四、
(1)
(2)
\[-270°+arctg(T_1\omega_x)+arctg(T_2\omega_x)=-180° \Rightarrow \omega_x=\dfrac{1}{\sqrt{T_1T_2}}\]
所以
\[Re=|G|=\dfrac{-K\sqrt{(T_1\omega_x)^2+1}\sqrt{(T_2\omega_x)^2+1}}{|\omega_x{}^3|}=\dfrac{-K\sqrt{\dfrac{T_1}{T_2{}^2}+1}\sqrt{\dfrac{T_2}{T_1{}^2}+1}}{\left(\dfrac{1}{\sqrt{T_1T_2}}\right)}\]
(3)
由奈式判据可知:\(Z=P-2N=0\),稳定
五、
(1)
求会分点:\(\dfrac{1}{d}+\dfrac{1}{d+1}=\dfrac{1}{d+2} \Rightarrow d=\begin{cases}-0.59\\-3.41\end{cases}\)
求虚轴交点:
\[D=s^2+(K^*+1)s+2K^*\]
| \(s^2\) | \(1\) | \(2K^*\) |
| \(s^1\) | \(K^*+1\) | |
| \(s^0\) | \(2K^*\) |
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