\(Z=P-2N=0-2(0-1)=2\),不稳定
七、解答:1.
\[G(z)=\frac{z-1}{z}z\left[\frac{1}{s(s+1)}\right]=\frac{z-1}{z}z\left[\frac{1}{s}-\frac{1}{s+1}\right]=1-\frac{z-1}{z-0.368}=\frac{0.632}{z-0.368}\]
闭环特征方程为 \(z+0.264=0\),可得 \(z=-0.264\) 稳定
-
\[\phi(z)=\frac{\dfrac{0.632}{z-0.368}}{1+\dfrac{0.632}{z-0.368}}=\frac{0.632}{z+0.264}\]
\[\frac{C(z)}{R(z)}=\frac{0.632z^{-1}}{1+0.264z^{-1}} \Rightarrow 0.264c(k-1)+c(k)=0.632r(k-1)\]
- 开环系统为0型,故 \(K_V=0\), \(K_p=\lim_{z\to1}\left[1+G(z)\right]=2\)
八、解答:
(1) 校正前: $\(GH=\frac{10}{s(2s+1)}\)$
定义法计算截止频率: \(2.21\)
相位裕度: $\(r=180°-90°-\arctan{2\omega_c}=67°\)$