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Sliding Mode Control for an Inhomogeneous Heat Equation with Global Constraint
Author(s) -
Zhang Shuang
Publication year - 2017
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1607
Subject(s) - constraint (computer aided design) , control theory (sociology) , bounded function , heat equation , sliding mode control , tracking error , generalization , mode (computer interface) , control signal , control (management) , stability (learning theory) , tracking (education) , basis (linear algebra) , track (disk drive) , mathematics , computer science , law , engineering , control system , mathematical analysis , physics , nonlinear system , mechanical engineering , geometry , quantum mechanics , artificial intelligence , machine learning , political science , electrical engineering , operating system , psychology , pedagogy
In this paper, an inhomogeneous heat equation with distributed load is controlled, on the basis of an infinite dimensional generalization of sliding‐mode control method. The control law is designed so that: (i) the temperature can track a desired reference signal, and (ii) the temperature can remain in a constrained region. We show that, with the designed control, the tracking error is bounded stable without violation of the constraint. The stability is proved under the designed control law. Numerical simulations are given to illustrate the effectiveness of the designed control law.