控制第2章系統(tǒng)的數學模型

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 ttxx22014.9.24周三到此！周三到此！q 頻率保持特性：若系統(tǒng)輸入為

2、簡諧信號，頻率保持特性：若系統(tǒng)輸入為簡諧信號， 則其穩(wěn)態(tài)輸則其穩(wěn)態(tài)輸 出也為同頻簡諧信號。即：出也為同頻簡諧信號。即： 若若tjeXtx0)()(00)( tjeAXty，則，則設設 為已知頻率，則根據線性系統(tǒng)的比例特性和微分特性，為已知頻率，則根據線性系統(tǒng)的比例特性和微分特性，有有 )()(22tytx 2222)()(dttyddttxd由線性系統(tǒng)的疊加原理由線性系統(tǒng)的疊加原理 )()()()(222222tydttydtxdttxd 設輸入信號設輸入信號 為單一頻率為單一頻率 的簡諧信號，即的簡諧信號，即)(tx tjeXtxo )(則有則有 )()()(2222txtjeXjdttxd

3、o 0)()(222 txdttxd 相應的輸出也應為相應的輸出也應為 0)()(222 tydttyd 即即于是輸出于是輸出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）機械系統(tǒng)一）機械系統(tǒng)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勵磁電流負載力矩ML電動機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. 比例環(huán)節(jié)比例環(huán)節(jié)mmLLN2

8、N1輸出正比于輸入輸出正比于輸入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 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油池高壓油油池閥芯負載油缸qqAxymcp2p1aadadiLi ReudtddekLdJM

11、Mdtm aMk iadamaLdd(),LsR IEUMk IJsMMEk ,LRiauai2=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( )( )(

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)（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

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

16、前向通道的傳遞函數之積每一反饋回路開環(huán)傳遞函數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)的傳遞函數八、考慮擾動的反饋控制系統(tǒng)的傳遞函數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狀態(tài)向量狀態(tài)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 則狀態(tài)空間表達式為則狀態(tài)空間表達式為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結結構構圖