“Tube Model Predictive Control with an Auxiliary Sliding Mode Controller”
Authors: Miodrag Spasic, Morten Hovd, Darko Mitic and Dragan Antic,Affiliation: University of Nis, Serbia and NTNU, Department of Engineering Cybernetics
Reference: 2016, Vol 37, No 3, pp. 181-193.
Keywords: Model Predictive Control, robustness, Sliding Mode Control, Mixed Integer Linear Program
Abstract: This paper studies Tube Model Predictive Control (MPC) with a Sliding Mode Controller (SMC) as an auxiliary controller. It is shown how to calculate the tube widths under SMC control, and thus how much the constraints of the nominal MPC have to be tightened in order to achieve robust stability and constraint fulfillment. The analysis avoids the assumption of infinitely fast switching in the SMC controller.
PDF (1747 Kb)
DOI: 10.4173/mic.2016.3.4DOI forward links to this article:
| [1] Miodrag Spasic, Darko Miti, Morten Hovd and Dragan Antic (2017), doi:10.1109/SISY.2017.8080561 |
| [2] Miroslav B. Milovanovic, Dragan S. Antic, Marko T. Milojkovic and Miodrag D. Spasic (2022), doi:10.1109/TCYB.2020.2998505 |
| [3] David Bedolla-Martinez, Yassine Kali, Maarouf Saad, Cristobal Ochoa-Luna and Mohammad Habibur Rahman (2023), doi:10.1016/j.engappai.2023.106966 |
| [4] David Bedolla-Martinez, Yassine Kali, Maarouf Saad, Cristobal Ochoa Luna and Mohammad H. Rahman (2023), doi:10.1109/PEDS57185.2023.10246735 |
| [5] Miodrag SPASI , Darko MITI , Sa a S. NIKOLI , Marko MILOJKOVI , Miroslav MILOVANOVI and An ela OR EVI (2024), doi:10.59277/PRA-SER.A.25.3.09 |
| [6] Miodrag Spasi , Darko Miti , Dragan Anti , Nikola Dankovi and Sa a S Nikoli (2024), doi:10.1177/00202940241302672 |
[1] Bemporad, A. and Morari, M. (1999). Bemporad, A, and Morari, M. Control of systems integrating logic, dynamics, and constraints. Automatica. 35(3):407 -- 427. doi:10.1016/S0005-1098(98)00178-2
[2] Bemporad, A., Morari, M., Dua, V., and Pistikopoulos, E.N. (2002). Bemporad, A, , Morari, M., Dua, V., and Pistikopoulos, E.N. The explicit linear quadratic regulator for constrained systems. Automatica. 38:3--20. doi:10.1016/S0005-1098(01)00174-1
[3] Benattia, S.E., Tebbani, S., and Dumur, D. (2015). Benattia, S, E., Tebbani, S., and Dumur, D. Hierarchical control strategy based on robust mpc and integral sliding mode - application to a continuous photobioreactor. In Proceedings of 5th IFAC Conference on Nonlinear Model Predictive Control. pages 212--217. doi:10.1016/j.ifacol.2015.11.285
[4] Corradini, M.L. and Orlando, G. (1997). Corradini, M, L. and Orlando, G. A vsc algorithm based on generalized predictive control. Automatica. 33(5):927--932. doi:10.1016/S0005-1098(96)00229-4
[5] Furuta, K. (1990). Furuta, K, Sliding mode control of a discrete system. Systems & Control Letters. 14(2):145--152. doi:10.1016/0167-6911(90)90030-X
[6] Garcia-Gabin, W., Zambrano, D., and Camacho, E.F. (2009). Garcia-Gabin, W, , Zambrano, D., and Camacho, E.F. Sliding mode predictive control of a solar air conditioning plant. Control Engineering Practice. 17(6):652--663. doi:10.1016/j.conengprac.2008.10.015
[7] Golo, G. and Milosavljevic, C. (2000). Golo, G, and Milosavljevic, C. Robust discrete-time chattering free sliding mode control. Systems & Control Letters. 41(1):19--28. doi:10.1016/S0167-6911(00)00033-5
[8] Incremona, G.P., Ferrara, A., and Magni, L. (2015). Incremona, G, P., Ferrara, A., and Magni, L. Hierarchical model predictive/sliding mode control of nonlinear constrained uncertain systems. In Proceedings of 5th IFAC Conference on Nonlinear Model Predictive Control. pages 102--109. doi:10.1016/j.ifacol.2015.11.268
[9] Inteco. (2011). Inteco, Modular Servo System - Manual. Inteco. .
[10] Mignone, D. (2001). Mignone, D, The REALLY BIG Collection of Logic Propositions and Linear Inequalities. Technical report. http://control.ee.ethz.ch/index.cgi?action=details;id=377;page=publications, .
[11] Milosavljevic, C. (1985). Milosavljevic, C, General conditions for the existence of a quasisliding mode on the switching hyperplane in discrete variable structure systems. Automation and Remote Control. 46(3):307--314. .
[12] Milosavljevic, C. (2004). Milosavljevic, C, Discrete-time vss. In A.Sabanovic, L.Fridman, and S.Spurgeon, editors, Variable Structure Systems: from Principles to Implementation, chapter5, pages 99--128. The Institution of Engineering and Technology, London. doi:10.1049/PBCE066E
[13] Mitic, D., Spasic, M., Hovd, M., and Antic, D. (2013). Mitic, D, , Spasic, M., Hovd, M., and Antic, D. An approach to design of sliding mode based generalized predictive control. In Proceedings of IEEE 8th International Symposium on Applied Computational Intelligence and Informatics (SACI) 2013. pages 347--351, 2013. doi:10.1109/SACI.2013.6608996
[14] Neelakantan, V.A. (2005). Neelakantan, V, A. Modeling, design, testing and control of a two-stage actuation mechanism using piezoelectric actuators for automotive applications. Ph.D. thesis, Ohio State University, Department of Mechanical Engineering. .
[15] Qin, S.J. and Badgwell, T.A. (2003). Qin, S, J. and Badgwell, T.A. A survey of industrial model predictive control technology. Control Engineering Practice. pages 733--764. doi:10.1016/S0967-0661(02)00186-7
[16] Rakovic, S.V., Kerrigan, E.C., Kouramas, K.I., and Mayne, D.Q. (2005). Rakovic, S, V., Kerrigan, E.C., Kouramas, K.I., and Mayne, D.Q. Invariant approximations of the minimal robustly positively invariant sets. IEEE Transactions on Automatic Control. pages 406 -- 410. doi:10.1109/TAC.2005.843854
[17] Rawlings, J.B. and Mayne, D.Q. (2009). Rawlings, J, B. and Mayne, D.Q. Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison, Wisconsin, USA. .
[18] Rubagotti, M., Castanos, F., Ferrara, A., and Fridman, L. (2011). Rubagotti, M, , Castanos, F., Ferrara, A., and Fridman, L. Integral sliding mode control for nonlinear systems with matched and unmatched perturbations. IEEE Transactions on Automatic Control. 56(11):2699--2704. doi:10.1109/TAC.2011.2159420
[19] Su, W.-C., Drakunov, S.V., and Ozguner, U. (2000). Su, W, -C., Drakunov, S.V., and Ozguner, U. An o(t2) boundary layer in sliding mode for sampled-data systems. IEEE Transactions on Automatic Control. 45(3):482--485. doi:10.1109/9.847728
[20] Utkin, V.I. (1978). Utkin, V, I. Sliding Modes and Their Applications in Variable Structure Systems. MIR, Moscow, USSR. .
[21] Young, K.D., Utkin, V.I., and Ozguner, U. (1999). Young, K, D., Utkin, V.I., and Ozguner, U. A control engineer's guide to sliding mode control. IEEE Transactions on Control Systems Technology. 7(3):328--342. doi:10.1109/87.761053
[22] Yu, X. and Kaynak, O. (2009). Yu, X, and Kaynak, O. Sliding-mode control with soft computing: A survey. IEEE Transactions on Industrial Electronics. 56(9):3275--3285. doi:10.1109/TIE.2009.2027531
BibTeX:
@article{MIC-2016-3-4,
title={{Tube Model Predictive Control with an Auxiliary Sliding Mode Controller}},
author={Spasic, Miodrag and Hovd, Morten and Mitic, Darko and Antic, Dragan},
journal={Modeling, Identification and Control},
volume={37},
number={3},
pages={181--193},
year={2016},
doi={10.4173/mic.2016.3.4},
publisher={Norwegian Society of Automatic Control}
};