Instant Notes: 5. Stability Analysis
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Gain Margin and Phase Margin: Refer to Fig.(21). Gain margin is a measure of how far the system is from the brink of instability. \[\text{Gain margin} = \frac{1}{M} > 1 \quad \Longrightarrow \quad \text{Stable system}\] A gain margin of greater than 1.7 is usually employed as a safety factor while tuning the controller. The higher the value of gain margin above unity, the more safer the operation of the process being controlled.
Phase margin is the additional lag needed to destabilize the system. \[\text{Phase margin} = 180  \phi_p\] where \(\phi_p\) = phase lag at the frequency for which AR = 1.