An Introduction to Disk Margins [Lecture Notes

Abstract

This article provides a tutorial introduction to disk margins. These are robust stability measures that account for simuitaneous gain and phase perturbations in a feedback system. The article first reviews the classical (gain only and phase -only) margins and their limitations. This motivates the use of disk margins, which are defined using a set of perturbations that has simuitaneous gain and phase variations. A necessary and sufficient condition is provided to compute the disk margin for a single -input, single -output feedback system. Frequency -dependent disk margins can also be computed, yielding additional insight. The article concludes with a discussion of stability margins for multiple -input, multiple output (MIMO) feedback systems. A typical approach is to assess robust stability "loop -at -a -time," with a perturbation introduced into a single channel and all other channels held at their nominal values. MIMO disk margins provide a useful extension to consider simultaneous variations in multiple channels. This multiloop analysis can provide a more accurate robustness assessment as compared to the one -loop -at -a -time approach.