七、
(1)
\[G(s) = \dfrac{10\left(\dfrac{s^2}{400}+\dfrac{s}{10}+1\right)}{s(s+1)(10s+1)} = \dfrac{10\left(\left(\dfrac{s}{20}\right)^2+2\times1\times\dfrac{s}{20}+1\right)}{s(s+1)\left(\dfrac{s}{0.1}+1\right)}\]
转折频率:0.1，1，20
\[L(0.1) = 20\lg\dfrac{10}{0.1} = 40\]
\[40 - 40\lg\dfrac{\omega_c}{0.1} = 0 \Rightarrow \omega_c = 1\]
如图所示:
(2)
\[\gamma = 180° + \varphi(1) = 不稳定\]
(3)
串联滞后校正
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