Question

Which of the following transfer function will have the greatest maximum overshoot?

(a) 9/(s^2+2s+9)

(b) 16/(s^2+2s+16)

(c) 25/(s^2+2s+25)

(d) 36/(s^2+2s+36)

I had been asked this question in an international level competition.

The question is from Time Response of Second Order Systems topic in section Time Response Analysis, Design Specifications and Performance Indices of Control Systems

Answer 1

The correct answer is (d) 36/(s^2+2s+36)

The explanation is: Comparing the characteristic equation with the standard equation the value of the damping factor is calculated and the value for the option d is minimum hence the system will have the maximum overshoot .