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- Title
Robust non-linear control design for systems governed by Burgers' equation subjected to parameter variation.
- Authors
Abbasi, Farshid; Velni, Javad Mohammadpour
- Abstract
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 v 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 v0. 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.
- Subjects
NONLINEAR control theory; ROBUST control; BURGERS' equation; PARAMETERS (Statistics); NEUMANN boundary conditions; SLIDING mode control
- Publication
IET Control Theory & Applications (Wiley-Blackwell), 2018, Vol 12, Issue 5, p582
- ISSN
1751-8644
- Publication type
Article
- DOI
10.1049/iet-cta.2017.0994