A specific closed-loop control system is to be designed for an under damped response to a step input. The specifications for the system are as follows:
10% < percent overshoot < 20%,
Settling time < 0.6 s.
(a) Identify the desired area for the dominant roots of the system.
(b) Determine the smallest value of a third root r3 if the complex conjugate roots are to represent the dominant response.
(c) The closed-loop system transfer function T(s) is third-order, and the feedback has a unity gain. Determine the forward transfer function G(s) = Y(s)/E(s) when the settling time to within 2% of the final value is 0.6 s and the percent overshoot is 20%.