1、本章主要内容时域分析法 1( ) 1( )( )r ttR ss21( )1( )( )r tttR ss 2311( )1( )( )2r tttR ss( )( )( )1r ttR s22( )sin1( )( )Ar tAttR ss ( ( ) )( ( ) )% %1 10 00 0% %( ( ) )p ph h t th hh h h(t)t时间时间tr上上 升升峰值时峰值时间间tpAB超调量超调量% =AB100%h(t)t调节时调节时间间tsh(t)t时间时间trAB超调量超调量% =AB100% ( )1( ),( )1C ssTRCR sTs( )( )dcRCc tr
2、 tdt/( )1,t Th tet .1)(.0)(;1368. 0)(;1)(0hdttdhTdttdhTdttdhtTtt。202( )1;( )10.368;( )0tt Ttdc tdtTdc tdtTdc tdt 特点： /1( ),0t Tc tetT /( )()(0)t Tc tt TTet )0()1 (21)(22teTTtttcTt( ( ) )1 10 00 0 / /1 10 00 01 10 0( ( ) )1 1( ( ) ) ( ( ) )1 1( (1 10 00 0 / / ) ) 0 0. . 1 11 10 01 1/ /1 10 0G G s ss
3、ss sG G s s H H s ss ss ss s 1 1 / /1 10 00 0 / /( ( ) )1 11 10 00 0 / /1 1/ /1 10 00 0h hh hh hK Ks ss sK Ks ss sK K 1 10 0. . 1 11 10 00 03 3h hK K 0 0. . 3 3h hK K 20一、二阶系统的数学模型( )(1)MKG ss T sKssTKsssMio2)()()(2222)()()(nnnsssRsCsMnTKKTM212222121( )( ) ( )2()(ss )nnnnC ss R sssss ss j11223345 05
4、1.21.01.61.40.80.60.40.2c(t)16182 4 6 8 1012140t213540222nnss122, 1nns1、欠阻尼二阶系统（0）21,21nndsjj n21nd1( )R ss2221( )( )( )2nnnC ss R ssss 22221()()nnndndssss2( )1cossin1ntddh tett 211sin()01ntdett arccos12 arctg (2)= 0，无阻尼 njs2, 1)0(cos1)(ttthn(3)=1，临界阻尼ns2, 1nnnnnssssssC1)(1)()(222)0()1 (1)(ttethntnt
5、nntedttdh2)(122, 1nns)1(1,)1(12221nnTT12/2112( )1,0/1/1t Tt Teeh ttTTT T 0123456789101112nt c(t)0.20.40.60.81.01.21.41.61.82.0=00.10.20.30.40.50.60.70.81.02.0 21rdnt21(t)1sin()01ntdhett 21sin()01n rtd ret( )1rh t0pt tdhdt0)cos()sin(tetedtddtnnn21()dtgt21tg ,2 , 0pdtd pt21pddt 2/ 121( )1sin()1ph te %
6、2sin()1 2/ 1()1ph te2/ 1%100%e)11 (2tne95.011)(2snsttteth=55 . 35 . 3nst5 . 45 . 4nst(取=2时) c(t)t0121e1n t-21e1n t-n1 T包络线(取=5时) =0.7 。2.参数 对单位阶跃响应性能的影响) 1( ssKs1KsKsKsRsC)1 ()()(2KKKn21,46. 0)1(ln)1ln(22pp211lnp2/ 1%100%e)/(53. 312sradtpn22)rad/s(46.12nK)rad(10. 1cos1) s (18. 012Kn) srad(14. 312nd)
7、 s (37. 07 . 01ndt) s (65. 0drt) s (17. 25 . 3nst02. 0)(80. 25 . 4stns( )( )( )( )1( )(1)1( )(1)m mG sKG sKs sG ss T sKG ss T sK2 22 22 22 2/ /( ( ) )/ / /2 2n nm mm mm mn nn nK KT Ts ss ss s T TK KT Ts ss s 2 21 1%100%16. 3%100%16. 3%e e s2 20. 730. 731 1p pd dn nt t s0. 4860. 486r rd dt t 3 31. 21
8、. 2s sn ntsts( (1 1) )m mK Ks s T T s s 2 2/ 1/ 1%30%0. 3100%30%0. 3100%e e 2 2lnln 0. 31. 2lnln 0. 31. 21 1e e 0. 360. 36 s2 20 0. . 1 11 1p pd dn nt t 1 12 231. 431. 431. 431. 433. 633. 60. 9340. 9341 1n ns s 2 22222221130( )1130( )( )( )224. 211301( )224. 211301( )n nnnnnG sG ss sssssG sssssG s 2
9、 2( )1129( )1129( )( )1( )(2)(24. 2)1( )(2)(24. 2)n nn ns sG sG sss ss sss ss s 0t(s)11.30.1h(t) 12() 1()(ndsssTKsG2222)(nndnsszszsznd2ndnddnndsrzzztln3)1ln(21ln)2ln(213222tdntndndretre)1sin(2)1sin(1)(2trethdntnd%1001%2pndtder21dndptntnKK22222)(nntnsssnttK2121( )2 / (2)1ntnntnG sKs sKznd2nddT211010)
10、(2sss) s (7,%4 .60%) s (01. 1, ) s (55. 0, ) s (35. 0sprdtttt10)101 (10)(2sKsst10.50.162ttnK2222)(nntnsss22. 01012ttntKK16. 32ntnKK. ) s (22. 2,%3 .16%, ) s (15. 1, ) s (77. 0, ) s (43. 0, )rad(316. 0sprdsstttte)()(1)()()()(sHsGsGsRsCsniimiisszsKsDsMsRsCs11)()()()()()()(10111011( )( )()( )mmmmnnnnb
11、sbsbsbM ssmnD sa sa sasaLLssssszsKsCqjrkkkkjmii1)2()()()(11221qjrkkkkkkjjssCsBssAsAsC112202)()0()1sin(1)1cos()(2121210tteBCteBeAAthkkrktkkkkkkrkkktkqjtsjkkkkj21( )(0.671)(0.010.081)ssss%,st12,31.5,49.2ssj 1s11( )0.6711ssTs33 0.672.01stTss %020.591( )(0.671)(0.010.081)sssss21( )0.010.081sss10.4,10ns2
12、/ 1%100%25%e3.50.88snts55 lim (t)0tk )(sG)(sHR(s)E(s)C(s)-)()()()()(1)()()()(11101110nmasasasabsbsbsbsDsMsHsGsGsRsCsnnnnmmmm0)(1110nnnnasasasasDrkkkkqjjmiisssszsKsDsMsC12211)2()()()()()( rkkktkkkkkkrkkktkqjtsjtteBCteBeAtckkkkj122121)0()1sin(1)1cos()()0(0)(01110 aasasasasDnnnn(0,0,1,2, )iain( )(0.1s
13、1)(0.25s 1)KG ss320.0250.350sssK 01230.025,0.351aaaaK1)00iaK22)0D 132020.3500.025114aaKDaaK320.0250.350sssK 0024113521 20 3113231nnns a a a sa a a aaaaascca40 51 60 73311313 31 2313 51 3313 71 43142434131313naaaaaaac aac aacc aacc aacsccc ccc0sna3s2s1 13 32 24 41 12 2 1 15 52 20 05 52 2 1234501s0s1
14、15 56 60 05 56 6 2 24 41 15 56 61 1 04s04473223456ssssss6543210127413401340(4)0( 6)01.5416.704sssssss043)(24sssF064)(3sssF043)(24sssF 043)(24sssF( 13)/2j sK11)2(2nnss-R(s)E(s)C(s)21223122)()(nnnnKsssKss02)(21223nnnKssssD0750075006 .34)(123KssssD1011123750006 .34750075006 .3475006 .3475001KsKsKss6 .3
15、401 K07500) 1(7500) 1(6 .34) 1(112131Ksss0750075006 .34)(123KssssD0)4 .74667500(8 .74336 .31112131Ksss4 .7466750006 .31)4 .74667500(8 .74336 .314 .746675006 .318 .743311011123KsKsKss3 .3211 Klim( )lim( )sssst tee tee t )()(11)()()(sHsGsRsEse( )( )( ) ( )1( )( )eR sE ss R sG s H s)()(1)(lim)(lim)(lim
16、00sHsGssRssEteesstssvnjjvmiisTssKsHsG11) 1() 1()()(000011lim( )( )lim(1)(1)1mn vijssijG s HssT s00( )( )( )( )vKG s H sG s HssvsvssssKsRse010lim)(limvsvssssKsRse010lim)(limsRsRtRtr)()( 1)(pssssskRsHsGRsHsGRsHsGsRse1)()(lim1)()(1lim)()(1)(lim000)()(lim0sHsGkspKRkReKkpssp1101psspkRek2)()(sRsRtRtrvssss
17、skRsHssGRsHssGsRsRsHsGse)()(lim)()(lim)()(1lim0020100lim)()(limvssvsKsHsGskssvek0KRkReKkvssv110)()(sKsHsGhhssKe10111111011hssssKee5)101 (1hhhssssKKKee32)(21)(sRsRtRtrasssskRsHsGsRsRsHsGse)()(lim)()(1lim20302020lim)()(limvssasKsHsGskssaek00ssaekKRkReKkassa)15(1sss8 . 0)(sE)(sC)(sR5) 1(14) 15(5)()(sss
18、sssHsG,1,0pvaKKKK 0;1;sssssseee TteTTtTsTsTsLte/231)(11)()()(TtTtess320011lim)(limsTsTsssEessss1( )1(s)1eTssGTs22( )sin( )r ttR ss1/2222( )1(1)t TTsTe tLeTssT 222222cossin(1)(1)TTttTT0sin)1(cos)1()(222222tTTtTTtess01lim)(lim)(22200sTsTsssEesssssKsRssKsTsssRsTssHsGSsRsEsteessnjmjijnjjssstss010111000l
19、im)(lim)1 ()1 ()()1 (lim)()(1)(lim)(lim)(lim稳态误差为)()(lim1)()(1lim)()(1)(lim)(lim0000sHsGRsHsGRsHsGssRsEsessssss sRsRtRtr)(),( 1)(称称为为位位置置误误差差系系数数 )()(lim0sHsGKsppsskRe 1于是于是 0,II0,I1,0sspsspsspekekkRekk型系统型系统型系统型系统型系统型系统0 00 00 00 0( )( )lim( )limlim( )lim1( )( )1( )( )limlim( )( )lim( )( )( )( )lim
20、( )( )sssss ss ss ss ssR ssR sesE sesE sG s HsG s HsRRRRssG s HssG s HsssG s HssG s Hs 2 2( ( ) )1 1( ( ) ), ,( ( ) )R Rr r t tR R t t t tR R s ss s 0 0l li im m( ( ) )( ( ) )v vs sK Ks sG Gs s H Hs s 称称为为静静态态速速度度误误差差系系数数ssssv vR Re ek k于于是是 0,II,I,0,0ssvssvssvekkRekkek型型系系统统型型系系统统型型系系统统)()(lim)()(l
21、im)()(1)(lim)(lim2022000sHsGsRsHsGssRsHsGssRsEsessssss 32)(),( 121)(sRsRtRttr数数称称为为静静态态加加速速度度误误差差系系 )()(lim20sHsGsKsaasskRe 于是于是 kRekkekekssassassa,II,0,I,0,0型系统型系统型系统型系统型系统型系统122502( ),( )50(1)G sG sss s2122( )( )2(50)(1)2502( )1( )( )(50)(1)500150(1)G sE sss sN sG s G ss ssss s002(50)lim( )lim0.2(
22、50)(1)500ssnsssesE ss ss0.4ssssrssneee1,10,00,Isspvaabcekkkakbkcckk 23( )11( )(0)(0)(0)(0)( )2!3!eeeeeE sssssR S )()0(! 31)0(!21)0()0()()()(32sRssssRssEeeeee 2012( )( ) ( )() ( )eE ss R sCC sC sR s 则012( )( )( )( )ssetC r tC r tC r t故。0121(0),(0),(0),2!eeeCCC 令230123( )( )( )eE ssCC sC sC sR S因此) 1(
23、) 11 . 0(10)(ssssG10210)(2ssss9) 1(11)102(10)()()(22ssssssssRssC)0(,3cos1)(ttetht 1 . 01011)(vssKe pt 0)(th0| 3sin33cosptttttete313pttg1： 令 3. stgtp94. 0)3 .5743.1814. 3(31)31(311%37%10011)(%pth2： st05. 0|3cos|ttetests305. 0ln3： 令 2221(0.11)0.1( )1( )0.11001000.1esssssG sssss100( )s(0.11)G ss4501230
24、,0.01,9 10 ,1.9 10 ,CCCC 242530 109 101.9 10sss 2402040035130500( )sincos0.055cos( 524.9 )ssoetCCCtCCCtt )590cos()590(90sin5sintttooo000( )() cos 90()2550cos 905( 5)1000255055.90cos( 590(116.62.94)976.280.055cos(524.9 )osseeoeooetjtjjtjjtt 212( )( )( )( )1( )( )( )nnGsEsCsN sG s Gs H s 220.04980.115
25、( )2525sscsdsEsss 解：2212222212/ (1)( )( )( )1/ (1)( )nnKs T sEsCsN sK Ks T sKN sT ssK K 010lim( )/ssnnsesEsnK )()() 1(/ ) 1(1) 1(/)(21212322212sNKKsTKKsTsTTsTKsNTssKsTsTKTssKsEiiiiiin0)(lim0212123220snKKsTKKsTsTTsTsKssEeiiiinsssn0211322212121lim( )ssnnsiiiiiesEssK TsTnnTT sTsK K TsK KsK 0( )/N sns1(
26、 )/N sns) s (1) s () s (G) s (G1) s (G) s ( vnnnnvnnnnvKsasasasKssasasasKsG )1()()1()(111111则则设设vnnnnvKsasasassKs )1()1()(1111 )()(,/1121121asasasKssGKnnnnvv 取取,)(1 ssGr 当加入当加入时时当当 221rss) s (G v11n1nnn221vK)1sasasa( s)ss1(K) s ( ,/,/1121vvKaK 取取vnnnnvKsasasassasKs )1()(11121)()(2312321asasasKssasGnnnnv
