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Design and stability analysis of adaptive fuzzy feedback controller for nonlinear systems by Takagi–Sugeno model-based adaptation scheme

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Abstract

This paper focuses on the design of a real-time adaptive Takagi–Sugeno (T–S) fuzzy-based dynamic feedback tracking controller to deal with the metallic sphere position control of a magnetic levitation system (MLS), which is an intricate and highly nonlinear system involving plant uncertainties and external disturbances. The dynamic model of this MLS is first constructed based on the concepts of geometry and motion dynamics. The objective of this proposed control strategies is to design a real-time adaptive controller with the help of Takagi–Sugeno type fuzzy-based output feedback techniques and to directly ensure the asymptotic stability of the closed-loop controlled system by Lyapunov stability theorem without the requirement of strict constraints, detailed system information, and auxiliary compensated controllers. Proposed adaptive tracking controller is developed in such a way such that all the states and signals of the closed-loop system are bounded and the trajectory tracking error is as small as possible. In this paper, the controller consists of adaptive and robustifying components whose role is to nullify the effect of uncertainties and achieve a desired tracking performance. Here, separate adaptive control laws have been proposed to automatically take care of external disturbance and uncertainties by designing a two-port controller. The first part stabilizes the nominal plant; without modeling uncertainties. The second part of the controller is to reject modeling uncertainties. The good transient control performance and robustness to uncertainties of the proposed adaptive control scheme for the MLS is verified by numerical simulations and real-time experimental results. These results demonstrate that, the proposed adaptive controller yields favorable control performance superior to that of PID and and Neuro-fuzzy network controller in terms of overshoot, settling time, mean square error and steady-state error and also it can guarantee the system stability and parameter convergence with a pole placement algorithm.

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Acknowledgments

The author would like to acknowledge the financial support of the MITS, Rajasthan, India for the experimental testing of the MLS and express his gratitude to the reviewers for their valuable comments.

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Authors and Affiliations

  1. Department of Electrical Engineering, RCC Institute of Information Technology, Kolkata, W.B., India

    Alok Kole

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  1. Alok Kole
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Correspondence to Alok Kole.

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Communicated by V. Loia.

Appendices

Appendix A

Figures 17 and 18 shows the parameters adaptation of the state matrix for the first rule with the initial conditions [0.002 0 0].

Appendix B

Figures 19 and 20 shows the parameters adaptation of the input matrix for the first rule with the initial conditions [0.002 0 0].

From the Figs. 17, 18, 19 and 20, it is observed that if state matrix \(A\) and input matrix \(B\) are adapted at time \(t\), then the feedback gain matrix \(F\) is also adapted and consequently estimated state track the measured state as \(t\). The convergence of the adaptive parameters of matrices \(A\) and \(B\) for Adaptive Control are shown in these plots.

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Kole, A. Design and stability analysis of adaptive fuzzy feedback controller for nonlinear systems by Takagi–Sugeno model-based adaptation scheme. Soft Comput 19, 1747–1763 (2015). https://doi.org/10.1007/s00500-014-1362-1

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