第二章 系統(tǒng)數(shù)學模型

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）機械系統(tǒng)一）機械系統(tǒng)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勵磁電流負載力矩ML電動機uaLRiauai2=constML勵磁電流負載力矩damLC uC Ma0L0uM(,)da0mL0C uC Maa0auuuLL0LMMMammda0amaL0LmL0L()() (

4、)()()()T TTC uuC T MMCMMammdam aLmL()()()TTTCuC TMCM2LammdamamL2ddddddMT TTC uC TC Mttt油池高壓油油池閥芯負載油缸qqAxymcp2p112pppmycyApqAyd( , )c/qf pxxp000(,)qq xp0,00,000( ,)(,)x px pqqxqqx pxpxpp油池高壓油油池閥芯負載油缸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. 比例環(huán)節(jié)比例環(huán)節(jié)mmLLN2N1輸出正比于輸入輸出正比于輸入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控制閥Q (t)1負載閥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油池高壓油油池閥芯負載油缸qqAxymcp2p1aadadiLi ReudtddekLdJMMdtm aMk iadamaLdd(),LsR IEUMk IJsMMEk ,LRiauai

11、2=constML勵磁電流負載力矩ML電動機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)分支點X1X2X3 (=X2)G(s)X1G(s)X2X3 (=X2)G(s)X1X2X3 (=X1)G(s)X1X2X3 (=X1)G(s)G(s)1相加點（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簡化步驟：簡化步驟：消除交叉回路，對嵌套回路，從里到外逐步化簡消除交叉回路，對嵌套回路，從里到外逐步化簡( )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、相加點處“ ”121GGH、232GGH、相加點處“ ”相加點處“+”iX( )E s( )B s1G2G3G1H2HoX123GG G123GGG、相加點處“ ”121GGH、232GGH、相加點處“ ”相加點處“+”iX( )E s( )B s1G2G3G1H2HoXB( )1Gs 前向通道的傳遞函數(shù)之積

16、每一反饋回路開環(huán)傳遞函數(shù)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、考慮擾動的反饋控制系統(tǒng)的傳遞函數(shù)八、考慮擾動的反饋控制系統(tǒng)的傳遞函數(shù)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