(3)
\[\xi = \cos\beta = \frac{\sqrt{3}}{2} \Rightarrow \beta = 30°\]
由于2个极点一个雾点是圆，圆心在原点，半径为\(\sqrt{2}\)
所以所求点为 \(s = -\dfrac{\sqrt{2}}{2} \pm \dfrac{\sqrt{6}}{2}j\)，推出闭环特征方程为
\[D = \left(s + \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2}j\right)\left(s + \frac{\sqrt{6}}{2} - \frac{\sqrt{2}}{2}j\right) = \left(s + \frac{\sqrt{6}}{2}\right)^2 + \frac{1}{2} = s^2 + \sqrt{6}s + 2 \Rightarrow \begin{cases} \xi = \dfrac{\sqrt{3}}{2} \\ \omega_n = \sqrt{2} \end{cases}\]
\[\sigma\% = e^{\frac{-\pi\xi}{\sqrt{1-\xi^2}}} \times 100\% = 0.43\%\]
\[t_s = \frac{3.5}{\xi\omega_n} = 2.86s\]
五、
(1)
\[G(s) = G_1G_2H = \frac{k_1k_2}{s(T_1s+1)(T_2s+1)}\]
相角范围：\(-90° \rightarrow -270°\)
\[G(j\omega) = -k_1k_2\frac{\omega^2(T_1+T_2) + j(\omega - T_1T_2\omega^3)}{\omega^4(T_1+T_2)^2 + (\omega - T_1T_2\omega^3)^2}\]
过第三象限和第二象限
与虚轴的交点：\(G\left(j\sqrt{\dfrac{1}{T_1T_2}}\right) = -\dfrac{k_1k_2T_1T_2}{T_1+T_2}\)
如图所示：
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