Consider the feedback control system in the figure below whe

Consider the feedback control system in the figure below, where g(s) = 1/(s + 2)(s + 6). The desired performance specifications for the closed-loop system are setting time T_s 1 sec., Can a P controller achieve the desired performance? Fully justify your answer and if it cannot achieve the desired performance, explain whether PI or PD is required.

Solution

No. A P-controller can not achieve the desired performance because it only reduces rise time and steady state erroe but increases the error overshoot. Hence the settling time can not be achieved for error tolerance of 2% or lesser.

A PD-controller decreases both the overshoot and settling time.

A PI-controller increases both overshoot and settling time.

MATLAB give the following settling times:

P controller (Kp=300): 1.54 s

PD controller (Kp=300, Kd=10): 0.917 s

PI controller (Kp=300, Ki=10): >2 s