Consider a unity feedback control system with the transfer function:
G(s) = K / [s(s+2)]
in the forward path.
(a) Design a proportional controller that yields a stable system with percent overshoot less than 5% for the step input.
(b) Find settling time and peak time of the closed-loop system designed in part (a).
(c) Design a PD compensator that reduces the settling time computed in (b) by a factor of 4 while keeping the percent overshoot less than 5%.
(d) Add a PI compensator that achieves zero steady-state error for a ramp input and does not change the transient response designed in (c) significantly.
(e) Merge the compensators designed in parts (c) and (d) to find the proportional, derivative, and integral gains of an equivalent PID compensator.