自动控制理论-时域分析

h(t)t时间时间tr上上 升升峰值时间峰值时间tpAB超调量超调量%=AB100%h(t)t调节时间调节时间tsh(t)t时间时间tr上上 升升峰值时间峰值时间tpAB超调量超调量%=AB100%调节时间调节时间ts图图3-2 一阶系统的结构图一阶系统的结构图C(s)-R(s)Ts1Ts1)(11)().()(sRTssRssC)()()()(trtctdtdcT11)()()(TssRsCsssR1)(TsssTssC1111.11)(TtetC1)()0(tTteT1斜率T11C(t)0.95T3T0.632TsTsTssTssC11111)(22)1()(TtTteTtTeTttCTtTe21)(ssR)1()()()(TteTtctrteTtet)(limTsTTsSC1111)(TteTtC1)(T1T121T21TT1)1(TssKKsTsKsRsCs2)()()()()()()(22tKrtKcdttdcdttcdT22222)()()(nnnssRsCsTKnTK210222nnss122,12,1nnPsssssRssCnnn1.2)()()(222121nnP122nnP22110212)()(pspsspspsssCn1P2P11)(00sssC121112)()(1ppssCnps222212)()(2ppssCnps)(121)(21221pepetCtptpn)0(t0A1A2A2p1ptpe2tpe12p5.11211nnjp221nnjp)()(2dndnnjsjsssC1P2P21njnn1022210)(dnsss10102222)()(1)(dnndnnsssssCtessdtdnnncos)(221-tesdtdndnsin)(221-)sin1(cos1)(2ttetCddtn)sincos1(1122tteddtn21nd11n221021sincos)143(0)sin(11)(2ttetCdtn21 arctgarccosdnn11np2,11)(00sssC1)(21nsnssCdsdnsnnssC)()(2221PPnj1210,221022)()()(nnnnssssssCtntnnteetC1)()1(1tentn)0(t1100njp2,10ttCncos1)(nndjn1P2P0nd0tn)(tC03.01.05.07.012tn21n)sin(11)(2tetCdtn)0(t)(trtrtt 1)(rtC21rnte0)sin(rdt0)sin(rdtktrdrtnrtnrt21ndrttp0)(pttdttdC)sin(pdnt0)cos(pddt)(pdttgnd21tgktpdktpdpt21ddptnptnptddpt21ddpt%100)()()(CCtCpp)(ptC)(C2111)(2etCp)sin(21sin)sin(211)(etCpp1)(Cpnpp8.04.0p%5.125p%100%100)()()(21eCCtCpppst%5%2)()()(CCtC)(stt 05.01)(C)sin(12tedtn)(stt 21tne)(stt)11ln1(ln111ln122nnst05.0nst211ln302.0nst211ln49.00nst3nst4stnnnststnndsTtN ddTT202.0nst3215.1N05.0nst4212Nnnrtptststpnpst)8.00(rtptntK1010)(2sss12n102n158.016.3n)1(10ss)1(10sssKt55.011221nrtgt01.112npt%4.60%10021ep63nst)05.0(315.12N)05.0(10)101(10)(2sKssttnK1012102n5.01012ntK216.010116.35.021016.3102)(sss5.016.3n%3.16p183.0N7.0rt15.1pt9.1st)()(assKsG%10p2%)5(stKassKs2)(KnKaan22%10%10021ep3.21.0ln1259.0232KKan23nst46.6)59.023()2(22aK011011.)(asasabsbsbsnnnnmmmmsssPsZsKsRssCrknknkkqiimjjr1)2()()()()()(12211qirknknkkknkknkkkiissCsBPsssC11222021)()(0ikkCqiknkrktktpiteetCnkki1210)1cos()(rknktkteCnkk12)1sin()0(tiPnkkikCkBiPnkkiPnkk AAfdfc)(t0)(limtCt011011.)(asasabsbsbsnnnnmmmm)(t0.011asasannnni21nknkkj)(t1)2()()()(11221qirknknkkimjjrssPsZsKsCqirkdkkdkkttitCteetCnkki11)sincos()(21nkdk0)(limtCt)(limtCt0.0111asasasannnn0na0naip0).()(.210111nnnnnnnpspspsaasaasaas).(211nnnaannnnaa1423231212.nnnaa.)1(210naaa,10),2,1,0(0niainppp,210.0111asasasannnn)0(0ansna2na6na4na1ns7na5na3na1na2ns1b4b3b2b3ns1c4c3c2c4ns1d4d3d2d2s1e2e1s1f0s1g13211nnnnnaaaaab15412nnnnnaaaaab17613nnnnnaaaaabib121211)(ccbbcd131312)(ccbbcd131512bbaabcnn141713bbaabcnn121311bbaabcnn劳斯稳定判据劳斯稳定判据（1）劳斯表第一列所有系数均不为零的情况劳斯表第一列所有系数均不为零的情况 如果劳斯表中第一列的系数都具有相同的符号，则如果劳斯表中第一列的系数都具有相同的符号，则系统是稳定的，否则系统是不稳定的。且不稳定根的个系统是稳定的，否则系统是不稳定的。且不稳定根的个数等于劳斯表中第一列系数符号改变的次数。数等于劳斯表中第一列系数符号改变的次数。5s4s3s6676171146658621106677916676586176672s26670626671s7916150677912667658677910s0210171462345sssss5s4s3s0s1s2s4s1s3s0s2s0 e（2 e-5）/e0522234ssss057432)1)(522(2345234ssssssssss5s0s1s2s3s4sjwjw6s3s4s5s3s4s016122)(24sss3s0s0248)(2ssdssd3s0161620128223456ssssss6s1s2s3s4s5s0s3s01612224ss08624 ss22,1js24,3js0ia0ia2.06.86n)2()()(22nnsskssGR(s)-E(s)1+C(s)sK)2(nnss222322)()(nnnnKssskss图3-20 例3-7系统结构图022223nnnKsss2.06.86n0750075006.3423Ksss6.3475007500346K3s2s1s0s07500k06.34750075006.34K132)1)(1)(1()(321sssKsGR(s)-111sTK122sTK133sTKC(s)图图3-21 例例3-8系统结构图系统结构图321KKKKsssTKs)1)(1)(1()(3210)1)(1)(1(321sTss01)()(32123231213321Ksss321323121323121321323121321)1()(KK+11KTTT3213s2s1s0s032103231210321TTT0)1()(323121321323121321K)(321TTT)(3231210)1(321K)()1(321TTTK)111(321)(321TTTKc1)111(321132cKcK2313321231212TTKc321T8cK3221102.24cK)()()(tCtCter)(tCr)()()(tbtrte)(tCr)()(trtCrR(t)-B(s)E(s)N(s)+C(s)(1sG)(2sG)(sH图3-22 反馈系统结构图sse)(limteetss（3-32）)()()(sHsEsEE(s)R(s)B(s)G(s)H(s)C(s)图3-23 给定输入作用下系统结构图)()()(1)()(sRsHsGsGsC)()()()()()(sCsHsRsBsRsE)()()()()(11sRssRsHsGer)()(11)(sHsGser)()(1)()()(limlimlim00sHsGssRssEteesstssniimjjsSsKsHsG11)1()1()()(（3-34）)()(lim0sHsGsKss2,1,0)()(111)()(1limlim00sHsGssHsGsessss)()(lim0sHsGKsppKpssKe110KssKKniimjjsp110)1()1(lim1niimjjspsssKK110)1()1(lim011pssKesse21)(ssR)()(11)()(1limlim020sHssGssHsGsessss)()(lim0sHssGKsvvssKe10)1()1(110limniimjjsvssKsK0vssKe11KsssKsKniimjjsv1110)1()1(limKKevss11niimjjsvsssKsK)1()1(10limvssKe1131)(ssR)()(11)()(12030limlimsHsGsssHsGsessss)()(20limsHsGsKsaaKassKe10)1()1(1120limniimjjsassKsKassKe10)1s(s)1s(KsKn1iim1jj20salimassKe112K)1s(s)1s(KsK2n1ii2m1jj20salimKKeass113niimjjsassKsK1120)1()1(lim01assKeIII系统类别静态误差系数阶跃输入)()(tIRtr斜坡输入r(t)=R t加速度输入2)(2RttrIIIpKaKKK0 00K0K000000pKRsse1KR1KRessassKReKRKR表3-1 输入信号作用下的稳态误差221)(CtttravpssKCKBKe1aKpKvK1ssR)(22)(sssR332)(sCsssR0Ks)K5.01(s3s223R(s)-C(s)12)(1()15.0(ssssk图3-24 例3-9系统结构图3s0s1s2s32)5.01(3KK K)12)(1()15.0()(ssssKsG)12)(1()15.0()(limlim00ssssKsGKsspKsssSKsssGKssv)12)(1()15.0()(limlim00KKKevpss55110)()()()()(sCsHsBsRsE)()()()(1)()(212sNsHsGsGsGsC)()()()()()(1)()()(212sNssNsHsGsGsHsGsEenR(s)-B(s)(1sG)(2sG+N(s)(sH图3-25 扰动输入作用下系统结构图C(s)()()(1)()()(212sHsGsGsHsGsensKsG1111)()1()(222ssKsG)t(1)s(R)t(rr)t(1)t(R)t(nnrRnR)()()()(1)()()(21200limlimsNsHsGsGsHssGteessss（3-38）)s(G)s(G11)s(21erR(s)-)(1sG)(2sG+N(s)图3-26 例3-10系统结构图C(s)0sRKK)s1)(s1(s)s1)(s1(s)s(G)s(G1)s(Rser21212120s210sssrlimlim)()(1)()(22sGsGsGsen121211202120)1)(1()1()()(1)()(limlimKRsRKKssssKssGsGsNssGennssssn1K1KReeenssnssrss)1()(111ssKsGsKsG2221)(0)()(1)(210limsGsGssResssr)()()(1)(2120limsNsGsGssGesssn0)1)(1()1(21212120limsRKKssssKsns0ssnssrsseee)(1sG111)(sGcR(s)(sGcE(s)(1sG)(2sGC(s)-+图3-27 按给定输入补偿的复合控制)()()()()()()(12sRsGsEsGsGsRsEc)()()(1)()(1)(212sRsGsGsGsGsEc)(1)(2sGsGc)(sGc)()()()()()()()(112sCsGsNsGsGsNsGsCc)()()(1)()(1)()(2112sNsGsGsGsGsGsCc)(1sG)(2sG)(sGcR(s)N(s)E(s)-+C(s)A图3-28 按扰动输入补偿的复合控制)(1)(1sGsGC)(1)(1sGsGC