控制第2章系统数学模型

1、),.,2 , 1 , 0(mjbj )()(.)()()()(.)()(01)1(1)(01)1(1)(txbtxbtxbtxbtxatxatxatxaiimimmimoononnon )(txi、)(txo、),.,2 , 1 , 0(niai oooii( ) 3 ( ) 7 ( ) 4 ( ) 5 ( )x tx tx tx tx toooii( ) 3( ) 7( )4( ) 5 ( )tx tx tx tx tx t2ooooii( ) 3( ) 7 ( ) 4( ) 5 ( )x tx tx tt x ttxx22014.9.24周三到此！周三到此！q 频率保持特性：若系统输入为

2、简谐信号，频率保持特性：若系统输入为简谐信号， 则其稳态输则其稳态输 出也为同频简谐信号。即：出也为同频简谐信号。即： 若若tjeXtx0)()(00)( tjeAXty，则，则设设 为已知频率，则根据线性系统的比例特性和微分特性，为已知频率，则根据线性系统的比例特性和微分特性，有有 )()(22tytx 2222)()(dttyddttxd由线性系统的叠加原理由线性系统的叠加原理 )()()()(222222tydttydtxdttxd 设输入信号设输入信号 为单一频率为单一频率 的简谐信号，即的简谐信号，即)(tx tjeXtxo )(则有则有 )()()(2222txtjeXjdttxd

3、o 0)()(222 txdttxd 相应的输出也应为相应的输出也应为 0)()(222 tydttyd 即即于是输出于是输出y(t)的唯一的可能解只能是的唯一的可能解只能是)()(otjoeyty ( )(1)o1o1o0o( )( )( )( )nnnna xtaxta x ta x t()(1)i1i1i0i( )( )( )( )mmmmb xtbxtb x tb x t21FbvFv2v1b21ddvFmtFv2v1m21dktvF v2v1Fk一）机械系统一）机械系统211di tCv21ddiLvtv2v1iCv2v1iL21vRiv2v1iRmfxkckxfmcxfkxcxmx

4、mx cx kxfd1ddiu LiRi tCtddqit.1Lq Rqq uCuiLRrTmfxJk1k2B1B21()Tk11()rkBfJ22.fmx B x k xxr122222.()()JmrxBBrx k r x rT0i1i2u1u2R2R1C2C11112111()di RiituC222122111d()di Ri tiitCC2221dituC2221122112212212dd()dduuRCRCRCRCRCuuttaadaddiLi ReutddekLddJMMtm aMk imamdmdmd1,TLRJTTCCRk kkJ令2ammdmam2LaLddddddT T

5、TCC TCttuMtMLRiauai2=constML励磁电流负载力矩ML电动机ua2La mmd am amL2ddddddMTTTCu CTCMttt mx cx kxfuiLRmfxkc.1Lq Rqq uC21Fbv21ddvFmt21dktvF 211dvtCi21ddvLit21viR)()()(.)()()()(.)()(01)1(1)(01)1(1)(mntxbtxbtxbtxbtxatxatxatxaiimimmimoononnon )().()().(01110111sXbsbsbsbsXasasasaimmmmOnnnn )(.)()(01110111mnasasasa

6、bsbsbsbsXsXnnnnmmmmio )(.)()()(01110111mnasasasabsbsbsbsXsXsGnnnnmmmmio 11ooi( )( ) ( )( )x tLXsLG s X s12,.,mz zz12,.,np pp120120()().()()().()(0)mnzzzbKppGpaii( ),( )/x tkX sk soo0lim( )lim( )tsx tssXi00lim( )( )lim( )(0)/ssG s X sGssss kGk1212()().()( )()().()nmK szszszG ssppssp1u2u1112111()di Ri

7、ituC222122111d()di Ri tiitCC2221dituC121 111IIR IUC s2122221IIIR IC sC si1i2u1u2R2R1C2C1222IUC si1i2u1u2R2R1C2C12112211221221()1RC R C sRCR CRCsUU211221122121( )()1GsR C R C sR CR CR Cs121 111IIR IUC s2122221IIIR IC sC s222IUC su (t)iu (t)oR1R2oi( )( )x tKx t( )G sKKo( )Xsi( )X s1. 1. 比例环节比例环节mmLLN2

8、N1输出正比于输入输出正比于输入ooid( )(d( )Tx tKxxttt1( )1G sRCs( )1KG sTsioo()k xxcx oi11( )11XkG scXcskTsskooicxkxkxio()xtT xt( )G sTso( )Xsi( )X sTso1iuRCu R1R2uoiii1Co1i( )( )( )UsG sU sRCs oi10dduuiCtRRqp1p2Akxixo21o()A ppkx21io()ppqA xxRioo2kxxxA Rooi2( )( )( )kXssXssX sA R( )G sTsoi1( )( ) dx tx ttT1( )G sT

9、so( )Xsi( )X s1Tso2111( )XsTs sTs1oo1( )( )x tLXstTxi(t)=1xo(t)0Ttx(t)12( )( )( )Q tQ tQ t控制阀Q (t)1负载阀2Q (t)h(t) )()(tAhdttQAssQsHsG1)()()( oid( )( )dutu tCRt oi( )11( )( )UsG sUsRCsTs u (t)iu (t)oRCTRC 222( )2nnnG sss(0)221( )21G sT sTs或o( )Xsi( )X s2222nnnssmfxkcmx cx kxf21( )G smscsk222( )2nnnG s

10、ssn,2kcmmkMJckJckM21( )( )sG sM sJscsk 21( )1G sLLCssRLRabcdou (t)u (t)iRi (t)i (t)Ci (t)Leso( )Xsi( )X soi( )()x tx t( )esG sx(t)t0 xi(t)xo(t)x(t)t0 xi(t)xo(t)x(t)t0 xi(t)xo(t)ALvB1h+h2h+h21()( )eshh tG s mycyApqAyqc1()pK xqK2qc,1(),()mscs YAPQAsYPK XQK油池高压油油池阀芯负载油缸qqAxymcp2p1aadadiLi ReudtddekLdJM

11、Mdtm aMk iadamaLdd(),LsR IEUMk IJsMMEk ,LRiauai2=constML励磁电流负载力矩ML电动机uao( )Xs1( )G s2( )G si( )X si( )X s1( )G s2( )G so( )Xsi( )X so( )Xs1( )G s2( )G so1( )Xso2( )Xs1( )G s2( )G si( )X so( )Xso( )( )/( )G sXsE so( )( )/( )H sB sXsk( )( )( )( )/( )G sG s H sB sE sXi(s)Xo(s)G(s)H(s)E(s)B(s)iio( )( )(

12、 )( )( )( )E sX sB sX sXs H soio( )( ) ( )( )( )( )( )XsG s E sG sX sXs H sioo( )( )( )( )( )( )G s X sG s XsXs Hs oBi( )( )( )( )1( )( )XsG sGsX sG s H sXi(s)Xo(s)G(s)E(s)1+G(s)G(s)Xo(s)Xi(s)分支点X1X2X3 (=X2)G(s)X1G(s)X2X3 (=X2)G(s)X1X2X3 (=X1)G(s)X1X2X3 (=X1)G(s)G(s)1相加点（X1X2X3 G(s)（ ）X1X3X2G(s)（X1X

13、3 X2G(s)G(s)（ ）X1X3X2G(s)G(s)11( )X s2( )Xs3( )Xs4( )Xs1( )X s2( )Xs3( )Xs4( )Xs( )X s( )X s( )X s( )X s( )X s( )X s( )X s( )X s( )R s1( )G s2( )G s3( )G s2( )Hs1( )H s3( )Hs( )C s简化步骤：简化步骤：消除交叉回路，对嵌套回路，从里到外逐步化简消除交叉回路，对嵌套回路，从里到外逐步化简( )R s1( )H s1( )G s2( )G s3( )G s3( )Hs2( )Hs( )C s11()Gs31()Gs( )C

14、 s111( )1( )( )G sG s Hs332( )1( )( )GsGs Hs213( )( )( )HsG s Gs2( )Gs( )R s1231122331133( )( ) ( )( )1( )( )( )( )( )( )( )( ) ( )( )G s G s G sGsG s H sG s H sG s H sG s H s G s H s( )R s1( )H s1( )G s2( )G s3( )G s3( )Hs2( )Hs( )C s11()Gs31()GsiX( )E s( )B s1G2G1H3G21HGoXiX( )E s( )B s1G2G3G1H2Ho

15、X iX( )B s( )E soX1231212321GG GGG HG G HiX( )E s( )B s1G2G1H3G21HGoXiXoX1231212321231GG GGG HG G HGG GiX( )B s( )E soX1231212321GG GGG HG G H123GG G123GGG、相加点处“ ”121GGH、232GGH、相加点处“ ”相加点处“+”iX( )E s( )B s1G2G3G1H2HoX123GG G123GGG、相加点处“ ”121GGH、232GGH、相加点处“ ”相加点处“+”iX( )E s( )B s1G2G3G1H2HoXB( )1Gs

16、前向通道的传递函数之积每一反馈回路开环传递函数iX1G2G1H3GoX2H5G4G5GoXiX1G2G1H23H G341 G G12534B121341252321( )1G G GG GGsG G HG GG G GG G H（）1+（）i( )Xs( )B s( )E s( )H s( )N so( )Xs1( )G s2( )Gs八、考虑扰动的反馈控制系统的传递函数八、考虑扰动的反馈控制系统的传递函数i( )Xs( )B s( )E s1( )G s( )H s2( )Gso( )Xs( )B s( )E s( )H s( )N so( )Xs1( )Gs2( )Gs112xB121G

17、GGGG H2NB121GGGG H122oi121211GGGXXNGG HGG H122oi121211GGGXXNGG HGG Hi1XH11NG HoX i1XHNoX 1, 1121且且若若HGHGG 121 HGG若若iRLCucud1ddiLRii tutC1ddcuxiCt 2cxu1121RuxxxLLL 211xxC112211100RxxLLuLxxC九、九、112LxRxxu1121RuxxxLLL 211xxC112211100RxxLLuLxxC2yx120 1xyxuXAXBTYC X状态向量状态向量12xxXuXAXBTuYC X + D)t ( idt)t (

18、duc)t (u)t (udt)t (diL)t (Ricc 121x) t (u) t ( y) t (ux) t (uxccc 则状态空间表达式为则状态空间表达式为2121210110110 xxyuLCxxLRLCxxx 2121211001011xxy)t(uLxxCLLRxxx1( )( )()( )TssssYGCIAB+ DUyu Tnnxxxxx121 nnxcxcxcy 2211ubxaxaxaxubxaxaxaxubxaxaxaxnnnnnnnnnnn 2211222221212112121111CxyBuAxx nnnnnnaaaaaaaaaA212221211211 nbbbB21 ncccC21 myru2y1y2u1u Tnnxxxxx121 Tmmyyyyy121 Trruuuuu121 DuCxyBuAxx nnnnnnaaaaaaaaaA212221211211 nrnnrrbbbbbbbbbB212221211211 mnmmnncccccccccC212221211211 mrmmrrdddddddddD212221211211DuCxyBuAxx CDx xuy结结构构图