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_\infty 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_\infty 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.

Characterization of PID and Lead/Lag compensators satisfying given H_infty specifications

BLANCHINI, Franco;MIANI, Stefano;VIARO, Umberto
2004-01-01

Abstract

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_\infty 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_\infty 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/881800
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