AP5.9 The unity negative feedback system in Figure AP5.9 has the process given by

The controller is a proportional plus integral control

ler with gains Kp and KI. The objective is to design the controller gains such that the dominant roots have a damping ratio ζ equal to 0.707. Determine the resulting peak time and settling time (with a 2%

criterion) of the system to a unit step input.

G(s) = 1 s(s+15)(s +25)