Consider the feedback control system in Fig. 14.8, and the following transfer functions:
\begin{aligned}G_{c} &=K_{c}\left(\frac{2 s+1}{0.1 s+1}\right) & G_{v} &=\frac{2}{0.5 s+1} \\G_{p} &=\frac{0.4}{s(5 s+1)} & G_{d} &=\frac{3}{5 s+1} \\G_{m} &=1 & &\end{aligned}
(a) Plot a Bode diagram for the open-loop transfer function.
(b) Calculate the value of K_{c} that provides a phase margin of 30^{\circ}.
(c) What is the gain margin when K_{c}=10 ?