串联滞后校正

G1=tf(10,[1 0]);
G21=tf(1,[0.05 1]);
G22=tf(1,[0.1 1]);
G2=series(G21,G22);
H=1;

1.计算串联校正装置的传递函数 Gc(s)和校正网络参数。

b=1/11;%分度系数,表示滞后深度
T=11;%时间常数
Gc=tf([b*T 1],[T 1]);
sprintf("校正网络参数b=%g,T=%g",b,T);
display(Gc);
Gc = s + 1 -------- 11 s + 1 Continuous-time transfer function.

2.画出校正后系统的对数坐标图,并求出校正后系统的ω′c及ν′。

G_ori=series(G1,G2);
G_corr=series(Gc,G_ori);
figure();
bode(G_ori,G_corr,Gc);grid;
legend('校正前','校正后','校正环节');title('串联滞后校正前后开环传递函数伯德图');
[Gm_ori,Pm_ori] = margin(G_ori);%Gm: gain margin幅值裕度,单位为一
[Gm_corr,Pm_corr] = margin(G_corr);%Pm: phase margin相角裕度
text=sprintf("校正前:幅值裕度:%g,相角裕度:%g\n校正后:幅值裕度:%g,相角裕度:%g" ...
,Gm_ori,Pm_ori,Gm_corr,Pm_corr)
text =
"校正前:幅值裕度:3,相角裕度:32.6133 校正后:幅值裕度:28.486,相角裕度:44.0019"

3.比较校正前后系统的阶跃响应曲线及性能指标,说明校正装置的作用。

Phi_ori=feedback(G_ori,H);
Phi_corr=feedback(G_corr,H);
figure();
stepplot(Phi_ori,Phi_corr);
legend('校正前','校正后');title('串联滞后校正前后闭环传递函数阶跃响应');
info_ori=stepinfo(Phi_ori);
info_corr=stepinfo(Phi_corr);
struct2table([info_ori,info_corr])
ans = 2×8 table
 RiseTimeSettlingTimeSettlingMinSettlingMaxOvershootUndershootPeakPeakTime
10.15651.60100.83791.389438.942101.38940.4091
20.91297.53060.90031.330032.996901.33002.4970

参考链接🔗

  1. What is Lag Compensator? Definition, Lag Angle, Advantages and Disadvantages of Lag Compensator - Electronics Coach