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.
Pole and Zero Locations
|Poles of dynamic system|
|Zeros and gain of SISO dynamic system|
|Natural frequency and damping ratio|
|Sort discrete-time poles by magnitude|
|Sort continuous-time poles by real part|
|Invariant zeros of linear system|
|Pole-zero plot of dynamic system|
|Plot pole-zero map for I/O pairs of model|