Assertion (A): All the systems which exhibit overshoot in transient

assertion-a-all-the-systems-which-exhibit-overshoot-in-transient

Assertion (A): All the systems which exhibit overshoot in transient response will also exhibit resonance peak in frequency response.

Reason (R): Large resonance peak in frequency response corresponds to a large overshoot in transient response.

A. Both A and R are true and R is the correct explanation of A

B. Both A and R are true and R is not the correct explanation of A

C. A is true but R is false

D. A is false but R is true

I got this question during an internship interview.

The origin of the question is Correlation between Time and Frequency Response in portion Frequency Response Analysis of Control Systems

Correct choice is A. Both A and R are true and R is the correct explanation of A

The explanation: For G<1/√2 frequency parameters ex Mr resonant peak and time response parameters eg. Mp peak overshoot are well correlated. For G>1/√2 the resonant peak Mr does not exist and the correlation breaks down. This is not a serious problem as for this range of G, the step response oscillations are well-damped and Mp is hardly perceptible.