Question

Gain margin and phase margin are measures of:

• A. Process efficiency
• B. Steady-state error
• C. Controller cost
• D. Relative stability

Hint:

Gain and phase margins don’t tell whether a system is simply stable or unstable — they tell how stable it is. That’s why they are used to judge relative stability.

Answer 1

The Correct Option is D

Gain margin and phase margin are important parameters in control systems used to assess the relative stability of a system rather than absolute stability.
Gain margin indicates how much gain can increase before the system becomes unstable. It is the amount (in dB) by which the gain can be increased before the phase reaches $-180^\circ$ and the system oscillates.
Phase margin indicates how much additional phase lag can be tolerated before the system becomes unstable. It is the difference between the actual phase and $-180^\circ$ at the gain crossover frequency.
These margins help engineers evaluate how “close” the system is to the verge of instability. While a system with zero margins might still be stable, it would be very sensitive and potentially dangerous in real-world applications.
Let’s assess the incorrect options:
- Process efficiency deals with resource utilization, not system stability.
- Steady-state error relates to accuracy, not stability margins.
- Controller cost is an economic factor and unrelated to frequency-domain analysis.
Thus, the correct answer is that gain margin and phase margin measure the relative stability of a system.