Kybernetika 52 no. 3, 478-495, 2016

Model following control system with time delays

Dazhong Wang, Shujing Wu, Wei Zhang, Guoqiang Wang, Fei Wu and Shigenori OkuboDOI: 10.14736/kyb-2016-3-0478


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.


time delays, nonlinear system, model following control system (MFCS), internal stable




  1. T. Akiyama, H. Hattor and S. Okubo: Design of the model following control system with time delays. IEEJ Trans. Electronics, Inform. Systems 118 (1998), 4, 497-502 (in Japaness).   CrossRef
  2. A. Boulkroune, M. M'Saad and H. Chekireb: 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
  3. C. Califano, L. A. Marquez-Martinez and C. H. Moog: Extended lie brackets for nonlinear time-delay systems. IEEE Trans. Automat. Control 56 (2011), 9, 2213-2218.   DOI:10.1109/tac.2011.2157405
  4. B. T. Cui and X. Y. Lou: 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
  5. O. Imer and T. Basar: Control of congestion in high-speed networks. European J. Control 7 (2001), 132-144.   DOI:10.3166/ejc.7.132-144
  6. Y. Lan and Y. Zhou: 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
  7. P. Liu and T. S. Chiang: $H_\infty$ 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. A. Maiti, A. Pal and G. Samanta: Effect of time-delay on a food chain model. Applied Math. Comput. 200 (2008), 189-203.   DOI:10.1016/j.amc.2007.11.011
  9. M. Ni and G. Li: 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
  10. S. Okubo: 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. M. Pai: 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. M. Pai: 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
  13. Q. Quan, D. Yang and K. Cai: 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
  14. C. O. Saglam, E. A. Baran, A. O. Nergiz and A. Sabanovic: 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. S. Srinathkumar: Model following control systems. Eigenstructure Control Algorithms: Applications to aircraft/rotorcraft handling qualities design. IET Digital Library, 2011.   CrossRef
  16. H. Su, G. Chen, X. Wang and Z. Lin: 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
  17. K. Tadeuse: 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
  18. C. H. Tsai, C. H. Wang and W. S. Lin: Robust fuzzy model-following control of robot manipulators. IEEE Trans. Fuzzy Systems 8 (2000), 462-469.   DOI:10.1109/91.868952
  19. Y. S. Wang, Q. H. Ma, Q. Zhu, X. T. Liu and L. H. Zhao: 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. D. Wang and S. Okubo: 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. D. Wang, S. Wu and S. Okubo: 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
  22. Y. S. Wang, G. Q. Shen and Y. F. Xing: 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. H. Wu: 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
  24. S. Wu, S. Okubo and D. Wang: Design of a model following control system for nonlinear descriptor system in discrete time. Kybernetika 44 (2008), 4, 546-556.   CrossRef
  25. Y. F. Xing, Y. S. Wang, L. Shi, H. Guo and H. Chen: 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. R. Yang and Y. Wang: 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
  27. J. Ying and Y. Yuan: 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
  28. T. Zhang and S. Ge: 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