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.

中文翻译：

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磁盘边距简介 [讲义]


本文提供了有关磁盘边距的教程介绍。这些是鲁棒的稳定性测量，可以解释反馈系统中的同时增益和相位扰动。本文首先回顾了经典的（仅增益和仅相位）裕度及其局限性。这激发了磁盘裕度的使用，磁盘裕度是使用一组具有同时增益和相位变化的扰动来定义的。提供了计算单输入、单输出反馈系统的盘余量的充分必要条件。还可以计算与频率相关的磁盘裕度，从而产生额外的洞察力。本文最后讨论了多输入多输出 (MIMO) 反馈系统的稳定性裕度。典型的方法是“一次循环”评估鲁棒稳定性，将扰动引入单个通道，并将所有其他通道保持在其标称值。 MIMO 磁盘余量提供了一个有用的扩展来考虑多个通道中的同时变化。与一次一个循环的方法相比，这种多循环分析可以提供更准确的鲁棒性评估。