Abstract
In this paper, we present an innovative strategy for nonlinear model predictive control by employing a discrete-time NARX-Laguerre model. This latter model is crafted through the expansion of discrete-time NARX model parameters using a set of five independent Laguerre bases. A notable benefit of this approach is a substantial reduction in the number of parameters compared to the classical NARX model. However, the realization of this reduction depends on the careful selection of optimal Laguerre poles that define these bases. The parameters of the NARX-Laguerre model are determined through a recursive methodology. This resulting model is subsequently applied in the implementation of nonlinear model predictive control. To formulate the optimization problem, we incorporate a performance criterion that takes into account both process input and output constraints. We assess the effectiveness of this novel approach to nonlinear model predictive control through experimentation on the Twin Rotor System.
Similar content being viewed by others
References
Adaily S, Mbarek A, Garna T, Ragot J (2018) Optimal multimodel representation by laguerre filters applied to a communicating two tank system. J Syst Sci Complex 31:621–646
Benabdelwahed I, Mbarek A, Bouzrara K, Garna T (2018) Non-linear system modelling based on NARX model expansion on Laguerre orthonormal bases. IET Signal Process 12:228–241
Benabdelwahed I, Mbarek A , Bouzrara K (2019) Model predictive control of 2-DOF helicopter based on MIMO ARX-Laguerre model. In: 6th international conference on electrical and electronics engineering (ICEEE), 16–17 April , Istanbul Turkey
Billings SA (1980) Identification of nonlinear systems-a survey. IEE Proc-D Control Theory Appl 127:272–285. https://doi.org/10.1049/ip-d.1980.0047
Bonassi F, Xie J, Farina M, and Scattolini R (2022) An offset-free nonlinear MPC scheme for systems learned by Neural NARX models. In: 2022 IEEE 61st conference on decision and control (CDC). pp 2123–2128
Bouzrara K, Garna T, Mbarek A (2013) Non-linear predictive controller for uncertain process modelled by GOBF-Volterra models. Int J Model Identif Control 19(4):307–322
Bouzrara K, Garna T, Ragot J, Messaoud H (2012) Decomposition of an ARX model on orthonormal Laguerre bases. ISA Trans 51:848–860
El Anes A, Bouzrara K, Ragot J (2018) Reduced model of linear systems via Laguerre filters. Trans Inst Meas Control 40(5):1510–1520
El Anes A, Bouzrara K (2017) Parameter complexity reduction of multivariable systems using genetic algorithm. ICCAD’17, Hammamet - Tunisia, January 19–21
El Anes A, Maraoui S, Bouzrara K (2017) Gradient method for optimal expansions of MIMO ARX model on Laguerre bases. ICCAD’17, Hammamet - Tunisia, January 19–21
El Anes A, Maraoui S, Bouzrara K (2016) Order reduction of MIMO ARX systems using Laguerre bases. Int J Eng Syst Model Simul 8:307–315
El Anes A, Maraoui S, Bouzrara K (2016) Optimal expansions of multivariable ARX processes on Laguerre bases via the Newton-Raphson method. Int J Adapt Control Signal Process 30:578–598
Feng K, Jiangang L, Jinshui C (2015) Nonlinear model predictive control based on support vector machine and genetic algorithm. Chin J Chem Eng 23:2048–2052
Garna T, Bouzrara K, Ragot J, Messaoud H (2013) Nonlinear system modeling based on bilinear Laguerre orthonormal bases. ISA Trans 52:301–317
Gnaba S, Garna T, Bouzrara K, Hassani RJM (2014) Online identification of the bilinear model expansion on Laguerre orthonormal bases. Int J Control 87:441–463
Jin Q, Wu S, Zhang R (2018) Improved constrained model predictive tracking control for networked coke furnace systems over uncertainty and communication loss. IEEE Trans Syst Man Cybern Syst 99:1–8
Mali P, Jagtap B, Pawar K (2012) Nonlinear process identification and model predictive control using neural network. Int J Eng Technol (IJET) 4:341–348
Marouani G, Mbarek A, Messaoud GTH (2015) Nonlinear model based predictive control using multiple models approach expanded on Laguerre bases. WSEAS Trans Syst Control 10:113–126
Mbarek A, Garna T, Bouzrara K (2020) System modeling based on ARX-Laguerre bases: system modeling based on Laguerre bases with filters on model input and output. LAP LAMBERT Academic Publishing, London
Mbarek A, Bouzrara K, Garna T, Ragot J, Messaoud H (2015) Laguerre-based modelling and predictive control of multi-input multi-output systems applied to a communicating two-tank system (CTTS). Trans Inst Meas Control 39(5):611–624. https://doi.org/10.1177/0142331215613150
Miguel AL-C, Garcia AP (2023) Linear and nonlinear model predictive control (MPC) for regulating pedestrian flows with discrete speed instructions. Phys A Stat Mech Appl 625:128996
Noraini M, Norashid A (2015) Control of bioethanol fermentation process: NARX-based MPC (NARX-MPC) versus linear-based MPC (LMPC). Chem Eng Trans (CET) 45:1297–1302
Peng H, Jiwei W, Vladimir S, Fei L, Xiaoli L (2022) Finite-time control of discrete-time semi-Markov jump linear systems: a self-triggered MPC approach. J Franklin Inst 359:6939–6957
Ramesh K, AbdShukor SR, Aziz N (2009) Nonlinear model predictive control of a distillation column using NARX model. Comput Aided Chem Eng 27:1575–1580
Tanguy N, Morvan R, Vilbe P, Calvez S (2000) Online optimization of the time scale in adaptative Laguerre-based filters. IEEE Trans Signal Process 48(4):1184–1187
Wang C, Geng Q, Liu F, Han M (2022) Interval type-2 T-S fuzzy MPC for CPS under hybrid attacks over a multi-channel framework. J Franklin Inst 359:9666–9689
Zhao J, Ma X, Zhao S, Fei J (2014) Hammerstein identification of supercharged boiler superheated steam pressure using Laguerre-Fuzzy model. Int J Heat Mass Transf 70:33–39
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ben Abdelwahed, I., Bouzrara, K. Nonlinear Model Predictive Control Based on Second-Order NARX-Laguerre Model for Twin Rotor System Control. Iran J Sci Technol Trans Electr Eng (2024). https://doi.org/10.1007/s40998-024-00725-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40998-024-00725-x