Calculadora de Margen de Fase Gratis
Determina el margen de fase de un sistema de lazo abierto para evaluar la estabilidad relativa.
Approximate Phase Margin
51.83 °
Approximate Phase Margin vs Damping Ratio (zeta)
Fórmula
## Phase Margin Phase margin is the additional phase lag that would bring the system to the verge of instability. It is measured at the gain crossover frequency (where the open-loop gain equals 1). ### Approximation for Second-Order Systems For a standard second-order system, the phase margin can be approximated from the damping ratio. A useful rule of thumb is PM ≈ 100 × zeta (in degrees) for zeta between 0.1 and 0.7. Adequate phase margin (typically 30-60°) ensures robustness against modeling errors and parameter variations.
Ejemplo Resuelto
A system with damping ratio zeta = 0.5.
- 014*zeta^4 = 4 × 0.0625 = 0.25
- 02sqrt(1 + 0.25) = sqrt(1.25) = 1.1180
- 03-2 × 0.25 + 1.1180 = 0.6180
- 042 × 0.5 / sqrt(0.6180) = 1.0 / 0.7861 = 1.2721
- 05PM = atan(1.2721) × 180/pi = 51.8°
- 06Simple approximation: 100 × 0.5 = 50°
Preguntas Frecuentes
What is a good phase margin?
A phase margin of 45-60° is generally considered good for industrial control systems. Below 30° the system becomes excessively oscillatory and sensitive to parameter changes. Above 70° may be unnecessarily conservative.
What happens when phase margin is zero?
Zero phase margin means the system is on the boundary of instability. Any small disturbance or parameter change could make the system oscillate indefinitely. Negative phase margin means the system is unstable.
How is phase margin measured experimentally?
Inject a sinusoidal signal into the open loop and measure the frequency response (Bode plot). Find the frequency where gain = 0 dB (gain crossover). The phase at that frequency plus 180° is the phase margin.
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