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Direct reduced order discretization of continuous‐time controller
Author(s) -
Anderson B. D. O.,
Chongsrid K.,
Limebeer D. J. N.,
Hara S.
Publication year - 1999
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199903)9:3<143::aid-rnc397>3.0.co;2-o
Subject(s) - discretization , controller (irrigation) , control theory (sociology) , approximation error , reduction (mathematics) , discrete time and continuous time , computer science , mathematics , discretization error , sampling (signal processing) , filter (signal processing) , mathematical optimization , control (management) , mathematical analysis , statistics , geometry , artificial intelligence , agronomy , computer vision , biology
In this paper, we investigate the problem of closed‐loop approximation of a continuous‐time controller by a low‐order discrete‐time controller with sample and hold devices and an anti‐aliasing filter. The problem is first reduced to an open‐loop problem of sampled‐data controller reduction with continuous‐time weights. The operator representing the error in approximation can be approximated (arbitrarily closely) by a time‐invariant discrete‐time system resulting from applying fast sampling and lifting. We propose a method for obtaining a low‐order discrete‐time controller which makes small the approximation error based on recasting the approximation problem as a four‐block ℋ ∞ problem. The latter can be solved efficiently by the method proposed by Glover et al . We also give a numerical example to verify the effectiveness of the method. Copyright © 1999 John Wiley & Sons, Ltd.