Question

A closed-loop transfer function is given by

T(s)=Y(s)/R(s)​=77(s+2)​/(s+7)(s²+4s+22).
Obtain the response of the closed-loop transfer function T(s)=Y(s)/R(s) to a unit step input. What is the settling time Ts​ (use a 2% criterion) and percent overshoot P.O.?

Answer 1

To obtain the response of the closed-loop transfer function T(s) to a unit step input we can find the inverse Laplace transform of T(s). the settling time Ts can be determined using the 2% criterion while the percent overshoot P.O. can be calculated using the formula P.O. = e^(-πζ/√(1-ζ^2)) * 100%.

Step-by-step explanation:

To obtain the response of the closed-loop transfer function T(s) to a unit step input, we can find the inverse Laplace transform of T(s). the inverse Laplace transform of T(s) can be calculated using partial fraction decomposition and the linearity property of the Laplace transform.

The settling time Ts can be determined using the 2% criterion, while the percent overshoot P.O. can be calculated using the formula P.O. = e^(-πζ/√(1-ζ^2)) * 100%, where ζ is the damping ratio.