22. For the unity feedback system given in
Figure P9.1 with
\begin{equation} G(s) = \frac{K}{s(s+5)(s+12)} \end{equation}do the following: [Section: 9.4]
a. Find the gain, K, for the uncompensated system
to operate with 30% overshoot.
b. Find the peak time and $K_v$ for the uncompensated
system.
c. Design a lag-lead compensator to decrease the
peak time by a factor of 2, decrease the percent
overshoot by a factor of 2, and improve the
steady-state error by a factor of 30. Specify all
poles, zeros, and gains.