A negative feedback control system is depicted in Figure CP4.8. Suppose that our design objective is to find a controller Gc(s) of minimal complexity such that our closed-loop system can track a unit step input with a steady-state error of zero.
(a) As a first try, consider a simple proportional controller
Gc(s) = K,
where K is a fixed gain. Let K = 2. Plot the unit step response and determine the steady-state error from the plot.
(b) Now consider a more complex controller

where K0 = 2 and K1 = 20. This controller is known as a proportional, integral (PI) controller. Plot the unit step response, and determine the steady-state error from the plot.
(c) Compare the results from parts (a) and (b), and discuss the trade-off between controller complexity and steady-state tracking error performance.
Figure CP4.8
A simple single-loop feedback control system.

Controller Process 10 s + 10 Ris) ns)