viewGoal(Req,S)The plot shows that how much gain or phase variation a system can tolerate without
going unstable can depend on the frequency of the perturbation.
Gain and Phase Margins
For SISO systems, the gain and phase margins at a frequency ω indicate how much the
gain or phase of the open-loop response L(jω) can change without loss of stability. For
example, a gain margin of 5dB at 2 rad/s indicates that closed-loop stability is maintained
when the loop gain increases or decreases by as much as 5dB at this frequency. Gain and
phase margins typically vary across frequencies.
For MIMO systems, gain and phase margins are interpreted as follows:
- Gain margin: Stability is preserved when the gain increases or decreases by up to the
gain margin value in each channel of the feedback loop. - Phase margin: Stability is preserved when the phase increases or decreases by up to
the phase margin value in each channel of the feedback loop.
In MIMO systems, the gain or phase can change in all channels at once, and by a different
amount in each channel. The Margins Goal and TuningGoal.Margins rely on the notion
of disk margin for MIMO systems. (See “Stability Analysis Using Disk Margins” (Robust
Control Toolbox).) Like SISO stability margins, gain and phase margins in MIMO systems
typically vary across frequency.
Combined Gain and Phase Variations
To assess robustness to changes in both gain and phase, use the following chart.
Stability Margins in Control System Tuning