Question:
The open-loop system is stable. The Nyquist plot encircles \( (-1, 0) \) once in the anti-clockwise direction. Find the closed-loop system stability.
The open-loop system is stable. The Nyquist plot encircles \( (-1, 0) \) once in the anti-clockwise direction. Find the closed-loop system stability.
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The Nyquist criterion helps in determining the stability of the closed-loop system based on the encirclements of \( (-1, 0) \).
- If the plot encircles \( (-1, 0) \) in the anti-clockwise direction, the system is unstable.
- If the plot encircles \( (-1, 0) \) in the anti-clockwise direction, the system is unstable.
Updated On: Feb 14, 2025
- Stable
- Unstable
- Marginally stable
- Cannot be determined
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The Correct Option is B
Solution and Explanation
Step 1: According to the Nyquist criterion, the stability of the closed-loop system can be determined by analyzing the Nyquist plot. The number of encirclements of the point \( (-1, 0) \) on the Nyquist plot corresponds to the number of poles in the right half-plane of the open-loop transfer function.
- If the Nyquist plot encircles \( (-1, 0) \) once in the anti-clockwise direction, this indicates that there is one unstable pole in the open-loop transfer function.
Step 2: Since the open-loop system is stable and encircles \( (-1, 0) \) once in the anti-clockwise direction, the closed-loop system will be unstable.
Thus, the closed-loop system is unstable.
- If the Nyquist plot encircles \( (-1, 0) \) once in the anti-clockwise direction, this indicates that there is one unstable pole in the open-loop transfer function.
Step 2: Since the open-loop system is stable and encircles \( (-1, 0) \) once in the anti-clockwise direction, the closed-loop system will be unstable.
Thus, the closed-loop system is unstable.
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