反饋控制系統(tǒng)的傳遞函數(shù)省公開課金獎(jiǎng)全國賽課一等獎(jiǎng)微課獲獎(jiǎng)?wù)n件

2.6反饋控制系統(tǒng)傳遞函數(shù)1/211閉環(huán)控制系統(tǒng)經(jīng)典結(jié)構(gòu)其中:

C(s)----系統(tǒng)輸出信號(hào);

R(s)----給定輸入信號(hào);

G1(s)、G2(s)----前向通路傳遞函數(shù),普通由控制器、執(zhí)行元件和受控對(duì)象等組成;

N(s)----系統(tǒng)擾動(dòng)信號(hào);B(s)----反饋信號(hào);

H(s)----反饋通路傳遞函數(shù)，普通表示反饋控制作用以及傳感器特征。閉環(huán)控制系統(tǒng)經(jīng)典結(jié)構(gòu)以下列圖所表示)(sB)(sE)(sN)(sC)(sH)(1sG)(2sG)(sR-輸入信號(hào)誤差信號(hào)干擾信號(hào)輸出信號(hào)反饋信號(hào)2/21結(jié)論：開環(huán)傳遞函數(shù)等于前向通路傳遞函數(shù)G(s)和反饋通路傳遞函數(shù)H(s)乘積。2閉環(huán)控制系統(tǒng)開環(huán)傳遞函數(shù)G(s)H(s)R(s)B(s)=0)(=sN定義：反饋信號(hào)B(s)與輸入信號(hào)R(s)之比()3/21

定義：系統(tǒng)主反饋回路接通以后，輸出信號(hào)C(s)與輸入信號(hào)R(s)之間傳遞函數(shù)，通慣用

(s)表示（）3閉環(huán)控制系統(tǒng)閉環(huán)傳遞函數(shù)0)(=sN4/21當(dāng)擾動(dòng)信號(hào)N（s）=0當(dāng)時(shí)有表明此時(shí)系統(tǒng)閉環(huán)傳遞函數(shù)只與H（S）相關(guān),與被包圍步驟無關(guān)。(s)G

(s),G215/214擾動(dòng)信號(hào)作用下閉環(huán)傳遞函數(shù)把系統(tǒng)輸入量以外作用信號(hào)均稱之為擾動(dòng)信號(hào)。定義：系統(tǒng)主反饋回路接通以后，輸出信號(hào)C(s)與擾動(dòng)信號(hào)N(s)之間傳遞函數(shù)，通慣用

n(s)表示,此時(shí)。0)(=sR6/21設(shè)輸入量R（s）=0_擾動(dòng)C(s)N(s)G2(s)G1(s)H(s)此時(shí)擾動(dòng)影響可被抑制當(dāng)時(shí)有7/215系統(tǒng)總輸出當(dāng)R(s),N(s)同時(shí)作用時(shí)：N(s)](s)R(s)[G(s)H(s)(s)GG1(s)G1212++=N(s)(s)H(s)(s)GG1(s)GR(s)(s)H(s)(s)GG1(s)(s)GG2122121+++=(s)C(s)CC(s)NR+=8/21E(s)＝R(s)－B(s)（1）在控制量R(s)作用下系統(tǒng)誤差傳遞函數(shù)_E(s)R(s)H(s)G2(s)G1(s)6誤差傳遞函數(shù)定義：閉環(huán)控制系統(tǒng)誤差E(s)為給定輸入信號(hào)R(s)與反饋信號(hào)B(s)之差。9/21稱為誤差傳遞函數(shù)

假設(shè)N(s)＝0，則?er(s)=10/21（2）在擾動(dòng)量N(s)作用下系統(tǒng)誤差傳遞函數(shù)+E(s)N(s)G2(s)－H(s)G1(s)假設(shè)R(s)＝0，則)()()(1)()()()(212sHsGsGsHsGsNsE+-==?en(s)11/21(3)在控制量R(s)和擾動(dòng)量N(s)同時(shí)作用時(shí)，系統(tǒng)總誤差)()()()(1)()()()()()(1121221sNsHsGsGsHsGsRsHsGsG+-+E(s)=E(s)＝Φer(s)R(s)－Φen(s)B(s)12/217多輸入－多輸出系統(tǒng)傳遞矩陣G1--G2G3G4C1C2R1R2對(duì)于多輸入－多輸出系統(tǒng)，可采取疊加定理來求系統(tǒng)傳遞矩陣。13/21當(dāng)r1(t)單獨(dú)作用時(shí)，系統(tǒng)簡(jiǎn)化為以下：+C1R1G2G4G3G1-C2R1G3-G1G2G4則有傳遞函數(shù)：(s)G11R1(s)(s)C(s)111-==C(s)G1(s)G2(s)G3(s)G41R1(s)(s)C(s)(s)G2221-==C(s)G1(s)G2(s)G3(s)G4(s)G4(s)G1-14/21當(dāng)r1(t)單獨(dú)作用時(shí)，系統(tǒng)簡(jiǎn)化為以下：+C2R2G3G1G2G4-C1R2G2-G4G3G1則有傳遞函數(shù)：(s)G11R2(s)(s)C(s)211-==C(s)G1(s)G2(s)G3(s)G4當(dāng)r2(t)單獨(dú)作用時(shí)，系統(tǒng)簡(jiǎn)化為以下：1R2(s)(s)C(s)(s)G3112-==C(s)G1(s)G2(s)G3(s)G4(s)G4(s)G1-15/21輸入量和輸出量之間關(guān)系為：C1(s)=G11(s)R1(s)+G12(s)R2(s)C2(s)=G21(s)R1(s)+G22(s)R2(s)輸入量和輸出量之間矩陣形式為：úúú?ùêêê?éúúú?ùêêê?é=úúú?ùêêê?éC1(s)C2(s)C11(s)C12(s)C21(s)C22(s)R1(s)R2(s)傳遞矩陣16/21對(duì)于m個(gè)輸入量和n個(gè)輸出量多輸入－多輸出系統(tǒng)傳遞矩陣，第i個(gè)輸出量Ci(s)與m個(gè)輸入量關(guān)系為：Ci(s)=Gi1(s)R1(s)+Gi2(s)R2(s)+……+Gim(s)Rm(s)描述n個(gè)輸出量和m輸入量之間矩陣形式為：úúúúúúúú?ùêêêêêêêê?éúúúúúúúú?ùêêêêêêêê?é=úúúúúúúú?ùêêêêêêêê?éC1(s)MMC2(s)C3(s)Cn(s)G11(s)G12(s)……G1m(s)G21(s)G22(s)……G2m(s)G31(s)G32(s)……G3m(s)Gn1(s)Gn2(s)……Gnm(s)MMMMMMR1(s)R2(s)R3(s)Rm(s)MM簡(jiǎn)記為C(s)=G

(s)R

(s)C(s)R(s)G(s)17/21例求下列圖所表示系統(tǒng)傳遞矩陣：)(sB)(sN)(sC)(sH)(1sG)(2sG)(sR-反饋信號(hào)+系統(tǒng)有2個(gè)輸入量，和它們相對(duì)應(yīng)輸出為：R(s)(s)H(s)(s)GG1(s)(s)GG(s)C2121R+=N(s)(s)H(s)(s)GG1(s)G(s)C212N+=18/21系統(tǒng)總輸出為：(s)C(s)CC(s)NR+=N(s)(s)H(s)(s)GG1(s)GR(s)(s)H(s)(s)GG1(s)(s)GG21221