1. What is Gain And Phase Margin?

Gain Margin (GM) and Phase Margin (PM) are critical stability measures in control systems. GM indicates how much gain can increase before system instability, while PM shows how much phase shift can be tolerated.

2. How Does the Calculator Work?

The calculator uses the standard formulas:

Where:

• \( |G(j\omega_{pc})| \) — Magnitude of transfer function at phase crossover frequency
• \( \arg(G(j\omega_{gc})) \) — Phase angle of transfer function at gain crossover frequency

Explanation: These margins quantify the relative stability of a control system and its robustness to parameter variations.

3. Importance of Stability Margins

Details: Adequate gain and phase margins ensure system stability and performance. Typical design requirements: GM > 6 dB and PM > 30-60 degrees.

4. Using the Calculator

Tips: Enter the magnitude of the transfer function at phase crossover frequency and the phase angle at gain crossover frequency. Ensure values are from Bode plot analysis.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for stability margins?
A: For most systems, GM > 6 dB and PM > 30° provide adequate stability. Higher margins indicate more robust systems.

Q2: How are crossover frequencies determined?
A: Phase crossover frequency (ω_pc) is where phase angle is -180°. Gain crossover frequency (ω_gc) is where magnitude is 0 dB.

Q3: What happens if margins are too small?
A: Small margins indicate poor stability - the system may oscillate or become unstable with small parameter changes.

Q4: Can margins be negative?
A: Yes, negative margins indicate instability. The system will oscillate or diverge under normal operation.

Q5: How do these relate to Nyquist stability criterion?
A: Gain and phase margins provide quantitative measures of how close the Nyquist plot is to the (-1,0) point.