Consider the control system shown in Fig.1. Design a compensator such that the unit-step response curve will exhibit maximum overshoot of 25% or less and settling time of 5 sec or less.
What I tried:
I'm not sure how to approach the solution but what I did was indicating the \$\zeta\$ & \$\omega_n\$ from the equations of Mp & ts as in here & then approached the typical solution which yielded the following results:
Results I could get:
\$\zeta = 0.4\$
\$\omega_n = 2\$
The question doesn't state any further information; it's a mid-term exam.