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APPROXIMATE LINEARIZATION OF CONTROL SYSTEMS WITH DISCONTINUOUS NON‐LINEARITIES
Author(s) -
Cebuhar Wenceslao A.
Publication year - 1995
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/j.1099-1514.1995.tb00025.x
Subject(s) - control theory (sociology) , linearization , feed forward , heuristic , dither , feedback linearization , context (archaeology) , simple (philosophy) , mathematics , nonlinear system , computer science , control (management) , mathematical optimization , control engineering , engineering , paleontology , philosophy , physics , epistemology , quantum mechanics , artificial intelligence , noise shaping , computer vision , biology
SUMMARY The class of systems containing elements with discontinuous input‐output characteristics (such as jumps, hysteresis, etc.) presents a serious challenge to control specialists. They are so difficult to treat analytically that they are normally dealt with using heuristic methods. In this paper a mathematical framework for such problems is presented and precise criteria for measuring the non‐linearity are introduced. Linearization is considered in a restricted but realistic sense (on average or at discrete times only). In this context the most common practical techniques such as dithering and pulse width modulation are analysed. In addition, a simple new approach for feedforward control is developed. It produces a locally optimal control, providing results that are superior to those from more standard precompensation techniques. An application of these ideas to a small travelling wave motor is included. Such motors have considerable dry friction and therefore provide significant examples of the kind of systems under consideration.