(2)
\[\sigma\% = e^{\frac{-\xi\pi}{\sqrt{1-\xi^2}}} \times 100\% = 10\% \Rightarrow \xi = 0.6\]
\[t_s = \frac{3.5}{\xi\omega_n} = 1.5 \Rightarrow \omega_n = 3.89\text{rad/s}\]
闭环传递函数：
\[D(s) = s^2 + (4 + 4K_1K_t)s + 4K_1\]
则 \(4K_1 = \omega_n^2\)，\(2\xi\omega_n = 4(K_1K_t + 1) \Rightarrow K_1 = 3.78, K_t = 0.044\)
五、
(1)
\[\frac{E(s)}{N(s)} = \frac{0 - C(s)}{N(s)} = -\frac{K_2}{s^2 + 4s + K_1K_2}\]
\[\frac{E(s)}{R(s)} = \frac{R(s) - C(s)}{R(s)} = \frac{s(s+4)}{s^2 + 4s + K_1K_2}\]
\[E(s) = -\frac{K_2}{s^2 + 4s + K_1K_2} \cdot \left(-\frac{1}{s}\right) + \frac{s(s+4)}{s^2 + 4s + K_1K_2} \cdot \left(\frac{4}{s} + \frac{3}{s^2}\right)\]
\[\Rightarrow e_{ss} = \lim s E(s) = 0.55\]
(2)
增大 K1
六、
开环脉冲传递函数 \(G(z) = (1-z^{-1})Z\left[\frac{1}{s(s+2)}\right] = \dfrac{1.73}{z-0.135}\)
（右上角红笔批注：0.432，划去原式中"1.73"）
\(D(z)=z-0.135+1.73=0 \Rightarrow z=-1.595\) 不稳定
（下方红笔批注：0.432）
七、
(1)
线性部分：\(G(s) = \dfrac{0.2}{s(5s+1)(10s+1)}\)
\[G(j\omega) = -0.2\frac{15\omega^2 + j\omega(1-50\omega^2)}{225\omega^4 + \omega^2(1-50\omega^2)^2}\]
相角范围：\(-90° \to -270°\)
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