\[\frac{C(s)}{R(s)} = \frac{5K_0K_1}{(s+5)(s^2+s)+5K_0K_1}\]
(3)
由劳斯判据可知系统稳定
\[G(s) = \frac{5K_0K_1}{s(s+1)(s+5)}, K_v = \lim_{s\to0} sG(s) = K_0K_1 \Rightarrow e_{ssr} = \frac{2}{K_0K_1}\]
当\(n(t) = n_1 + n_2t\)
\[\frac{E(s)}{N(s)} = \frac{C(s)}{N(s)} = \frac{\dfrac{k_0k_2}{s^2+s}}{1+\dfrac{5k_0k_1}{s(s^2+s)}+\dfrac{5}{s}}\]
\[= \frac{k_0k_2s}{s(s^2+s)+5(s^2+s)+5k_0k_1}\]
\[e_{ssn} = \lim_{s\to0} sNE/N = \frac{k_2n_2}{5k_1}\]
(4)
对扰动端前馈校正
五、
(1)
\[G(s)H(s) = \frac{k(s+2)}{s(s+1)}\]
开环极点0，-1，开环零点-2
实轴上的根轨迹：\((-\infty,-2]\)，\([-1,0]\)
分离点：\(\dfrac{dG(s)}{ds} = 0 \Rightarrow s_1 = -0.59, s_2 = -3.41\)
渐进线：\(\sigma_a = \dfrac{-1-(-2)}{2-1} = 1\)，\(\Phi_a = \dfrac{(2k+1)\pi}{2-1}(k=0)\)
根轨迹如图：