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# Article

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Keywords:
time delays; model following control system (MFCS); internal stable; nonlinear system
Summary:
Design of model following control system (MFCS) for nonlinear system with time delays and disturbances is discussed. In this paper, the method of MFCS will be extended to nonlinear system with time delays. We set the nonlinear part $f(v(t))$ of the controlled object as $||f(v(t))||\leq\alpha+\beta||v(t)||^\gamma$, and show the bounded of internal states by separating the nonlinear part into $\gamma\geq 0$. Some preliminary numerical simulations are provided to demonstrate the effectiveness of the proposed method.
References:
[1] Akiyama, T., Hattor, H., Okubo, S.: Design of the model following control system with time delays. IEEJ Trans. Electronics, Inform. Systems 118 (1998), 4, 497-502 (in Japaness).
[2] Boulkroune, A., M'Saad, M., Chekireb, H.: Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction. Inform. Sci. 180 (2010), 24, 5041-5059. DOI 10.1016/j.ins.2010.08.034 | MR 2726676 | Zbl 1205.93086
[3] Califano, C., Marquez-Martinez, L. A., Moog, C. H.: Extended lie brackets for nonlinear time-delay systems. IEEE Trans. Automat. Control 56 (2011), 9, 2213-2218. DOI 10.1109/tac.2011.2157405 | MR 2865783
[4] Cui, B. T., Lou, X. Y.: Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos, Solitons, Fractals 39 (2009), 1, 288-294. DOI 10.1016/j.chaos.2007.01.100 | Zbl 1197.93135
[5] Imer, O., Basar, T.: Control of congestion in high-speed networks. European J. Control 7 (2001), 132-144. DOI 10.3166/ejc.7.132-144
[6] Lan, Y., Zhou, Y.: High-order ($\mathcal{D}^{\alpha}$)-type iterative learning control for fractional-order nonlinear time-delay systems. J. Optim. Theory Appl. 156 (2013), 153-166. DOI 10.1007/s10957-012-0231-2 | MR 3019308 | Zbl 1263.93099
[7] Liu, P., Chiang, T. S.: $H_\infty$ output tracking fuzzy control for nonlinear systems with time-varying delay. Applied Soft Computing 12 (2012), 9, 2963-2972. DOI 10.1016/j.asoc.2012.04.025
[8] Maiti, A., Pal, A., Samanta, G.: Effect of time-delay on a food chain model. Applied Math. Comput. 200 (2008), 189-203. DOI 10.1016/j.amc.2007.11.011 | MR 2421636 | Zbl 1137.92366
[9] Ni, M., Li, G.: A direct approach to the design of robust tracking controllers for uncertain delay systems. Asian J. Control 8 (2006), 412-416. DOI 10.1111/j.1934-6093.2006.tb00293.x | MR 2382994
[10] Okubo, S.: Nonlinear model following control system using stable zero assignment. Trans. Soc. Instrument and Control Engrs. 28 (1992), 8, 939-946 (in Japaness). DOI 10.9746/sicetr1965.28.939
[11] Pai, M.: Robust tracking and model following of uncertain dynamics systems via discrete-time integral sliding mode control. Int. J. Control Automat. Syst. 7 (2009), 3, 381-387. DOI 10.1007/s12555-009-0307-4
[12] Pai, M.: Design of adaptive sliding mode controller for robust tracking and model following. J. Frankl. Inst. 347 (2010), 1837-1849. DOI 10.1016/j.jfranklin.2010.10.003 | MR 2739815 | Zbl 1214.93029
[13] Quan, Q., Yang, D., Cai, K.: Adaptive compensation for robust tracking of uncertain dynamic delay systems. Acta Automat. Sin. 36 (2010), 8, 1189-1194. DOI 10.3724/sp.j.1004.2010.01189 | MR 2768236
[14] Saglam, C. O., Baran, E. A., Nergiz, A. O., Sabanovic, A.: Model following control with discrete time SMC for time-delayed bilateral control systems. In: Proc. 2011 IEEE International Conference on Mechatronics, Istanbul 2011. DOI 10.1109/icmech.2011.5971262
[15] Srinathkumar, S.: Model following control systems. Eigenstructure Control Algorithms: Applications to aircraft/rotorcraft handling qualities design. IET Digital Library, 2011.
[16] Su, H., Chen, G., Wang, X., Lin, Z.: Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica 47 (2011), 2, 368-375. DOI 10.1016/j.automatica.2010.10.050 | MR 2878286 | Zbl 1207.93006
[17] Tadeuse, K.: Application of the drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencil. Int. J. Appl. Math. Comput. Sci. 23 (2013), 1, 29-33. DOI 10.2478/amcs-2013-0003 | MR 3086469
[18] Tsai, C. H., Wang, C. H., Lin, W. S.: Robust fuzzy model-following control of robot manipulators. IEEE Trans. Fuzzy Systems 8 (2000), 462-469. DOI 10.1109/91.868952
[19] Wang, Y. S., Ma, Q. H., Zhu, Q., Liu, X. T., Zhao, L. H.: An intelligent approach for engine fault diagnosis based on Hilbert-Huang transform and support vector machine. Applied Acoustics 75 (2014), 1-9. DOI 10.1016/j.apacoust.2013.07.001
[20] Wang, D., Okubo, S.: A design of model following control system for linear neutral system with time-delay. IEEJ Trans. ELS. 128 (2008), 11, 1657-1663 (in Japaness). DOI 10.1541/ieejeiss.128.1657
[21] Wang, D., Wu, S., Okubo, S.: Design of the state predictive model following control system with time-delay. Int. J. Appl. Math. Comput. Sci. 19 (2009), 2, 247-254. DOI 10.2478/v10006-009-0020-8 | Zbl 1167.93346
[22] Wang, Y. S., Shen, G. Q., Xing, Y. F.: A sound quality model for objective synthesis evaluation of vehicle interior noise based on artificial neural network. Mechanical Systems and Signal Processing 45 (2014), 1, 255-266. DOI 10.1016/j.ymssp.2013.11.001
[23] Wu, H.: Adaptive robust tracking and model following of uncertain dynamical systems with multiple time-delays. IEEE Trans. Automat. Control 49 (2004), 611-616. DOI 10.1109/tac.2004.825634 | MR 2049823
[24] Wu, S., Okubo, S., Wang, D.: Design of a model following control system for nonlinear descriptor system in discrete time. Kybernetika 44 (2008), 4, 546-556. MR 2459072 | Zbl 1173.93387
[25] Xing, Y. F., Wang, Y. S., Shi, L., Guo, H., Chen, H.: Sound quality recognition using optimal wavelet-packet transform and artificial neural network methods. Mechanical Systems and Signal Processing 66-67 (2016), 875-892. DOI 10.1016/j.ymssp.2015.05.003
[26] Yang, R., Wang, Y.: Finite-time stability analysis and control for a class of nonlinear time-delay Hamiltonian systems. Automatica 49 (2013), 2, 390-401. DOI 10.1016/j.automatica.2012.11.034 | MR 3004704
[27] Ying, J., Yuan, Y.: Pattern formation in a symmetrical network with delay. Nonlinear Analysis: Real World Appl. 14 (2013), 1102-1113. DOI 10.1016/j.nonrwa.2012.08.020 | MR 2991137
[28] Zhang, T., Ge, S.: Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain. Automatica 43 (2007), 6, 1021-1033. DOI 10.1016/j.automatica.2006.12.014 | MR 2306749 | Zbl 1282.93152

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