Question

Which one of the following statements is correct for gain margin and phase margin of two closed-loop systems having loop functions G(s) H(s) and exp(-s) G(s) H(s)?

(a) Both gain and phase margins of the two systems will be identical

(b) Both gain and phase margins of G(s) H(s) will be more

(c) Gain margins of the two systems are the same but phase margins of G(s) H(s) will be more

(d) Phase margins of the two systems are the same but gain margin of G(s) H(s) will be less

I had been asked this question in examination.

This interesting question is from Correlation between Time and Frequency Response in division Frequency Response Analysis of Control Systems

Answer 1

The correct option is (c) Gain margins of the two systems are the same but phase margins of G(s) H(s) will be more

The explanation: The factor exp (-st) is the cause of the term transportation lag (time delay). The effect of e^-st term is simply to rotate each point of the G(s) H(s) plot by an angle wT rad in the clockwise direction. So the phase margin of the system reduces as T increases. But since |e^-s| =1, therefore the gain margins of both the systems are the same.