图 5-22 \(G(s)=\dfrac{20(3s+1)}{s^2(6s+1)(s^2+4s+25)(10s+1)}\)对数幅频渐近特性(MATLAB)

最小相位振荡环节：\(\omega_2=1\)，斜率减小 40dB/dec。

最小相位振荡环节：\(\omega_3=5\)，斜率减小 40dB/dec。

最小交接频率：\(\omega_{\min}=\omega_1=0.1\)。

② 绘制低频段(\(\omega<\omega_{\min}\))渐近特性曲线。因为 \(\upsilon=1\)，\(20\lg K=20\lg0.032=-29.9\text{dB}\)，则低频段渐近线斜率 \(k=-20\text{dB/dec}\)，并且通过点\((1,20\lg0.032)=(1,-29.9\text{dB})\)。

③ 绘制频段 \(\omega\geq\omega_{\min}\)渐近特性曲线。

\(\omega_{\min}\leqslant\omega<\omega_2\)，\(k=0\text{dB/dec}\)

\(\omega_2\leqslant\omega<\omega_3\)，\(k=-40\text{dB/dec}\)

\(\omega\geqslant\omega_3\)，\(k=-80\text{dB/dec}\)

系统开环对数幅频渐近特性曲线如图 5-23 所示。

MATLAB 文本：exe515.m

G1=tf(10,[2,1]);
G2=tf(50,[conv(conv([1,0,0],[1,1,1]),[6,1])]);
G3=tf(40*[1,0.5],conv(conv([1,0.2],[1,0]),[1,1,1]));
G4=tf(10*[1,0.2],conv([1,0,0],[1,0.1]));
G5=tf(20*[3,1],conv(conv([1,0,0],[6,1]),conv([1,4,25],[10,1])));
G6=tf(8*[1,0.1],conv(conv([1,0],[1,1,1]),[1,4,25]));
[x0,y0,w1]=bode(G1);[x1,y1]=bd_asymp(G1,w1);
[x0,y0,w2]=bode(G2);[x2,y2]=bd_asymp(G2,w2);
[x0,y0,w3]=bode(G3);[x3,y3]=bd_asymp(G3,w3);
[x0,y0,w4]=bode(G4);[x4,y4]=bd_asymp(G4,w4);
[x0,y0,w5]=bode(G5);[x5,y5]=bd_asymp(G5,w5);
[x0,y0,w6]=bode(G6);[x6,y6]=bd_asymp(G6,w6);
figure(1);semilogx(x1,y1),grid;

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