An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems. (English) Zbl 1485.93124
Summary: In this paper, an online algorithm is proposed for the identification of unknown time-varying input delay in the case of discrete non-linear systems described by decoupled multimodel. This method relies on the minimization of a performance index based on the error between the real system and the partial internal models outputs. In addition, a decoupled internal multimodel control is proposed for the compensation of discrete non-linear systems with time-varying delay. This control scheme incorporates partial internal model controls. Each partial controller is associated to a specified operating zone of the non-linear system. The switching between these controllers is ensured by a supervisor that contains a set of local predictors. A simulation example is carried out to illustrate the significance of the proposed time-varying delay identification algorithm and the proposed internal multimodel control scheme.
MSC:
| 93B30 | System identification |
| 93C43 | Delay control/observation systems |
| 93C10 | Nonlinear systems in control theory |
Keywords:
time-varying delay identification; internal multimodel control; delayed systems; decoupled polynomial multimodel; discrete non-linear systemsReferences:
| [1] | Richard, J. P., Time-delay systems: an overview of some recent advances and open problems, Automatica, 39, 10, 1667-1694 (2003) · Zbl 1145.93302 · doi:10.1016/S0005-1098(03)00167-5 |
| [2] | Seuret, A., Commande et observation des systèmes à retards variables: théorie et applications (2006), Ecole Centrale de Lille: Ecole Centrale de Lille, France |
| [3] | Xu, L.; Ding, F.; Gu, Y.; Alsaedi, A.; Hayat, T., A multi-innovation state and parameter estimation algorithm for a state space system with d-step state-delay, Signal Process., 140, 97-103 (2017) · doi:10.1016/j.sigpro.2017.05.006 |
| [4] | Xu, L., A proportional differential control method for a time-delay system using the Taylor expansion approximation, Appl. Math. Comput., 236, 391-399 (2014) · Zbl 1334.93125 · doi:10.1016/j.amc.2014.02.087 |
| [5] | Ferretti, G.; Maffezzoni, C.; Scattolini, R., The recursive estimation of time delay in sampled-data control systems, chapter Control and Dynamic Systems, Adv. Theory Appl, 73, 159-206 (1995) · Zbl 0850.93177 |
| [6] | Keviczky, L., Combined identification and control: another way, Control Eng. Pract., 4, 685-698 (1996) · doi:10.1016/0967-0661(96)00052-4 |
| [7] | Tuch, J.; Feuer, A.; Palmor, Z. J., Time delay estimation in continuous linear time invariant systems, IEEE Trans. Automat. Contr., 39, 823-827 (1994) · Zbl 0807.93006 · doi:10.1109/9.286261 |
| [8] | Elnaggar, A.; Dumont, G. A.; Elshafei, A., New method for delay estimation (1990), Honolulu, Hawaii |
| [9] | Ren, X. M.; Rad, A. B., Identification of nonlinear systems with unknown time delay based on time-delay neural networks, IEEE Transactions Neural Networks, 18, 5, 1536-1541 (2007) · doi:10.1109/TNN.2007.899702 |
| [10] | Barbot, J. P.; Zheng, G.; Floquet, T.; Boutat, D.; Richard, J. P., Delay estimation algorithm for nonlinear time-delay systems with unknown inputs (2012), Boston, USA · doi:10.3182/20120622-3-US-4021.00032 |
| [11] | Garcia, C. E.; Prett, D. M.; Morari, M., Model predictive control: theory and practice - a survey, Automatica, 25, 335-348 (1989) · Zbl 0685.93029 · doi:10.1016/0005-1098(89)90002-2 |
| [12] | Avalos, G. G.; Orozco, R. G., A procedure to linearize a class of non-linear systems modelled by bond graphs, Math. Comput. Model. Dyn. Syst., 21, 1, 38-57 (2015) · Zbl 1310.93039 · doi:10.1080/13873954.2013.874360 |
| [13] | Filev, D., Fuzzy modeling of complex systems, Int. J. Approx. Reason., 5, 3, 281-290 (1991) · Zbl 0738.93048 · doi:10.1016/0888-613X(91)90013-C |
| [14] | Orjuela, R., Contribution à l’estimation d’état et au diagnostic des systèmes représentés par des multimodèles (2008), Institut National Polytechnique de Lorraine: Institut National Polytechnique de Lorraine, France |
| [15] | Touzri, M.; Naceur, M.; Soudani, D., New internal multi-model controller for a linear process with a variable time delay, Int. J. Control Energy Electrical Eng, 1, 1-9 (2014) |
| [16] | Duviella, E.; Charbonnaud, P.; Chiron, P.; Carrillo, F. J., Supervised internal multi-model control of a dam-gallery open-channel system (2005) |
| [17] | Zribi, A.; Chtourou, M.; Djemel, M., Internal multiple models control based on robust clustering algorithm, Nonlinear Dyn. Syst. Theory, 11, 1, 99-112 (2011) · Zbl 1223.93077 |
| [18] | Touati, N.; Soudani, D.; Naceur, M.; Benrejeb, M., On an internal multimodel control for nonlinear multivariable systems - a comparative study, Int. J. Advanced Comput. Sci. Appl., 4, 7, 66-71 (2013) |
| [19] | Murray-Smith, R.; Johansen, T., Multiple Model Approaches to Modelling and Control (1997), Taylor & Francis: Taylor & Francis, London |
| [20] | Orjuela, R.; Marx, B.; Ragot, J.; Maquin, D., Nonlinear system identification using heterogeneous multiple models, Int. J. Appl. Math. Comput. Sci., 23, 1, 103-115 (2013) · Zbl 1293.93217 · doi:10.2478/amcs-2013-0009 |
| [21] | Bahri, N.; Atig, A.; Ben Abdennour, R., Multimodel and neural emulators for non-linear systems: application to an indirect adaptive neural control, Int. J. MODEL. IDENT. CONTROL, 17, 4, 348-359 (2012) · doi:10.1504/IJMIC.2012.051086 |
| [22] | Bahri, N.; Messaoud, A.; Ben Abdennour, R., A multimodel emulator for nonlinear system controls, Int. J. Sci. Tech. Autom. control comput. eng., 5, 1, 1500-1515 (2011) |
| [23] | Venkat, A. N.; Vijaysai, P.; Gudi, R. D., Identification of complex nonlinear processes based on fuzzy decomposition of the steady state space, J Process Control, 13, 6, 473-488 (2003) · doi:10.1016/S0959-1524(02)00120-8 |
| [24] | Ksouri-Lahmari, M.; Borne, P.; Benrejeb, M., Multimodel: the construction of model bases, Int. J. Stud. Inform. Control, 13, 3, 199-210 (2004) |
| [25] | Mezghani, S.; Elkamel, A.; Borne, P., Multimodel control of discrete systems with uncertainties, Electron. Int. J. Adv. Model. Optimization, 3, 2, 7-17 (2001) · Zbl 1115.93327 |
| [26] | Ltaief, M.; Abderrahim, K.; Ben Abdennour, R.; Ksouri, M., Contributions to the multimodel approach: systematic determination of models’ base and validities estimation, Int. J. Automation Syst. Eng, 2, 3 (2008) |
| [27] | Ltaief, M.; Messaoud, A.; Ben Abdennour, R., An optimal systematic determination of models’ base for multimodel representation: real time application, Int. J. Automation Comput., 11, 6, 644-652 (2014) · doi:10.1007/s11633-014-0815-4 |
| [28] | Messaoud, A.; Ltaief, M.; Ben Abdennour, R., Supervision based on partial predictors for a multimodel generalized predictive control: experimental validation on a semi-batch reactor, Int. J. MODEL. IDENT. CONTROL, 6, 4, 333-340 (2009) · doi:10.1504/IJMIC.2009.024740 |
| [29] | Talmoudi, S.; Abderrahim, K.; Ben Abdennour, R.; Ksouri, M., Experimental validation of a systematic determination approach of a models’ base, Wseas Trans. Electron., 1, 2, 410-416 (2004) |
| [30] | Talmoudi, S.; Abderrahim, K.; Ben Abdennour, R.; Ksouri, M., Approach using neural networks for complex systems modeling and identification, Nonlinear dynamics Syst. Theory, Int. J. Res. Surveys, 8, 3 (2008) · Zbl 1397.93054 |
| [31] | Xu, L., Application of the newton iteration algorithm to the parameter estimation for dynamical systems, J. Comput. Appl. Math., 288, 33-43 (2015) · Zbl 1314.93062 · doi:10.1016/j.cam.2015.03.057 |
| [32] | Xu, L.; Chen, L.; Xiong, W., Parameter estimation and controller design for dynamic systems from the step responses based on the newton iteration, Nonlinear Dyn., 79, 3, 2155-2163 (2015) · doi:10.1007/s11071-014-1801-7 |
| [33] | Xu, L., The damping iterative parameter identification method for dynamical systems based on the sine signal measurement, Signal Process., 120, 660-667 (2016) · doi:10.1016/j.sigpro.2015.10.009 |
| [34] | Wang, X., Modelling and multi-innovation parameter identification for Hammerstein nonlinear state space systems using the filtering technique, Math. Comput. Model. Dyn. Syst., 22, 2, 113-140 (2016) · Zbl 1339.93106 · doi:10.1080/13873954.2016.1142455 |
| [35] | Wang, Y.; Ding, F., Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model, Automatica, 71, 308-313 (2016) · Zbl 1343.93087 · doi:10.1016/j.automatica.2016.05.024 |
| [36] | Wang, Y.; Ding, F., Filtering-based iterative identification for multivariable systems, IET Control Theory Appl., 10, 8, 894-902 (2016) · doi:10.1049/iet-cta.2015.1195 |
| [37] | Wang, Y.; Ding, F., The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique, Signal Process., 128, 212-221 (2016) · doi:10.1016/j.sigpro.2016.03.027 |
| [38] | Wang, Y.; Ding, F., Recursive least squares algorithm and gradient algorithm for Hammerstein-Wiener systems using the data filtering, Nonlinear Dyn., 84, 2, 1045-1053 (2016) · Zbl 1354.93158 · doi:10.1007/s11071-015-2548-5 |
| [39] | Wang, Y.; Ding, F., Recursive parameter estimation algorithms and convergence for a class of nonlinear systems with colored noise, Circuits Syst. Signal Process., 35, 10, 3461-3481 (2016) · Zbl 1346.93369 · doi:10.1007/s00034-015-0210-6 |
| [40] | Marquardt, D., An algorithm for least-squares estimation of nonlinear parameters, SIAM J Appl Math, 11, 2, 431-441 (1963) · Zbl 0112.10505 · doi:10.1137/0111030 |
| [41] | Mars, N. J.I.; Van Arragon, G. W., Time delay estimation in nonlinear systems, IEEE Trans. Acoustics Speech Signal. Process., 29, 3, 619-621 (1981) · doi:10.1109/TASSP.1981.1163571 |
| [42] | Tan, Y., Time-varying time-delay estimation for nonlinear systems using neural networks, Int. J. Appl. Math. Comput. Sci., 14, 1, 63-68 (2004) · Zbl 1171.94386 |
| [43] | Shaltaf, S. J.; Mohammad, A. A., Neural networks based time-delay estimation using dct coefficients, Am. J. Appl. Sci., 6, 4, 703-708 (2009) · doi:10.3844/ajassp.2009.703.708 |
| [44] | Landau, I. D.; Zito, G., Digital Control Systems: Design, Identification and Implementation (2006), Springer: Springer, London,U.K |
| [45] | Economou, C. G.; Morari, M.; Palsson, B. O., Internal model control: extension to nonlinear system, Ind. Eng. Chem. Process. Des. Dev., 25, 2, 403-411 (1986) · doi:10.1021/i200033a010 |
| [46] | Messaoud, A.; Ltaief, M.; Ben Abdennour, R., Supervision based on a multipredictor for an uncoupled state multimodel predictive control (2010), Hammamet, Tunisia |
| [47] | Narendra, K. S.; Annaswamy, A. M., Stable Adaptive Systems, Dover Publications, Mineola, NY (1989) · Zbl 0758.93039 |
| [48] | Pagès, O.; Bernard, C.; Raul, O.; Pascal, M., Control system design by using a multi-controller approach with a real-time experimentation for a robot wrist, Int. J. Control., 75, 16, 1321-1334 (2002) · Zbl 1032.93053 · doi:10.1080/0020717021000023753 |
| [49] | Nagy, A. M.; Mourot, G.; Marx, B.; Ragot, J.; Schutz, G., Systematic multi-modeling methodology applied to an activated sludge reactor model, Ind. Eng. Chem. Res., 49, 6, 2790-2799 (2010) · doi:10.1021/ie8017687 |
| [50] | Ben Atia, S.; Messaoud, A.; Ltaief, M.; Ben Abdennour, R., Synthesis of multi-observers for discrete-time nonlinear systems with delayed output, Int. J. Sci. Tech. Autom. control comput. eng., 8, 1, 1966-1981 (2014) |
| [51] | Ben Atia, S.; Messaoud, A.; Ben Abdennour, R., Supervised model predictive control for discrete-time nonlinear systems with time-varying delay, Int. J. Comput. Appl., 114, 12, 1-8 (2015) · doi:10.5120/20027-1547 |
| [52] | Messaoud, A.; Ltaief, M.; Ben Abdennour, R., Supervision based on a multipredictor for an uncoupled state multimodel predictive control (2010) |
| [53] | Narendra, K.; Parthasarathy, K., Identification and control of dynamical systems using neural networks, IEEE Transactions Neural Networks, 1, 1, 4-27 (1990) · doi:10.1109/72.80202 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
