Frequency response and the Bode plot
A graph of how the output's magnitude and phase change with frequency when a sine wave is put in. Stability is judged from the phase and gain margins.
Bode plot
The horizontal axis is frequency (logarithmic) and there are two vertical axes.
- Magnitude (dB): the output/input ratio. 20 dB = 10×, 0 dB = 1×
- Phase (°): how far the output lags the input
Stability margins
On the Bode plot of the open loop L(s) = C·P
| Measure | Where to read it | Meaning | Target |
|---|---|---|---|
| Phase margin | Phase + 180° at the frequency where the magnitude is 0 dB | Room to survive more delay | 45 to 60° |
| Gain margin | The negative of the magnitude at the frequency where the phase is -180° | Room to survive more gain | 6 dB or more |
A small phase margin means more overshoot and ringing in the step response. Roughly, a 45° phase margin gives around 20% overshoot.
RoadmapSee where this note sits in Control Engineering→Bandwidth
The frequency at which the closed-loop magnitude falls to -3 dB. It says how fast a change in target the system can follow. The current-loop bandwidth is usually set at 5 to 10 times that of the speed loop.
Measuring
Besides simulation, you can measure a Bode plot on a real system by feeding in a small sine-wave target at several frequencies and recording the output. The frequency-response feature in motor-drive tuning tools works this way.