Stability Analysis using Bode Plots

From the Bode plots, we can say whether the control system is stable, marginally stable or unstable based on the values of these parameters.

• Gain cross over frequency and phase cross over frequency
• Gain margin and phase margin

Phase Cross over Frequency

The frequency at which the phase plot is having the phase of -180⁰ is known as phase cross over frequency. It is denoted by ωpc. The unit of phase cross over frequency is rad/sec.

Gain Cross over Frequency

The frequency at which the magnitude plot is having the magnitude of zero dB is known as gain cross over frequency. It is denoted by ωgcωgc. The unit of gain cross over frequency is rad/sec.

The stability of the control system based on the relation between the phase cross over frequency and the gain cross over frequency is listed below.

·        If the phase cross over frequency ωpcωpc is greater than the gain cross over frequency ωgcωgc, then the control system is stable.

·        If the phase cross over frequency ωpcωpc is equal to the gain cross over frequency ωgcωgc, then the control system is marginally stable.

·        If the phase cross over frequency ωpcωpc is less than the gain cross over frequency ωgcωgc, then the control system is unstable.

Gain Margin

Gain margin GMGM is equal to negative of the magnitude in dB at phase cross over frequency.