We have three potential controllers, GC(s) for our system.

1.

GC(s) = K (Proportional controller)

2.

GC(s)=sK (Integral controller)

3.

GC(s)= K(1 + )1s (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, use the root locus for all positive K to determine a value of K such that the design specifications are satisfied.

b)

Repeat part (a) for the integral controller.

c)

Repeat part (a) for the PI controller.

d)

Compare and contrast the three controllers obtained in parts (a) – (c), concentrating your discussion on the steady-state errors and transient performance.