線性系統(tǒng)的頻域分析MATLAB實驗

1、武漢工程大學(xué)實驗報告專業(yè)班號_組別指導(dǎo)教師陳艷菲姓名同組者實驗名稱線性系統(tǒng)的頻域分析實驗日期第次實驗實驗?zāi)康膶嶒瀮?nèi)容實驗結(jié)果及分析四、實驗心得與體會一、實驗?zāi)康? 熟練掌握用MATLA語句繪制頻域曲線。2 掌握控制系統(tǒng)頻域范圍內(nèi)的分析校正方法。3 掌握用頻率特性法進行串聯(lián)校正設(shè)計的思路和步驟。二，實驗內(nèi)容。4i 某單位負(fù)反饋控制系統(tǒng)的開環(huán)傳遞函數(shù)G(s) &T吊 為，試設(shè)計一超前校正裝置,50Kv 20s使 校正后系統(tǒng)的靜態(tài)速度誤差系數(shù)，相位裕量，增益裕量20lgKg 10dB繪制伯德圖程序，以及計算穿越頻率，相位裕量ans =相位 Inf 9.0406頻率 Inf 3.1425 e=5; r

2、=50; r0=9; phic=(r-r0+e)*pi/180;gm1,pm1,wcg1,wcp1=marg in(num 0,de n0);gm1,pm1,wcg1,wcp1=margi n(num 0,de n0); alpha=(1+s in (phic)/(1-si n(phic)gm1,pm1,wcg1,wcp1=margi n(num 0,de n0); alpha =6.1261gm1,pm1,wcg1,wcp1=marg in(num 0,de n0 );gm1,pm1,wcg1,wcp1num0=20; de n0=2,1,0; w=0.1:1000;margi n(num

3、O,de nO) grid;原系統(tǒng)的伯德圖：80Bode DiagramGm = Inf dB (at Inf rad/sec), P m = 9.04 deg (at 3.14 rad/sec)6040o20JBOr6dhnaa Mmsuresanp53T80num/de n =1.2347 s + 10.20154 s + 1校正之后的系統(tǒng)開環(huán)傳遞函數(shù)為num/de n =6.1734 s + 50.20154 sA4 + 1.6046 sA3 + 3.4031 sA2 + 2 salpha =6.1261;il,ii=mi n(abs(mag1-1/sqrt(alpha);wc=w( i

4、i); T=1/(wc*sqrt(alpha);numc=alpha*T,1; de nc=T,1;nu m,de n=series( num O,de nO,nu mc,de nc);gm,pm,wcg,wcp=margi n(nu m,de n); prin tsys( nu mc,de nc)disp( D ?y?o6 ?叮 3?a? ?卩 Yo_e y?)aprintsys(num,den) mag2,phase2=bode( nu mc,de nc,w); mag,phase=bode( nu m,de n, w); subplot(2,1,1);semilogx(w,20*log1

5、0(mag),w,20*log10(mag1),-,w,20*log10(mag2),-.);grid; ylabel( -u ?(db); title( -Go,-Gc,GoGc );subplot(2,1,2);semilogx(w,phase,w,phase1,- ,w,phase2, -,w,(w-180-w),:);grid; ylabel(? a ?(0); xlabel( ?卩?e (rad/sec);title( D ?y? o-u ?卩?a,?=m2str(20*log10(gm1),db ，？ a ?a?=,num2str(pm1),0;D ?yoo o -u ?卩?a,?

6、=m2str(20*log10(gm),db , ? a ?a ?=,num2str(pm), 0);-Go,-Gc,GoGc矯正后系統(tǒng)的伯德圖矯正之前系統(tǒng)單位階躍響應(yīng)50246810比較矯正前后系統(tǒng)的響應(yīng)情況：可以看出超前矯正使系統(tǒng)的調(diào)節(jié)時間變短， 響應(yīng)更加迅速, 但是超調(diào)量偏大，對改善系統(tǒng)的動態(tài)性能起到了巨大的作用。k2某單位負(fù)反饋控制系統(tǒng)的開環(huán)傳遞函數(shù)為G(s) E，試設(shè)計一個合適的滯后校正網(wǎng)絡(luò)，使系統(tǒng)階躍響應(yīng)的穩(wěn)態(tài)誤差約為0.04,相角裕量約為45原系統(tǒng)的伯德圖:ans =0.3200 -30.00451.73222.7477num0=25; den 0=co nv(1,1,co nv

7、(1,1,1,1); w=logspace(-1,1.2);gm1,pm1,wcg1,wcp1=margi n(num 0,de n0);mag1,phase1=bode( num 0,de n0 ,w);gm1,pm1,wcg1,wcp1margi n(num 0,de n0)grid;由此可以看出，相位裕量小于0，系統(tǒng)不穩(wěn)定40ADOreau.kn9aM-400,StBode DiagramGm = -9.9 dB (at 1.73 rad/sec) , P m = -30 deg (at 2.75 rad/sec)200-20IQeacesanp-90-18010-270-1 010 1

8、0Frequency (rad/sec)num0=25; de n0=co nv(1,0,co nv(1,0,1,0); w=logspace(-1,1.2); gm1,pm1,wcg1,wcp1=marg in(n um0,de n0);mag1,phase1=bode( num0,de n0 ,w);gm1,pm1,wcg1,wcp1margin(n um0,de nO)grid;e=10; r=45; r0=pm1;phi=(-180+r+e);il,ii=min( abs(phase1-phi);wc=w( ii); beit=mag1(ii); T=10/wc; n umc= T,1

9、; den c= beit*T,1;n um,de n=series( num0,de n0,n umc,de nc);gm,pm,wcg,wcp=marg in(n um,de n);pr in tsys( numc,de nc)disp( D ?y?o 6 ?卩丨 3?a? ?卩 Yo_e y?printsys(num,den) mag2,phase2=bode( numc,de nc,w);mag,phase=bode( num,de n, w);1subplot(2,1,1);semilogx(w,20*log10(mag),w,20*log10(mag1), ),-.);grid;

10、ylabel( u ?卩(db); title(subplot(2,1,2); semilogx(w,phase,w,phase1, grid; ylabel(? a ?(0); xlabel(title(1), 0D ?yo o-Go,-Gc,GoGc?卩? e (rad/sec)D ?y? o u ?卩?d,r?=i2str(20*log10(gm1).o u ?卩?d,r?=m2str(20*log10(gm),db,w,20*log10(mag2);,w,phase2,);db,w,(w-180-w).）；，？ a ? a ?=,num2str(pm,? a ? d ?=,num2st

11、r(pm),O);-Go,-Gc,GoGc矯正后系的伯德圖統(tǒng)矯正前系統(tǒng)的單位階躍響應(yīng)Sca：E矯正后系統(tǒng)的單位階躍響應(yīng)由矯正前后系統(tǒng)的單位階躍響應(yīng)比較可以看出，系統(tǒng)進過矯正之后由不穩(wěn)定變?yōu)榉€(wěn)定。3某單位負(fù)反饋控制系統(tǒng)的開環(huán)傳遞函數(shù)為G(s)K，試設(shè)計一滯后-超s(s 1)(s 2)前校正裝置，使校正后系統(tǒng)的靜態(tài)速度誤差系數(shù)Kv 10s1，相位裕量500，增益裕量20lgKg 10dB。原系統(tǒng)伯德圖及程序:Bode DiagramGm = 1.58 dB (at 1.41 rad/sec) , Pm = 5.02 deg (at 1.29 rad/sec)50xlagHTesah-wo1503

12、僅180225/卜二_ _-L70-210101010程序：num0=5; denO=conv(1,0,conv(1,1,1,2); w=logspace(-1,1.2);gm1,pm1,wcg1,wcp1=margi n(num 0,de nO);mag1,phase1=bode( num 0,de nO ,w);gm1,pm1,wcg1,wcp1margi n(num 0,de n0)grid;ans =1.20005.02391.41421.2885系統(tǒng)穩(wěn)定裕量過小，臨界穩(wěn)定-Go,-Gc,GoGc校 正后：幅 值裕量=24.4406db相位裕量=71.5870矯正后系統(tǒng)伯德圖矯正程序及

13、結(jié)果:num/den =14.9975 sA2 + 9.1921 s + 114.9975 sA2 + 70.9235 s + 1校正之后的系統(tǒng)開環(huán)傳遞函數(shù)為num/den =74.9877 sA2 + 45.9604 s + 514.9975 sA5 + 115.916 sA4 + 243.7654 sA3 + 144.8469 sA2 + 2 swc=1.4142; beit=10; T2=10/wc; lw=20*log10(w/1.58)-9.12;il,ii=mi n(abs(lw+20); w1= w(ii); numc1=1/w1,1;denc1=1/ (beit*w1),1;

14、numc2= T2,1;denc2= beit*T2,1;n umc,de nc=series (n umc1,de nc1, numc2,de nc2);n um,de n=series( num0,de n0,n umc,de nc);printsys(numc,denc)disp(D ?y?o 6 ?卩丨 3?a? ?卩 Yo_e y?a： pri ntsys( num,de n)mag2,phase2=bode( numc,de nc,w);mag,phase=bode( num,de n, w);gm,pm,wcg,wcp=margi n(n um,de n); subplot(2,

15、1,1);semilogx(w,20*log10(mag),w,20*log10(mag1), ),-.);grid; ylabel(,w,20*log10(mag2u ?卩(db); title(-Go,-Gc,GoGc);subplot(2,1,2); semilogx(w,phase,w,phase1, grid;title(ylabel(? a ?(0); xlabel(,0);?卩? e (rad/sec)D ?yo 6 o u ? i ?d,r?m2str(20*log10(gm),w,phase2,);db , ?,w,(w-180-w),a ? a ?=,num2str(pm);矯正前系統(tǒng)的單位階躍響應(yīng):fiurHijn 1 1d卸1;ElZe