IntermediateTopic 54 of 101Signals, Control & Comms
Gain and phase margin
Measures of how far a system is from instability.
In depth
Gain margin: factor by which gain can increase before instability at the phase-crossover frequency; phase margin: extra phase lag allowed at the gain-crossover frequency (0 dB). Typical targets: GM >6 dB, PM 45–60°. PM≈100ζ for second-order systems. Margins indicate robustness to uncertainty and delay.
Key points
- Delay reduces phase margin
- Read from Bode plot
- Sensitivity peak
ExampleA phase margin of 60° gives about 10% overshoot in many loops.
What is Gain and phase margin?
Measures of how far a system is from instability.
Why is it important to understand gain and phase margin?
Gain and phase margins tell you how much room the design has before instability, which is essential for robust control.
What is gain margin?
The amount of gain increase that would make the loop unstable, measured at the frequency where the phase is minus 180 degrees.
What is phase margin?
The extra phase lag needed to reach instability at the frequency where the loop gain is one.
How is Gain and phase margin used in practice?
Typical applications include checking that a loop has at least 6 dB of gain margin for safety, adjusting a controller so the phase margin is 45 degrees and explaining why a loop becomes oscillatory after a sensor is replaced by a slower one.
What should I learn before Gain and phase margin?
Study "Frequency response methods" first (topic 53 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Gain and phase margin?
Delay reduces phase margin. Read from Bode plot. Sensitivity peak.
Can you give an example of Gain and phase margin?
A phase margin of 60° gives about 10% overshoot in many loops.
What comes after Gain and phase margin?
The next topic is "Nyquist stability criterion", which builds directly on this one.
How difficult is Gain and phase margin?
It is classed as Intermediate in Signals, Control & Comms (topic 54 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.