线性时不变系统的复频域综合

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1、lcN)()(1sSslchcDD1)( sylcN)()(1sSslchcDD1)( sy( )N s1D ( ) s( )Ks( ) s)( su)( sy( ) s1KK( )( )( )GsN s DsKD ( )( )()( )hcLcsD S sDKs11( )( )( )( )( )( ),phclclckpiikD sD S sDsN sNssS skns11)(111ssssspkkKKlcNlchcDD1)( sylcNlchcDD1)( sy( )N s( )Ks( ) s)( su)( sy( ) s1D ( ) sH1HKHK( )( )( )GsN s Ds1HK1

2、1D( )H( )( )( )()( )hcLcsD sKsHD S sHDKs) s (D) s (N) s (G10) s (Dkciink,kkkp1iip21*n*2*1,) s ()s (*n1i*i1HKHK*HKG(s,K)N(s)D(s)detD(s)(s)1N(s)D (s)s (s )s (s )s (s )s (s)s (p)kk(n1-p)kk(n2kn1n*1 -p1211hcDH 1p1(s)(s)-10K(s)( )-10hclcD Ds1hclchcD) s (,D,D和) s (*)s (s )s (s )s (s )s (s)s (p)kk(n1-p)kk(

3、n2kn1n*1 -p1211hcDH 01-01-) s () s (s)p1构造构造) s (DD-(s)(s)Klc-1hchcDH 01-01-) s () s (s)p122211211kkp21kHKDDDDs1-01-0s1-) s () s () s (s(s)S(s)(s)Dp21) s () s (detD*HKp21lc1 -hcp21D,D,DDDK,K,KKiiiikpDkpKii1k1k1ii( )ss1KD,i1,p0ss110s1CFCF-1*fhcCFG(s)N(s)D(s)(detD) detD(s)(s)1G(s)N(s)D(s),不可简约*n*2*1,)

4、 s ()s (*n1i*ipjcjjj 1k =D( ),kns*CF( )Ds1112()()*12( )( )( )( )pnkknknkknpsss ss ss s1212*CF( )( )( )101D ( )1pkpkksssssss *CF( )Ds*( )jjcjCFkkDs*fhc( )CFnDsDI的列次系数阵1G(s)N(s)D (s)lcN)()(1sSslchcDD1)( sylcN)()(1sSslchcDD1)( sy( )N s1D ( ) sM( ) s( ) s)( su)( sy( ) s*CF( )( )( )M sDsD sCFCFK)()(1sSs)

5、( sy)()(1sSs( )( )M s X s)( sy1N(s)D ( ) sM( ) ( )s Y s)( su( ) s+( ) ( )M ssCFCF( )( )( ) ( ),( )( )( ) ( )F sT s M s X s H sT s M s Y s)()(1sSs)( sy)()(1sSs1( )( )Ts F s)( sy1N(s)D ( ) s1( )( )Ts H s)( su( ) s+( ) ( )M ssCFCFCF1( )( )( )( )LN s Dss N s-1L不可简约不可简约D)()(1sSs)( sy)()(1sSs1( )( )uTs Ns

6、)( sy1N(s)D ( ) s1( )( )yTs Ns)( su( ) s+( )( )( )( ),( )( )( )( )LyuLH sL s DsNsNsF sL s NsCFCF1( )( )( ) ( )N s Dss N s-1L不可简约不可简约Drjr1rq( )( )1,2,max( ),( )LLLLDsqqDsjqDsDs分母矩阵行次数，*12(1),psss(1)*(1)(1)1T(1)1101(1)(1)1(1)2(1)121( )()( )( )( )( )ppprprpppppssssssss ss ss ss11121( )1( )( )1( )pssssT

7、 sss11(1)( )( )(2)( )( ),( )yuTs NsMFDTs NsMFDs-1K为真为真当且仅当D(s)D为正则真1CFCF-1*fhcCFG(s)N(s)D(s)(detD) detD(s)(s) s (N) s (D) s (D) s (N) s (GL-1L1) s (DL) s (D) s (N) s (G1CFF)s (D)s (D)s (MCF11121( )1( )( )1( )pssssT sss) s (i) s (N) s (L(s)DH(s)yL)s (NL(s),y) s (L(s)N) s (F(s)NLu) s (T1) s (N) s (T)

8、s (N) s (Ty1u1和123222211210( )2221 421sssssGsssssss *12,342,1,42jj 1-1LLG(s)N(s)D(s)=D (s)N (s),不可简约jcjririLpqjrij 1i 1k =D( ),k =D ( )k =knss) s (DL (s)y (s)uC ()s()Gs v(s)*12,nm其中G( )( )( ),ssks k 循环为非零常数) s (gij) s (g1t2t1k2k)s (Gt kt ) s (GkG(s)221111)s (KGI)s (G) s (GK) s (GI (s)G) s (G()Gs (s)

9、u v(s)K)s(y C ()s()Gs v(s)1t)s(y 2t()Gs v(s)C (s)s(y 1t2t)s (Gt kt ) s (GkG(s)22111010( )( )nnnnD sD sDsDN sN sN sN(s)h-1cC(s)=D ( )( )cs Ns不可简约CF1010deg( )( )( )cmccmccmccmccD smD sD sD sDN sN sN sN(s)C1G( )( )( )1 1( )( ) ( )( ) ( )( )( )( )CFCFCFCFccCFcsDs NsDsD s D sN s N sq qNsN s N s阵阵*1110*(

10、)( ),0,1,n mn mCFn mn mhhDsksFsFsFs FFkhn mk 任意非零常数10101010*101 1( )1( )1 1( )1( )1 1( )nnnnmccmccmccmccn mCFn mD sD sDsDqN sN sN sND sD sD sDqN sN sN sNDsFsFsF多项式阵多项式阵多项式阵多项式阵多项式阵0n0n0nm0n0n0nDD00NN000DD00S0NN0000DD00NN*h*cC(s),s ( ),1,n( )( )( )( )( )( ),( )CFhccCFccmcGshmDs D sNs N sDsDsNsSFT综合补偿

11、器使闭环极点对方程求解对方程T求解cc0c0c1c1cmcm01n+mT = DNDNDNF=F FFC ()s()Gs v(s)1t)s(y mmin1,11-1LLG(s)N(s)D (s)=D (s)N (s)mmin , 1t11G(s)kG(s)t 1t ) s (G) s (D) s (Nt ) s (G1101nn01nnNsNsN) s (NDsDsDD(s)n0n0n0n0n0n0NN00DD0000NN000DD000NN00DDSllS1 l(s)C1mc0c0c1c1cmcmm01nm 1DNDNDNSF FFn mF*nmnm 1CFnmnm 110D(s)(s)FsFsFsFk(s)Cmc0c1mcmcc0c1mcmcNsNsN) s (NDsDsD(s)D) s (N) s (D) s (Cc1c) s (Ct) s (C1C ()s()Gs v(s)K+-()Gs y ()s()Gs()Gs