Stability: phase margin and compensation
Stability: phase margin and compensation
💡 Key Takeaways
- Define stability in a feedback system and explain phase margin as a measure of how close the system is to instability.
- Read and interpret Bode plots to identify phase margin and gain margin.
- Explore compensation techniques (lead and lag) and how they modify phase margin to stabilize the system.
- Apply practical guidelines to set a target phase margin for robust, well-damped performance.
❓ Frequently Asked Questions
What is phase margin and why is it important?
Phase margin is the extra phase lag a feedback system can tolerate before becoming unstable. It is measured at the gain crossover (where |L(jω)| = 1); a larger phase margin means more stability and less risk of oscillations.
What does compensation mean in control systems?
Compensation means adding or adjusting a network in the feedback path to shape the loop gain for better stability and performance—for example, lead compensation to increase phase margin or lag compensation to improve steady-state accuracy.
What is a lead compensator, and how does it affect stability?
A lead compensator adds phase lead (positive phase) around a target frequency, increasing phase margin and speeding up the response. It helps improve stability without sacrificing too much low-frequency gain.
What is a lag compensator, and how does it affect stability?
A lag compensator adds low-frequency gain with a small phase lag, improving steady-state accuracy. It typically causes little change to bandwidth but can slightly reduce phase margin if the crossover moves to frequencies where the lag is more pronounced.
How do you read phase margin from a Bode plot?
Find the gain crossover (0 dB). Read the phase at that frequency; the phase margin is 180° plus that phase (for negative feedback).