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Stability Analysis

Gain and phase margins, pole and zero locations

Stability is a standard requirement for control systems to avoid loss of control and damage to equipment. For linear feedback systems, stability can be assessed by looking at the poles of the closed-loop transfer function.

Gain and phase margins measure how much gain or phase variation at the gain crossover frequency will cause a loss of stability. Together, these two quantities give an estimate of the safety margin for closed-loop stability. The smaller the stability margins, the more fragile stability is.


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polePoles of dynamic system
zeroZeros and gain of SISO dynamic system
dampNatural frequency and damping ratio
dsortSort discrete-time poles by magnitude
esortSort continuous-time poles by real part
tzeroInvariant zeros of linear system
pzmapPole-zero plot of dynamic system
iopzmapPlot pole-zero map for I/O pairs of model
allmarginGain margin, phase margin, delay margin, and crossover frequencies
marginGain margin, phase margin, and crossover frequencies