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The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is −180°. This system has

1. one LHP pole and one RHP zero at the same frequency.
2. one LHP pole and one LHP zero at the same frequency.
3. two LHP poles and one RHP zero.
4. two RHP poles and one LHP zero.

Correct answer: one LHP pole and one RHP zero at the same frequency.

Solution

The system exhibits a constant magnitude in the Bode plot, indicating a first-order behavior, while the high-frequency phase of -180° suggests the presence of a zero that cancels out the effect of a pole, resulting in one left-half plane (LHP) pole and one right-half plane (RHP) zero at the same frequency.

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