實(shí)驗(yàn)五線性控制系統(tǒng)的頻域響應(yīng)分析2

1、練習(xí) 5-1代碼：num=1;den=10.41;bode(num,den);練習(xí) 5-2代碼：num=25;den=1 4 25;mag,phase,w=bode(num,den)gm,pm,wcg,wcp=margin(mag,phase,w)bode(num,den)titlelujun;xlabelx;ylabely;結(jié)果：gm =2.7623e+003pm =69.8297wcg =262.5545wcp =5.8059練習(xí) 5-3代碼：num1=5;num2=20;den=conv(1 1 0,0.1 1);G1=tf(num1,den)sys1=feedback(G1,1)den

2、1=sys1.den1roots(den1)mg1,pm1= margin(num1,den)subplot(121),bode(num1,den)grid;G2=tf(num2,den)sys2=feedback(G2,1)den2=sys2.den1roots(den2)mg2,pm2= margin(num2,den)subplot(122),bode(num2,den)grid;1、當(dāng) K=5 時(shí)：特征根 ans =-10.5011-0.2494 + 2.1678i-0.2494 - 2.1678i因?yàn)檫\(yùn)行結(jié)果中特征根都為負(fù)實(shí)部，根據(jù)系統(tǒng)穩(wěn)定的充要條件可知系統(tǒng)穩(wěn)定。幅值裕度 (db)和

3、相位裕度 ( )mg1 = 2.2000pm1 = 13.57092、當(dāng) K=20 時(shí)：特征根 ans =-11.62050.3103 + 4.1370i0.3103 - 4.1370i因?yàn)檫\(yùn)行結(jié)果中特征根有正實(shí)部和負(fù)實(shí)部，根據(jù)系統(tǒng)穩(wěn)定的充要條件可知系統(tǒng)不穩(wěn)定。幅值裕度 (db)和相位裕度 ( )mg2 =0.5500pm2 =-9.6566練習(xí) 5-4程序代碼：a=1 36 205 750;roots(a)b=-3.0000 + 4.0000i -3.0000 - 4.0000ipoly(b)G1=tf(750,1 36 205 750);G2=tf(750,1 6 25);subplot(

4、121), step(G1, G2) grid;subplot(122),bode(G1,G2)grid;、主導(dǎo)極點(diǎn)b=-3.0000 + 4.0000i -3.0000 - 4.0000i、系統(tǒng)的低階模型ans =1625750G (s)s2 6s 253、如圖所示：練習(xí) 5-5程序代碼：num=2 5 1;den=1 2 3;nyquist(num,den)練習(xí) 5-6、代碼：G1=tf(1300,1 52 100 0);G2=tf(5200,1 52 100 0);subplot(121),bode(G1)grid;subplot(122),bode(G2)grid;、代碼：G1=tf(

5、1300,1 521000);G2=tf(5200,1 521000);subplot(121),nyquist(G1)grid;subplot(122),nyquist(G2)grid;3、根軌跡的繪制：命令格式：繪制系統(tǒng)根軌跡圖r,k=rlocus(num,den)r,k=rlocus(num,den,k)r,k=rlocus(a,b,c,d)r,k=rlocus(a,b,c,d,k)練習(xí) 5-7代碼：G1=tf(1.5,conv(1 1 0,1 2);rlocus(G1)練習(xí) 5-8代碼：k=0.25,0.42,1.5,2,4,6,8;holdonfori=1:length(k)num= k(i) 2*k(i);den=1 2 3;bode(num,den);endholdoff幅值裕度 (db)和相位裕度：mg = Infpm =Infmg =Infpm =Infmg =Infpm =119.0365mg =Infpm =105.8266mg =Infpm =93.4847mg =Infpm =91.2649mg =Infpm =90.5840程序代碼：num=1 2;den=1 2 3;rlocus(num,den);由圖可知：增益 K從 0 變到無窮時(shí)，根軌跡不會(huì)越過虛軸進(jìn)入右半 S平面，故閉環(huán)系統(tǒng)對(duì)所有的K值都是穩(wěn)定的。程序代碼：k=0.