110010002A001001B16500( )(6)(12)KG ss ss% 5%0.5sts0.2sse 0.2sse05K 05K 166

26100B 005C 0D 1182520118001CQ167% 5%0.5sts31(510)ps3110100ps168169170%4.97%0.3sts1714.4.2 全维状态观测器设计172xAx BuyCx173()xA HC x Bu Hy x y174AAB C,A B CHK,A B 1 101011xxuyx 176, ,A B C1101210211A 1110B 120 1C , ,A B C1254HK 1774.4.3 降维状态观测器设计178,x Ax Buy CxxPx, ,A B C11111112222221220 xxxBAAuyIxxxBAA 1x1xy2x2222212111122()xA xA yB uyA yBuA x（4-38） 179212()A yB u111()yA yBu222122111212()() ()xAHA xH y A y BuA y Buy 2zxHy222122212211121()()()()zxHyAHAzAHAHAHAyBHB u12xyx