Open AccessRobust non‐linear control design for systems governed by Burgers' equation subjected to parameter variation
Author(s) -
Abbasi Farshid,
Mohammadpour Velni Javad
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0994
Subject(s) - control theory (sociology) , mathematics , controller (irrigation) , a priori and a posteriori , robust control , approximation error , tracking error , burgers' equation , control system , mathematical analysis , partial differential equation , computer science , control (management) , engineering , agronomy , biology , epistemology , artificial intelligence , philosophy , electrical engineering
In this study, a robust sliding mode controller is proposed for dynamic systems governed by Burgers' equation with Neumann boundary conditions in the presence of parameter variations. The main objective is to design a reduced‐order model based controller at a nominal value of the system parameter that stabilises the full‐order model while being robust with respect to model uncertainties in the obtained reduced‐order model. The model uncertainties resulted from the variation of the parameter ν are discussed under two categories; first, the error arising from the change in the states of the full‐order model, and second, the error associated with the estimated proper orthogonal decomposition basis functions at the nominal value of ν 0 . In this work, the boundedness of the error functions is studied and an estimation of these bounds is obtained in terms of the reduced‐order model and matrices of the full‐order system that are known a priori . Next, the bounds on the error functions are used to design a reduced‐order sliding mode controller that guarantees the stability of the full‐order model obtained via a finite element approximation of the Burgers' equation for a trajectory tracking problem.