CP7.7 Consider the feedback control system in Figure CP7.7. We have three potential controllers for our system:

1. G s c( ) = K (proportional controller)

2. G s c( ) = K s (integral controller)

3. G s c( ) = + K s ( ) 1 1/ (proportional, integral (PI)

controller).

The design specifications are Ts 1 ≤ 0 s 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 , < < K ∞

and determine the value of K so that the design specifications are satisfied.

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.