A control system is stable if:

• A. GM negative, PM positive
• B. Both zero
• C. GM zero, PM negative
• D. GM positive, PM positive

Answer: (D)

A control system's stability is determined by its gain margin (GM) and phase margin (PM). Gain margin refers to the amount of gain increase that a system can tolerate before it becomes unstable, while phase margin measures how close the system is to becoming unstable in the frequency domain.

A system is deemed stable when both gain margin and phase margin are positive. Positive gain margin indicates that the system can withstand an increase in gain without becoming unstable, while a positive phase margin signifies that there is a buffer between the point of instability and the current phase response of the system. This buffer allows the system to remain stable even with potential disturbances or variations in parameters.

In contrast, when either the gain margin or phase margin is zero or negative, it signifies that the system is either critically stable or unstable, leaving no room for fluctuations. Therefore, a control system is stable if both measures are positive, confirming that it can handle changes in system dynamics without losing stability.