Consider the feedback control system in Figure CP7.7. We have three potential controllers for our system:
1. Gc(s) = K (proportional controller)
2. Gc(s) = K/s (integral controller)
3. Gc(s) = K(1 + 1/s) (proportional, integral (PI) controller)
The design specifications are Ts ‰¤ 10 seconds and P.O. ‰¤ 10% for a unit step input.
(a) For the proportional controller, develop an m-file to sketch the root locus for 0 (b) Repeat part (a) for the integral controller.
(c) Repeat part (a) for the PI controller.
(d) Co-plot the unit step responses for the closed-loop systems with each controller designed in parts (a)-(c).
(e) Compare and contrast the three controllers obtained in parts (a)-(c), concentrating on the steady-state errors and transient performance.
Figure CP7.7
A single-loop feedback control system with controller Gc(s).

Controller Process Risi s2