第二章 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 ttxx2( )(1)o1o1o0o( )( )( )( )nnnna xta

2、xta x ta x t()(1)i1i1i0i( )( )( )( )mmmmb xtbxtb x tb x t21FbvFv2v1b21ddvFmtFv2v1m21dktvF v2v1Fk一）机械系统一）机械系统211di tCv21ddiLvtv2v1iCv2v1iL21vRiv2v1iRmfxkckxfmcxfkxcxmxmx cx kxfd1ddiu LiRi tCtddqit.1Lq Rqq uCuiLRrTmfxJk1k2B1B21()Tk11()rkBfJ22.fmx B x k xxr122222.()()JmrxBBrx k r x rT0i1i2u1u2R2R1C2C11

3、112111()di RiituC222122111d()di Ri tiitCC2221dituC2221122112212212dd()dduuRCRCRCRCRCuuttaadaddiLi ReutddekLddJMMtm aMk imamdmdmd1,TLRJTTCCRk kkJ令2ammdmam2LaLddddddT TTCC TCttuMtMLRiauai2=constML励磁电流负载力矩ML电动机uaLRiauai2=constML励磁电流负载力矩damLC uC Ma0L0uM(,)da0mL0C uC Maa0auuuLL0LMMMammda0amaL0LmL0L()() (

4、)()()()T TTC uuC T MMCMMammdam aLmL()()()TTTCuC TMCM2LammdamamL2ddddddMT TTC uC TC Mttt油池高压油油池阀芯负载油缸qqAxymcp2p112pppmycyApqAyd( , )c/qf pxxp000(,)qq xp0,00,000( ,)(,)x px pqqxqqx pxpxpp油池高压油油池阀芯负载油缸qqAxymcp2p1mycyApqAyd( , )c/qf pxxp000(,)qq xp0 ,00 ,000(,)(,)xpxpqqxqqx pxpxpp qqccc1()KKKKpxxqyKAmyc

5、yAp2cqc (/) (/)mycAKyAKKx整理得整理得mx cx kxfuiLRmfxkc.1Lq Rqq uC21Fbv21ddvFmt21dktvF 211dvtCi21ddvLit21viR)()()(.)()()()(.)()(01)1(1)(01)1(1)(mntxbtxbtxbtxbtxatxatxatxaiimimmimoononnon )().()().(01110111sXbsbsbsbsXasasasaimmmmOnnnn )(.)()(01110111mnasasasabsbsbsbsXsXnnnnmmmmio )(.)()()(01110111mnasasasa

6、bsbsbsbsXsXsGnnnnmmmmio 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 RiituC222122111d()di Ri tiitCC2221dituC121 111IIR

7、IUC s2122221IIIR IC sC si1i2u1u2R2R1C2C1222IUC si1i2u1u2R2R1C2C12112211221221()1RC R C sRCR CRCsUU211221122121( )()1G sR 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mmLLN2N1输出正比于输入输出正比于输入ooid( )(d( )Tx tKxxttt1( )1G sR

8、Cs( )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 sTso( )Xsi( )X s1Tso2111( )XsTs sTs1oo1( )( )x tL

9、XstTxi(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 sssn,2kcmmkMJckJckM21( )( )sG sM sJscsk 21( )1G

10、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 ReudtddekLdJMMdtm aMk iadamaLdd(),LsR IEUMk IJsMMEk ,LRiauai

11、2=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( )( )( )( )( )( )E sX sB sX sXs H soio( )( ) ( )( )(

12、)( )( )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)（X1X3 X2G(s)G(s)（ ）X1X3X2G(s)G(s)11( )X s2( )Xs3( )

13、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 s111( )1( )( )G sG s Hs332( )1( )( )GsGs Hs213

14、( )( )( )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 s1G2G3G1H2HoX iX21HG( )E s( )B s3GoX121211G GG G HiX( )B s(

15、 )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 前向通道的传递函数之积

16、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( )Gs112xB121GGGGG H2NB121GGGG H122oi121211GGGXXNGG HGG H122oi121211GGGXXN