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

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4 Author(s)
F. Blanchini ; Dept. of Math. & Comput. Sci., Univ. of Udine, Italy ; A. Lepschy ; S. Miani ; U. Viaro

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.

Published in:

IEEE Transactions on Automatic Control  (Volume:49 ,  Issue: 5 )