穿越频率为：7.91
相位裕度为：
\[\varphi(\omega_c) = 180° - 90° - arctg\,\omega_c - arctg\,0.1\omega_c - arctg\,0.25\omega_c + arctg\,0.5\omega_c = 7.5\]
稳定
七、
开环传递函数：
\[G(z) = \frac{z-1}{z}z\left\{\frac{1}{s(s+1)}\right\} = \frac{z-1}{z}\left\{\frac{z}{z-1} - \frac{z}{z-0.368}\right\}\]
\[= \left(1 - \frac{z-1}{z-0.368}\right) = \frac{0.632}{z-0.368}\]
\[\Rightarrow D(z) = z - 0.368 + 0.632\]
\[\Rightarrow z < 1, 稳定\]
八、
\[D(s) = s^3 + 3s^4 + 12s^3 + 24s^2 + 32s + 48 = 0\]
| \(s^3\) | 1 | 12 | 32 |
|---|---|---|---|
| \(s4\) | 3 | 24 | 48 |
| \(s^3\) | 4 | 16 |