Phase margin of a system is used to specify which of the following ?

Frequency response
Absolute stability
Relative stability
Time response

The correct answer is: C. Relative stability.

Phase margin is a measure of how close a system is to instability. It is defined as the angle by which the phase of the open-loop transfer function of a system leads the phase of a unity-gain reference signal at the frequency where the magnitude of the open-loop transfer function is unity.

A system is said to be stable if the phase margin is greater than or equal to 180 degrees. If the phase margin is less than 180 degrees, the system is said to be unstable.

The phase margin is a useful tool for designing and analyzing control systems. It can be used to determine the stability of a system and to design controllers that will improve the stability of a system.

Here is a brief explanation of each option:

  • Option A: Frequency response. The frequency response of a system is the magnitude and phase of the output of a system as a function of the input frequency. The frequency response can be used to determine the stability of a system, but it is not as useful as the phase margin for this purpose.
  • Option B: Absolute stability. Absolute stability is a property of a system that is independent of the initial conditions. A system is said to be absolutely stable if it is stable for all initial conditions. The phase margin is not a measure of absolute stability.
  • Option C: Relative stability. Relative stability is a property of a system that is dependent on the initial conditions. A system is said to be relatively stable if it is stable for some initial conditions. The phase margin is a measure of relative stability.
  • Option D: Time response. The time response of a system is the output of a system as a function of time. The time response can be used to determine the stability of a system, but it is not as useful as the phase margin for this purpose.
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