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Profoundly Robust Controlling Strategy for Uncertain Nonlinear Mimo System Using T–S Fuzzy System

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Abstract

In this paper, we addressed the problem of developing a robust control scheme for the MIMO nonlinear system; to achieve this, we adopt nonlinear systems with plant uncertainties, time-delayed uncertainties, and external disturbances. A fuzzy logic system is used to approximate the unknown nonlinear functions, and a Takagi–Sugeno (T–S) fuzzy observer is presented for state estimations. The designed control law works on basis of indirect T–S fuzzy control and utilizes two online approximations which allowed instantaneous insertion of finding gains of delayed state uncertainties. The benefit of employing a T–S fuzzy system is utilize of analytical results which are linear instead of approximating functions of nonlinear system with online update laws. The T–S fuzzy tracking control utilizes variable structure control method to resolve the system uncertainties, time-delayed uncertainty, and the external disturbances such that H ∞ tracking performance is achieved. The control rules are derived based on a Lyapunov criterion and the Riccati inequality such that all states of the system are uniformly ultimately limited. Therefore, the effect can be reduced to any prescribed level to achieve H ∞ tracking performance. A two-connected inverted pendulums system on carts used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Anjuman Institute of Technology and Management, Bhatkal, Karnataka, India

    A. K. Iqbal Ahammed

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  1. A. K. Iqbal Ahammed
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Correspondence to A. K. Iqbal Ahammed.

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Iqbal Ahammed, A.K. Profoundly Robust Controlling Strategy for Uncertain Nonlinear Mimo System Using T–S Fuzzy System. Int. J. Fuzzy Syst. 19, 1104–1117 (2017). https://doi.org/10.1007/s40815-016-0225-6

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  • DOI: https://doi.org/10.1007/s40815-016-0225-6

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