Problem #3: (25 pts) - SHOW YOUR WORK!
Consider the feedback control system shown below, where $G(s) = \frac{1}{s+2}$
a) Determine the control coefficients K and $K_h$ to achieve a maximum overshoot of 0.25 (or 25%)
and a peak time of 1 second. Also, report damping ratio ($\zeta$) and undamped natural frequency ($\omega_n$)
of the system.
b) Using the coefficients found in (a), calculate the exact rise time, and 2% settling time.
c) Plot the response of the control system (CLTF) in MATLAB/Simulink and, by marking on the
plot, show that the response of the system has satisfied the expected transient response
specifications i.e. maximum overshoot, peak time, rise time, and settling time.