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Distributed control of nonlinear diffusion systems by input–output linearization
Author(s) -
Maidi Ahmed,
Corriou JeanPierre
Publication year - 2014
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/rnc.2892
Subject(s) - heat equation , control theory (sociology) , nonlinear system , linearization , distributed parameter system , controller (irrigation) , feedback linearization , nonlinear control , mathematics , semigroup , boundary (topology) , diffusion , diffusion equation , stability (learning theory) , partial differential equation , computer science , mathematical analysis , control (management) , engineering , physics , metric (unit) , operations management , quantum mechanics , artificial intelligence , machine learning , agronomy , biology , thermodynamics
SUMMARY This paper addresses the distributed control by input–output linearization of a nonlinear diffusion equation that describes a particular but important class of distributed parameter systems. Both manipulated and controlled variables are assumed to be distributed in space. The control law is designed using the concept of characteristic index from geometric control by using directly the PDE model without any approximation or reduction. The main idea consists in the control design in assuming an equivalent linear diffusion equation obtained by use of the Cole–Hopf transformation. This framework helps to demonstrate the closed‐loop stability using some concepts from the powerful semigroup theory. The performance of the proposed controller is successfully tested, through simulation, by considering a nonlinear heat conduction problem concerning the control of the temperature of a steel plate modeled by a nonlinear heat equation with Dirichlet boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd.