Question

The incorrect statement with respect to Bode Plots is

• A. Gain margin and phase margin both are positive then system is stable
• B. Gain margin is measured above the \(0\,dB\) axis, then system is unstable
• C. If the phase margin is measured below the \(-180^\circ\) axis, the system is stable
• D. Absolute and relative stability of only minimum-phase system can be determined

Hint:

For stability using Bode plots: \[ GM>0\;dB \] and \[ PM>0^\circ \] indicate a stable system. Negative gain margin or negative phase margin generally indicates instability.

Answer 1

The Correct Option is C

Concept: Bode plots are frequency-response plots used to determine stability, gain margin and phase margin of control systems. For a stable closed-loop system: \[ \text{Gain Margin} > 0\, dB \] and \[ \text{Phase Margin} > 0^\circ. \]

Step 1: Recall the definition of phase margin.
Phase margin is measured at the gain crossover frequency. \[ PM=180^\circ+\angle G(j\omega)H(j\omega) \] A positive phase margin indicates stability.

Step 2: Interpret a phase margin below \(-180^\circ\).
If the phase response goes below \[ -180^\circ, \] the phase margin becomes negative. A negative phase margin indicates that the system is unstable. Therefore the statement \[ \text{If phase margin is measured below } -180^\circ, \text{ system is stable} \] is false.

Step 3: Check the remaining options.
Option (A) is correct because positive gain margin and positive phase margin imply stability. Option (B) is correct because negative gain margin corresponds to instability. Option (D) is also a standard limitation associated with Bode-plot stability analysis.

Step 4: Final Answer.
Hence the incorrect statement is \[ \boxed{\text{Option (C)}} \]