Stability Margins


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Stability Margins
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1 Introduction to Stability Margins

Stability margins are essentially metrics for the stability and performance of the closed loop system. The higher the margins the more stable the system will be and the smaller the transient response oscillations will be.

Many SISO systems behave similarly. Specifically they behave in such a way that when the gain increases past a critical point the system becomes unstable.

1.1 Stability Margin Guidelines

See Also

It is often difficult to sum up the "goodness" of a controller design. The most common metrics of a control system are

  • Phase Margin
  • Gain Margin

Other common metrics are

  • Open Loop Crossover Frequency
  • Closed Loop Bandwidth (typically 1.5 to 2x the Open Loop Crossover)
  • Disturbance Rejection Bandwidth (typically approximately 1/3 the Closed Loop Bandwidth or 3/5 the Open Loop Crossover)
  • Closed Loop Peaking (max value of the Closed Loop frequency response)
  • Disturbance Rejection Peaking

Conservative closed loop margins are:

Phase: > 40 deg
Gain: > 12 dB

Typically the transient response of systems with phase margin less than 40 deg oscillate and the lower the phase margin the more the system will oscillate. Lower gain margins don't seem to have the same transient response issues. However, the system is less robust to system gain changes. My experience suggests that sensor scale factors can change with environmental conditions such as temperature.