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An ISM-based CNF tracking controller design for uncertain MIMO linear systems with multiple time-delays and external disturbances

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Abstract

In this paper, a combination of integral sliding mode and composite nonlinear feedback method is proposed for fast and accurate robust tracking and model following of uncertain multiple-input multiple-output linear systems with multiple time-delays and external disturbances. The composite nonlinear feedback technique allows following the reference trajectory within a given accuracy and the invariance property of the integral sliding mode method rejects the disturbances and preserves the stability of the closed-loop system. By using the Lyapunov–Krasovskii functional, the conditions for asymptotic stabilization are obtained in the form of linear matrix inequalities. To improve the tracking performance for different reference amplitudes, a new nonlinear function is included in the control law and is optimally tuned using a modified random search algorithm. The selection of sliding surface and the existence of the sliding mode are two significant issues, which have been addressed. This scheme not only guarantees robustness against time-delays and uncertainties, but also avoids chattering phenomenon and reaching phase. Finally, the simulations are provided to verify the theoretical results. The results show that the proposed method leads to great improvement on the tracking error and the control effort compared to the available methods.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran

    Vahid Johari Majd

  2. Department of Electrical Engineering, Faculty of Engineering, University of Zanjan, P.O. Box 38791-45371, Zanjan, Iran

    Saleh Mobayen

Authors
  1. Vahid Johari Majd
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  2. Saleh Mobayen
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Correspondence to Saleh Mobayen.

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Majd, V.J., Mobayen, S. An ISM-based CNF tracking controller design for uncertain MIMO linear systems with multiple time-delays and external disturbances. Nonlinear Dyn 80, 591–613 (2015). https://doi.org/10.1007/s11071-015-1892-9

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  • DOI: https://doi.org/10.1007/s11071-015-1892-9

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