利用matlab研究频率特性

1、K值绘制Nyquist和 回区 宜：xv AJ0u- den 仁co nv(0 1 1,c on v(0 2 1,0 10 1); G1=tf( nu m1,de n1); num2=0 0 5; den 2=co nv(0 1 1,c on v(0 2 1,0 10 1); G2=tf( nu m2,de n2); subp lot(121) Nyquist(G1,G2) subp lot(122) Bode(G1,G2) 求得增益裕度和相位裕度 Gm, Pm,Wcg ,Wcp =marai n(G1) Gm = 19.8024 Pm = -180 Wcg = 0.8063 Wcp = 0

2、Gm, Pm,Wcg ,Wcp =margi n(G2) Gm = 3.9605 Pm = 49.0377 Wcg = 0.8063 Wcp =0.3656 回区I Nyquist 判据: 系统是稳定的。 j Figure No, 1 O O O O O O 5 5 0 1 - 1 - 10 10 Frequency (rad/sec) o o _5 - o 5 5 9 3 9 仝 1 - 1 1 - - E - 詈二首d NycFJist Disgrsn 105 Real Axis o o o 5 1 di - 和 0 I or - num仁0 0 1; den 仁c on v(0 1 0,

3、c onv(0 1 1,0 2 1); G1=tf( nu m1,de n1); num2=0 0 5; den 2=c on v(0 1 0,c onv(0 1 1,0 2 1); G2=tf( nu m2,de n2); subp lot(121) Nyquist(G1,G2) subp lot(122) Bode(G1,G2) 回 80 Nyquist Diagram ISO - 空芒aislj_se- -80二J- -1500-1000 -500 Real Axis Bode Diagram -270 -2D2 10 10 10 Frequency frad/sec) 求得增益裕度和相

4、位裕度 Gm, Pm,Wcg ,Wcp =margi n(G1) Gm =1.5000 Pm = 11.4304 Wcg = 0.7071 Wcp =0.5715 Gm, Pm,Wcg ,Wcp =margi n(G2) Gm =0.3000 Pm = -28.0814 Wcg =0.7071 Wcp = 1.2126 Nyquist 判据: 系统是稳定的。 i*J Figure No. 1 num1=0 0 1; den 仁c on v(1 0 0,0 1 1); G1=tf( nu m1,de n1); num2=0 0 5; den 2=c on v(1 0 0,0 1 1); G2=t

5、f( nu m2,de n2); subp lot(121) Nyquist(G1,G2) sub plot(122) Bode(G1,G2) 求得增益裕度和相位裕度 Gm, Pm,Wcg ,Wcp =margi n( G1) Gm = Inf Pm = -40.9750 Wcg = NaN Wcp =0.8685 Gm, Pm,Wcg ,Wcp =margi n(G2) Gm =I nf Pm =-58.3182 Wcg =NaN Wcp = 1.6203 Nyquist 判据： 系统是不稳定的。 回冈 J FigurB Rd. XnsvrtlindoT 耳片】P kA/*/闭归二 100

6、1TO Myquist Diagram 0 閱 同 w 加 10011 -1500-1000-5M ReW Axis HP) Bode ftegram -2-1a 10 10 10 10 K W % 111 - - - Freciusnor (radfteoj num仁CO nv(0 0 1,0 1 1); den 仁c on v(1 0 0,0 2 1); G1=tf( nu m1,de n1); num2= conv(0 0 5,0 1 1); den 2=c on v(1 0 0,0 2 1); 回冈 6 Myquist Diagram 10 10 Freciusnoy (racJfte

7、oj j5 Reel Axis G2=tf( num2,de n2); sub plot(121) Nyquist(G1,G2) sub plot(122) Bode(G1,G2) 求得增益裕度和相位裕度 Gm, Pm,Wcg ,Wcp =margi n( G1) Gm =I nf Pm =-19.2738 Wcg =Inf Wcp =0.8205 Gm, Pm,Wcg ,Wcp =margi n(G2) Gm =I nf Pm =-14.2414 Wcg =Inf Wcp =1.6707 Nyquist 判据： 系统是不稳定的。 J Figure Rd. num1=0 0 0 1; den

8、仁1 0 0 0; G1=tf( num1,de n1); num2=0 0 0 5; den 2=1 0 0 0; G2=tf( num2,de n2); sub plot(121) Nyquist(G1,G2) sub plot(122) Bode(G1,G2) 求得增益裕度和相位裕度 Gm, Pm,Wcg ,Wcp =margi n(G1) Gm =I nf Pm = -90.0000 Wcg = NaN Wcp =1 Gm, Pm,Wcg ,Wcp =margi n(G2) Gm =I nf Pm =-90.0000 Wcg =NaN Wcp =1.7100 Nyquist 判据： 系

9、统是不稳定的。 (6) 回 Filt Edit 些 Iniirt Taels 世 ind*w Htlp Real Axis x 10 o 覆一bbe 一 -50 -90 150 1OQ 50 -135 .160 -J25 -27D num1=conv(0 0 1,conv(0 1 1,0 2 1); den1=1 0 0 0; G1=tf(num1,den1); num2=conv(0 0 5,conv(0 1 1,0 2 1); den2=1 0 0 0; G2=tf(num2,den2); subplot(121) Nyquist(G1,G2) subplot(122) Bode(G1,G

10、2) 求得增益裕度和相位裕度 Gm,Pm,Wcg,Wcp=margin(G1) Gm =0.1667 Pm =53.4109 Wcg =0.7071 Wcp =2.2434 Gm,Pm,Wcg,Wcp=margin(G2) Gm =0.0333 Pm =81.4814 Wcg =0.7071 Wcp =10.0641 Nyquist 判据： 系统是稳定的。 7) Filt Edit 些*w lAMft Tdeli Window Hfclf num仁co nv(0 0 1,co nv(0 5 1,0 15 1); den 仁co nv(0 1 0,c onv(0 1 1,co nv(0 2 1,

11、co nv(0 10 1,0 20 1); G1=tf( num1,de n1); num2=co nv(0 0 5,co nv(0 5 1,0 15 1); den 2=co nv(0 1 0,c onv(0 1 1,c onv(0 2 1,co nv(0 10 1,0 20 1); G2=tf( num2,de n2); sub plot(121) Nyquist(G1,G2) sub plot(122) Bode(G1,G2) 求得增益裕度和相位裕度 Gm, Pm,Wcg ,Wcp =margi n(G1) Gm =2.5940 Pm =20.8239 Wcg =0.5770 Wcp =

12、 0.3334 Gm, Pm,Wcg ,Wcp =margi n(G2) Warning: The closed-lo op system is un stable. Gm =0.5188 Pm =-14.6107 Wcg =0.5770 Wcp =0.7975 Nyquist 判据: 系统是不稳定的。 (8) Figure No. 1 口回冈 File Edi t Vi ew Inzflrt Foolz Window Help 昌 |k AT* / 妙 E C Nycwist Di 的 r3tn -4- Real Axis 5 0 5 15 2 hr Lr - 0 丄 J 25 Z * o

13、c o Q 5 o 1 3 3 4 9 - - - - Bode Diagram num1=0 0 1; den 仁0 1-1; G1=tf( num1,de n1); num2=0 0 5; den 2=0 1-1; G2=tf( num2,de n2); sub plot(121) Nyquist(G1,G2) sub plot(122) Bode(G1,G2) 求得增益裕度和相位裕度 Gm, Pm,Wcg ,Wcp =margi n(G1) Warning: The closed-lo op system is un stable. Gm =1 Pm =0 Wcg =0 Wcp =0 G

14、m, Pm,Wcg ,Wcp =margi n(G2) Gm =0.2000 Pm =78.4630 Wcg =0 Wcp =4.8990 Nyquist 判据: 系统是稳定的。 (9) Figure Nd. L 口回区 Eili Edit ViIpitrt世心氐 Htlp QH 俸 A Z / 炉 0 y NycFJist DiagrafTi 20 Bodt Diagram o o o o J 7 (g山号芒Be -135 -100 10 1U Fred Lie ncy frad/sec) num1=0 0 -1; den 仁0 -1 1; G1=tf( num1,de n1); num2=

15、0 0 -5; den 2=0 -1 1; G2=tf( num2,de n2); sub plot(121) Nyquist(G1,G2) sub plot(122) Bode(G1,G2) 求得增益裕度和相位裕度 Gm, Pm,Wcg ,Wcp =margi n(G1) Warning: The closed-lo op system is un stable. Gm =1 Pm =0 Wcg =0 Wcp =0 Gm, Pm,Wcg ,Wcp =marai n(G2) Gm =0.2000 Pm =78.4630 Weg =0 Wep = 4.8990 (10) Pile Edil Vi

16、ew Inzert T ftols. 回冈 Nyquist 判据: 系统是稳定的。 VinJov Help II 启H昌k A /* / I观闭C Real Axis num1=0 0 1; den 仁c on v(0 1 0,0 1 1); G1=tf( num1,de n1); num2=0 0 5; den 2=co nv(0 1 0,0 1 1); G2=tf( num2,de n2); sub plot(121) Nyquist(G1,G2) sub plot(122) Bode(G1,G2) 求得增益裕度和相位裕度 Gm, Pm,Wcg ,Wcp =margi n( G1) Gm

17、=I nf Pm =51.8273 Weg =Inf Wep =0.7862 Gm, Pm,Wcg ,Wcp =margi n(G2) Gm =I nf Pm =25.1801 Wcg =Inf Wcp =2.1270 Nyquist 判据： 系统是不稳定的。 4.单位负反馈系统开环传递函数 (1)当K=4，计算系统的增益裕度，并通过 MATLAB验证； 如果希望增益裕度为16dB，求出对应的K值，并通过MATLAB验证。 解: (1)计算：由,h=-20lg(A(w)=-L(w)dB 代入. 当k=4时系统的增益裕度为Gm=1.5 Matlab 验证： num=0 0 4; den=con v(0 1 0,co nv(0 1 1,0 1 2); G=tf(nu m,d