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Characterization of PID and lead/lag compensators satisfying given H∞ specifications

机译：满足给定H∞规格的PID和超前/滞后补偿器的特性

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摘要

This note deals with the problem of characterizing a class of second-order three-parameter controllers [including proportional-integral-derivative (PID) and lead/lag compensators] satisfying given H∞ closed-loop specifications. Design characterizations of similar form as in the recent work on PID control, are derived for a larger class of compensators using simple geometric considerations. Specifically it is shown that, given the value of one parameter: i) the region of the plane defined by the other two parameters where the considered H∞ constraint is satisfied, consists of the union of disjoint convex sets whose number can be bounded by means of the pancake-cutting formula, and ii) the closed-loop pole distribution can be related to them. An example illustrates how the method can be applied to design a PID controller in the case of bounded sensitivity.
机译：本文讨论了表征满足给定H∞闭环规格的一类二阶三参数控制器（包括比例积分微分（PID）和超前/滞后补偿器）的问题。使用简单的几何考虑因素，为一类较大的补偿器推导了与最近的PID控制工作类似的设计特征。具体来说，它表明，给定一个参数的值：i）由其他两个参数定义的满足H∞约束的平面区域由不相交凸集的并集组成，其数目可以通过煎饼切割公式的公式，ii）闭环极点分布可能与它们有关。一个示例说明了在有限灵敏度的情况下如何将该方法应用于设计PID控制器。

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