Which of the following represents a system with a phase margin of 0°?

• A. Marginally stable
• B. Unstable
• C. Stable
• D. Critically stable

Answer: (A)

A system with a phase margin of 0° is characterized as marginally stable. In control theory, phase margin is an indicator of how close a system is to instability. When the phase margin is exactly 0°, it means that at the frequency where the gain crosses unity, the phase shift is -180°, which puts the system on the verge of oscillation. This marginal stability indicates that while the system may not exhibit divergent behavior, it does not have enough phase margin to ensure stable response under all conditions. Therefore, it is likely to oscillate or respond slowly to disturbances without necessarily returning to its equilibrium state.

In contrast, a positive phase margin indicates a stable system that can withstand disturbances, while a negative phase margin suggests the system is unstable. A system that is critically stable would be at the boundary of stability but typically involves a specific phase margin that is non-zero, usually implying a precise balance between the feedback and input, leading to steady but potentially oscillatory behavior. Thus, the answer that indicates a system with a phase margin of 0° is appropriately identified as marginally stable.