過程控制課程講義多變量控制系統(tǒng)

1、例一：爐溫控制系統(tǒng)例一：爐溫控制系統(tǒng)控制器控制器功放功放例二：曲軸處理例二：曲軸處理例三：發(fā)電廠鍋爐控制例三：發(fā)電廠鍋爐控制Q水水 導(dǎo)致導(dǎo)致 H 同時(shí)同時(shí)P Q燃燃 導(dǎo)致導(dǎo)致 P 同時(shí)同時(shí)H 1s1s4 1s3 1s2 1s4 )410(4)310(32)210()110(0212211222111 UUYUUYYRUYRUs圖圖如如上上。則則：可可的的靜靜態(tài)態(tài)耦耦合合系系統(tǒng)統(tǒng)結(jié)結(jié)構(gòu)構(gòu)，令令于于系系統(tǒng)統(tǒng)中中無無積積分分環(huán)環(huán)節(jié)節(jié)，在在考考慮慮穩(wěn)穩(wěn)態(tài)態(tài)情情況況時(shí)時(shí)，由由9/2/,6592)332(3442)610()510(6/1/,6198)44(23323)510()610()610(442)

2、410()210()110()510(3323)310()210()110(121222122212122121121112121112122211RYRRYRRYYRRRRYRYRRYRRYYRRRRYYRRYYRRY有關(guān)但還與主要決定于可見，在穩(wěn)態(tài)下，得代入在將式有關(guān)但還與主要決定于可見，在穩(wěn)態(tài)下，得代入在將式中得帶入式和式將式中得帶入式和式將式xdzy.mdl改變改變r(jià)1,r2值值加加4種干擾種干擾212211R237228R23716YR23712R237232Y xdzy1.mdl改變改變r(jià)1,r2值值加加4種干擾種干擾1s1s4 1s3 1s2 1s4 1s1s4 1s3 1s2

3、1s4 1s1s4 1s3 1s2 1s4 21212121221112221122122182222217432RRYRRYUUYUUYYRUYRU可求得：1s1s4 1s3 1s2 1s4 1s3 1s1s4 解耦等效方框圖解耦等效方框圖14 sxdzy2.mdl改變改變r(jià)1,r2值值加加4種干擾種干擾 ij 1111K 。222212122121K;K;K K21 Kc2K12K111U 1Y 2Y 2UK22112112221122122112221121212112221112222112221111111222222111112lim1KKKKKKKKKKKKKKKKKKKKUYK

4、KKKKKUYcKcc同理：K21 Kc2K12K111U 1Y 2Y 2UK22211222112211222222211222112112212121211222112112121212211222112211111111KKKKKKKKKKKKKKKKKKKKKKKK212211212211YXVWZWYXVWZVUYXVWZXYXVWZZUZVXWUYUZUVYUXUWY即sqrpZXVWZYsYrUYqYpUsXVWZWrXVWZVqXVXZXpXVWZZ1,1,1,1,22211211212211顯然第二放大系數(shù)為：令。第一放大系數(shù)直接求得所以第二放大系數(shù)可由即：中各元素的倒數(shù)值，

5、中的元素是矩陣矩陣引入矩陣經(jīng)推導(dǎo)得：即ijijTTTZVXWsrqpsqrpIsrqpZVXWsqrp1)(111111sXVWZWrXVWZVqXVXZXpXVWZZ, nnanna2n2na1n1nnna2n2a2222a21212na1n1a1212a11111n21ijijaijaijijnnaa2na1nna2a22a21na1a12a11nn2n1nn22221n11211ijijijijij.U.U.UY.YY)(1.可可寫寫作作所所以以一一般般情情況況下下，矩矩陣陣，的的代代數(shù)數(shù)余余子子式式的的元元素素為為矩矩陣陣由由相相對(duì)對(duì)增增益益的的定定義義有有記。每一列元素之和也是，行元

6、素之和均為即相對(duì)增益矩陣中每一由矩陣知識(shí)：111, 111niijnjij211222112211222222211222112112212121211222112112121212211222112211111111KKKKKKKKKKKKKKKKKKKKKKKK111111112112221121122112211222112211221111新的無耦合系統(tǒng)。變量重新配對(duì)，可組成；，時(shí)，有當(dāng)；，時(shí)，即系統(tǒng)無耦合，當(dāng)100010211222112211211222112112222121211121YYUUYXYA)BA(A0B)BA/(ABXKYX1YB)BA(A)BA(A)BA/(AAX

7、K1B)BA(BYK1A)BA(AYK)BA/(AXBAYBAXY222222211211 靜態(tài)增益：靜態(tài)增益：，則，則和和液體液體，調(diào)節(jié)量為，調(diào)節(jié)量為和成分和成分解：被調(diào)量為總流量解：被調(diào)量為總流量3 . 07 . 0X7 . 03 . 0YBA, 3 . 0XXX1XX1XYBAX)Y1()YX(1YXYX111a111111則則如果如果 輸入量與其它通道輸出量之間的耦合輸出量與其它通道輸入量之間的耦合 nnnnnnPPPPPPPPP.222222111211Pn1Pn2),.2 , 1)(Y).(Y.).(Y).(Y, 1i11,11n2121222212121111niYVUVYVYV

8、UVYVYVUVYVYVUVnikkkikiijnnnnnnnnnnn 即即 nnVVV.00.0.00.02211 0.0.021221112nnnnVVVVVV)(Y, 1i nikkkikiijYVUV nikkkikiiiYVVU, 1iY nnnnnnVVVVVVVVV1.1.1212222111211),.,2 , 1,;(detdetdetdetidetdetdetdet)1(det11njiijPPVPPVVPPjTTTTTTPTadjTTPijijiiiijijijijij ：規(guī)范來表示，轉(zhuǎn)換如下規(guī)范來表示，轉(zhuǎn)換如下該對(duì)象一定可用該對(duì)象一定可用是非奇異矩陣，則是非奇異矩陣，則

9、規(guī)范對(duì)象，若規(guī)范對(duì)象，若同樣，對(duì)于一個(gè)同樣，對(duì)于一個(gè)列所得的矩陣。列所得的矩陣。行第行第中刪去第中刪去第是由矩陣是由矩陣式中，式中， ) s (G.) s (G) s (G.) s (G.) s (G) s (G) s (G.) s (G) s (G) s (Gpnn2pn1pnn2p22p21pn1p12p11pp對(duì)對(duì)象象：DKNKKKDKNDKKKKKKKKKKsGKsGKnnnnnnnnpijsijpijij122112122221112110.00.0.00.0,.)(lim)(由解耦條件：的穩(wěn)態(tài)增益，則為設(shè)620. 0620. 0380. 0620. 0100582. 2,11582

10、. 1582. 215 . 410017 . 2582. 2)(,15 . 4115 . 4117 . 2582. 117 . 2582. 21DKNDKsssDssssGp解：要求目標(biāo)矩陣為：例：11112211)()()()()()()()()()()()()()()()(),()()(sIssGsGsIssWsWssWIsGsGsWsWsWIssWRsYspcncnpnn式中：則數(shù)陣為設(shè)該系統(tǒng)的開環(huán)傳遞函此時(shí)數(shù)：設(shè)解耦后的閉環(huán)傳遞函11CNG1s21 1s1 21CNG12CNG22CNG s5100s1s51s500s1s1s1001s1)s (I ) s () s (W1解：解： 1

11、s1001s1) s (ssssssssssssWsGsGpcn51) 1)(12(012510011110121)()()(111CNG1s21 1s1 21CNG12CNG22CNGDGN,DNGP.P0.0.P00.0PDP.PP.P.PPP.PPPG1ppnn02211nn2n1nn22221n11211p 有有為為：要要求求解解耦耦后后的的目目標(biāo)標(biāo)矩矩陣陣設(shè)設(shè)對(duì)對(duì)象象 1s5 .16)1s15(603. 01s5 .16)1s20(715. 01s5 .16)1s15(294. 01s5 .16)1s15(7 . 0)1s5)(1s20(7 .27001s101)1s5)(1s20(7 .27)1s5)(1s15(4 .281