\[G(j\omega) = \frac{Ke^{-0.8j\omega}}{j\omega}, |G(j\omega)| = \frac{K}{\omega}, (j\omega) = -0.8\omega - 90°\]
令\(\varphi(j\omega) = -0.8\omega - 90° = -180° \Rightarrow \omega = \frac{5\pi}{8}, |G(j\omega)| = \frac{8K}{5\pi}\)
如图所示：
(2)
\[P = 0, Z = P - 2N = 0 \Rightarrow -\frac{8K}{5\pi} > -1 \Rightarrow 0 < K < \frac{5\pi}{8}\]
三、
(1)
\[G(s) = \frac{10}{s(s+1)}\]
(2)
\[\frac{L(1) - L(\omega_c)}{\lg 1 - \lg \omega_c} = -40 \Rightarrow \omega_c = 3.16\]
\[\gamma = 180° + (\omega_c) = 180° - 90° - \arctan 3.16 = 17.56° > 0\]
系统稳定
(3)
串联超前校正，增大相角裕度，快速性增加，改善平稳性，抗