根轨迹图
(2)
由(1)得 \(0<k<48\)
(3)
由根轨迹可知，分离点处有重根 \(-0.85\) 此时 \(k=3.1\)
\(D(s)=s^3+6s^2+8s+3.1\)
\[\dfrac{D(s)}{(s+0.85)^2} = s+4.3 = 0 \Rightarrow s=-4.3\]
六、
(1)
\[G(s) = \dfrac{k}{s\left(\dfrac{s}{2}+1\right)\left(\dfrac{s}{6}+1\right)}\]
\(20\lg k = 45.1 \Rightarrow k = 180\)
\[\Rightarrow G(s) = \dfrac{180}{s\left(\dfrac{s}{2}+1\right)\left(\dfrac{s}{6}+1\right)}\]
\(\gamma = 180° + \varphi(12.6) = -55.52°\)
(2)
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