第二章 線性系統(tǒng)的數(shù)學(xué)描述(2)

1、自動控制原理杭州電子科技大學(xué)杭州電子科技大學(xué)“自動控制原理自動控制原理”精品課程課題組精品課程課題組2008.102006年度浙江省精品課程( )G s( )R s( )C s元件的結(jié)構(gòu)圖( )G s( )R s( )C s結(jié)構(gòu)圖的相加點(a)和分支點(b)(a)( ),( )u t U s ( ),( )r tR s( )( )u tr t( )( )U sR s+(b)( ),( )u t U s( ),( )u t U s小結(jié)小結(jié)：任何系統(tǒng)都可以由信號線、函數(shù)方塊、信號：任何系統(tǒng)都可以由信號線、函數(shù)方塊、信號引出點及求和點組成的方塊圖來表示。引出點及求和點組成的方塊圖來表示。max()s

2、sesrcsuKKEKaasuK u2212212211aaa aabmbbmm ammmdiuR iLEdtdEKdtMC iddJfMdtdtJJJifffi211cmiziz電位器電橋：電位器電橋：放大器：放大器：減速器減速器-齒輪系統(tǒng)齒輪系統(tǒng)(1)(1)列寫各元件列寫各元件的微分方程的微分方程(2)象方程象方程( )( )( )ercsss( )( )sseUsKs( )( )aasUsK Us( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)

3、(sr )(sc )(se ( )( )( )ercsss( )( )sseUsKs( )( )aasUsK Us)(sr )(sc )(se ( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)(sr )(sc )(se sK)(sUs( )( )( )ercsss( )( )sseUsKs( )( )aasUsK Us)(se sK)(sUs( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )

4、( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ssaK)(sUs)(sUa)(sr )(sc )(se sK)(sUsaK)(sUa( )( )( )ercsss( )( )sseUsKs( )( )aasUsK Us( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmss

5、i( )( )bbmE sK ss)(sIamC)(sMm( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)(sMm)(sm sfJs 21( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)(sm sKb)(sEb( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC

6、Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)(sm i1)(sc ( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss閉環(huán)系統(tǒng)結(jié)構(gòu)圖（無干擾作用）( )G s( )H s( )R s( )E s( )C s( )B s+-( )( ) ( );C sG s E s( )( )( );E sR sB s( )( ) ( )BsH s C s( )( )( )( )B sG s H sE s( )( )( )

7、C sG sE s( )G s( )H s( )R s( )E s( )C s( )B s+-( )( ) ( )C sG s E s( )( )( )( )( ) ( )E sR sB sR sH s C s( )( )( )1( )( )C sG sR sG s H s( )G s( )H s( )R s( )E s( )C s( )B s+-( )( )( )1( )( )G sC sR sG s H s擾動作用下的閉環(huán)系統(tǒng)結(jié)構(gòu)圖1( )G s( )H s( )R s( )E s( )C s( )B s+-2( )G s擾動( )N s+212( )( )( )1( )( ) ( )NG

8、 sCsN sG s G s H s1212( )( )( )( )1( )( )( )RG s G sCsR sG s G s H s2112( )( )( )( )( ) ( )( )1( )( )( )RNG sC sC sCsG s R sN sG S G s H s1( )G s( )H s( )R s( )E s( )C s( )B s+-2( )G s擾動( )N s+( )iG s1,2,in12( )( )( )( )nG sG s G sG s123( )( )( )G sG sG s0( )X s4( )X s(b)1( )G s2( )G s3( )G s0( )X s

9、1( )X s2( )X s3( )X s(a)4( )X s( )1( ) ( )G sG s H s( )R s( )C s(b)( )G s( )H s( )R s( )E s( )C s( )B s+ (a)( )( )( )( )1( )( )C sG sG sR sG s H s相加點前移(a) +( )G s( )R s( )Q s( )C s +( )G s( )R s( )C s( )Q s1( )G s(b)相加點后移 +( )G s( )R s( )C s( )Q s( )G s(b)(a) +( )G s( )R s( )Q s( )C s分支點前移(b)( )G s(

10、 )R s( )C s( )G s( )C s(a)( )G s( )R s( )C s( )C s分支點后移1( )G s(b)( )G s( )R s( )C s( )R s(a)( )G s( )R s( )C s( )R s相鄰相加點的移動ADCB +(a)DC +A +B(b)相鄰分支點的移動AAAAA(a)AAAAA(b)G1G2G3G4H3H2H1abG1G2G3G4H3H2H1G41請你寫出結(jié)果請你寫出結(jié)果,行嗎？行嗎？錯！錯！G2H1G1G3G1G2G3H1G2無用功無用功向同類移動向同類移動G1G1G4H3G2G3H1H1H3G1G4G2G3H3H1引言信號流圖12345x

11、xxxx1245xxxx125xxx232;xxx2432;xxxx343;xxx2532xxxx24532;xxxxx3453;xxxx44xx232xxx和44xx2532xxxx 和44xx1kkkPP(1)(2)(3)()1( 1)mmLLLL (1)L(2)L(3)L()mL某系統(tǒng)的結(jié)構(gòu)圖+1G1H3G2G2H( )R s( )C s1123PGG G1123LGG G 2121LGG H3232LGGH(1)12312123212311 ()1LLLLGG HG G HGG G 11 1231111122123121232( )( )1 ()1GG GPPC sPR sLLLGG

12、GGG HG G HR(s)C(s)L1= G1 H1L2= G3 H3L3= G1G2G3H3H1L4= G4G3L5 = G1G2G3L1L2= (G1H1) (G3H3) = G1G3H1H3L1L4=(G1H1)(G4G3)=G1G3G4H1 G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s)

13、 G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s)H3(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G1(s) G2(s) G3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s)G4(s)G3(s) H1(s)H3(s) G1(s) G2(

14、s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s)P2= G4G3P1=G1G2G31=12=1+G1H1C(s)R(s)=?請寫出結(jié)果G1(s)G3(s)H1(s)G2(s)H3(s)H2(s)R(s)C(s)N(s)E(S)G1(s)G3(s)H1(s)G2(s)H3(s)H2(s)R(s)C(s)N(s)E(S)P1=11=1+G2H2P11= ?E(s)=1+ G2H2+ G1G2H3-G1H1G2 H2- G1H1(G2H3)R(s) N(s)(1+G2H2) (- G3G2H3)+R(s)E(S)G1(s)G3(s)H1(s)G2(s)H3(s)H2(s)C(s)N(s)R(s)E(S)G3(s)G2(s)H3(s)E(S)R(s)G1(s)H1(s)H2(s)C(s)P2= - G3G2H32= 1P22=?P1= G2H31= 1N(s)G1(s)H1