Distributed parameter systems; Sliding mode; Sobolev space; State observer; Strongly continuous semigroup; Complementary analysis; Convection-diffusion models; Error dynamics; Infinite dimensional; Linear reaction; Sliding modes; Sliding-mode observer; States observer; Control and Systems Engineering; Computer Science (all); Mechanical Engineering; Electrical and Electronic Engineering; General Computer Science
Abstract :
[en] Significant improvements and a thorough complementary analysis are proposed for an infinite-dimensional sliding mode state observer for a linear reaction–convection–diffusion system subject to bounded disturbances, that was analyzed in Dimassi et al. (2018). Compared to the previous article, the observer model features a simplified discontinuous input applied on the error dynamics such that the on-line computation of the state time derivative at the boundary is no longer needed. An abstract representation of the state observer is given, and a particular attention is paid to its well-posedness on a Sobolev space despite the discontinuity. The exponential stability of the error dynamics is established by considering one boundary measurement and a continuous approximation of the discontinuous input. The results are illustrated by means of numerical simulations.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Mohet, Judicaël ; University of Namur, Department of Mathematics and naXys, Namur, Belgium
Hastir, Anthony ; University of Namur, Department of Mathematics and naXys, Namur, Belgium
Dimassi, Habib; University of Sousse, High Institute of applied sciences and technology of Sousse, Cité Taffala (Ibn Khaldoun), Sousse, Tunisia
Winkin, Joseph J.; University of Namur, Department of Mathematics and naXys, Namur, Belgium
Vande wouwer, Alain ; Université de Mons - UMONS > Faculté Polytechniqu > Service Systèmes, Estimation, Commande et Optimisatio
Language :
English
Title :
Infinite-dimensional sliding mode observer analysis for a disturbed linear reaction–convection–diffusion model
F107 - Systèmes, Estimation, Commande et Optimisation
Research institute :
Research Institute for Biosciences
Funders :
Fonds De La Recherche Scientifique - FNRS
Funding text :
This research was conducted with the financial support of F.R.S-FNRS. Anthony Hastir is a FNRS Research Fellow under the grant CR 40010909 and was previously under the grant FC 29535. The authors wish to thank the anonymous reviewers for their constructive comments, which helped them to improve the original manuscript significantly.
Levaggi, L., Sliding modes in Banach spaces. Differential Integral Equations, 15, 2002.
Spurgeon, S.K., Sliding mode observers: A survey. Int. J. Syst. Sci. 39 (2008), 751–764.
Guo, R., Li, Y., Lv, M., Design of infinite sliding mode state observer with application to CO2 absorption system of space station. Acta Astronaut., 161, 2019.
Pisano, A., Orlov, Y., Usai, E., Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J. Control Optim. 49:2 (2011), 363–382, 10.1137/090781140.
Cristofaro, A., Robust distributed control of quasilinear reaction–diffusion equations via infinite-dimensional sliding modes. Automatica 104 (2019), 165–172, 10.1016/j.automatica.2019.02.039.
Dimassi, H., Winkin, J., Vande Wouwer, A., A sliding mode observer for a linear reaction–convection–diffusion equation with disturbances. Systems Control Lett., 2018, 40–48.
Winkin, J., Dochain, D., Ligarius, P., Dynamical analysis of distributed parameter tubular reactors. Automatica, 2000, 349–361.
Mott, H., Green, A., On Danckwerts’ boundary conditions for the plug-flow with dispersion/reaction model. Chem. Eng. Commun. 202:6 (2015), 739–745.
Paulsen, V.I., Raghupathi, M., An Introduction to the Theory of Reproducing Kernel Hilbert Spaces Cambridge Studies in Advanced Mathematics, 2016, Cambridge University Press, 10.1017/CBO9781316219232.
Hastir, A., Mohet, J., Winkin, J.J., A frequency domain approach to Kalman filtering on Hilbert spaces: Application to Sturm–Liouville systems with pointwise measurement. Annu. Rev. Control 55 (2023), 379–389, 10.1016/j.arcontrol.2023.02.003.
Curtain, R., Zwart, H., Introduction to Infinite-Dimensional Systems Theory: A State-Space Approach. 2020, Springer Verlag.
Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations Applied mathematical sciences, 1983, Springer, New York, United States.
V. Utkin, H. Lee, Chattering Problem in Sliding Mode Control Systems, in: International Workshop on Variable Structure Systems, 2006. VSS’06, 2006, pp. 346–350, http://dx.doi.org/10.1109/VSS.2006.1644542.
H.K. Khalil, High-gain observers in nonlinear feedback control, in: 2008 International Conference on Control, Automation and Systems, 2008, pp. xlvii–lvii.
