大林算法控制器設(shè)計(jì)

1、2. Gs=e-1ss(s+1)采樣周期T0.5s，試用達(dá)林算法設(shè)計(jì)數(shù)字控制器D(z)。寫(xiě)出設(shè)計(jì)過(guò)程，對(duì)比輸出與給定的效果波形，并顯示控制器輸出波形。 解：廣義對(duì)象的脈沖傳遞函數(shù)：Gz=Z1-e-TssGs=Z1-e-Tsse-1sss+1 =Ze-s-e-s1+T1s2s+1 =z-21-z-1Z1s2-1s+1s+1 =z-21-z-10.5z-11-z-12-11-z-1+11-e-0.5z-1 =z-30.1065(1+0.8474z-1)1-z-1(1-0.6065z-1)根據(jù)達(dá)林算法，構(gòu)成的慣性環(huán)節(jié)與滯后時(shí)間=1s的純滯后環(huán)節(jié)串聯(lián)而成的理想閉環(huán)系統(tǒng)。設(shè)T=0.5ss=1Ts+1e-

2、s=e-1s0.5s+1它所對(duì)應(yīng)的理想閉環(huán)脈沖傳遞函數(shù)：z=Z1-e-Tsss=Z1-e-Tsse-NTsTs+1 =z-N-11-e-TT1-e-TTz-1因?yàn)镹=T=2， T=0.5s， T=0.5s所以：z=0.632z-31-0.368z-1所求數(shù)字控制器為：Dz= zGz 1- z =0.632z-31-0.368z-1z-30.10651+0.8474z-11-z-11-0.6065z-1(1-0.632z-31-0.368z-1) =5.9341-z-1(1-0.6065z-1)1+0.8474z-1(1-0.368z-1-0.632z-3)在Gz中可以看到有一個(gè)零點(diǎn)z=-0.8

3、474靠近z=-1，所以如果不對(duì)達(dá)林算法進(jìn)行修正必會(huì)產(chǎn)生振鈴現(xiàn)象，令因子(1+0.8474z-1)中的z=1即Gz=0.1967z-31-z-1(1-0.6065z-1)修正后的數(shù)字控制器為：Dz=3.2121-z-1(1-0.6065z-1)1-0.368z-1-0.632z-3仿真圖如下：已知某過(guò)程對(duì)象的傳遞函數(shù)為：Gs=3e-0.5s0.6s+1期望的閉環(huán)系統(tǒng)時(shí)間常數(shù) T=0.25s ,采樣周期 T=0.5s 。試用大林算法設(shè)計(jì)數(shù)字控制器；解：被控對(duì)象為一階慣性環(huán)節(jié)，則廣義對(duì)象脈沖傳遞函數(shù)，閉環(huán)系統(tǒng)脈沖函數(shù)和數(shù)字調(diào)節(jié)器脈沖傳遞函數(shù)分別如下： G(z)=Z1-e-TssKe-sT1s+1=Kz-N-11-e-TT11-e-TT1z-1z=Z1-e-Tsse-sTs+1=z-N-11-e-TT1-e-TTz-1Dz= zGz 1- z =1-e-TT1-e-TT1z-1K1-e-TT11-e-TTz-1-1-e-TTz-N-1根據(jù)已知可得:K=3, T=0.25s, T=0.5s, N=T=0.50.5=1,T1=0.6所以：Gz=1.695z-21-0.435z-1z=0.865z