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Adaptive Neuro-Fuzzy vibration control of a smart plate

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  • In the present paper, the vibration supression of a smart plate with the use of ANFIS (Adaptive Neuro-Fuzzy Inference System) is investigated. The whole system consists of a nonlinear mechanical model, which is an extension of the von Kármán plate model with control. The structure is subjected to external disturbances and generalized control forces. Initial and boundary conditions are set up. The initial boundary value problem is spatially-discretized by a time spectral method. The obtained discretized model is a system of nonlinear ordinary differential equations (ODEs) with respect to time. A neuro-fuzzy inference system is built and tested in order to create a nonlinear controller for the vibration supression of the plate. More specifically, a Sugeno-type fuzzy inference system is employed and trained through ANFIS. The inputs of the controller are the displacement and the velocity and the output is the control force. An effective optimization procedure is proposed and numerical results are presented.

    Mathematics Subject Classification: Primary: 74K20, 35Q74, 34H05, 93C42; Secondary: 74S25, 65T40.

    Citation:

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  • Figure 1.  The structure of a fuzzy inference system

    Figure 2.  Displacement (input 1) membership functions

    Figure 3.  Velocity (input 2) membership functions

    Figure 4.  Control force (output) membership functions

    Figure 5.  Displacement before and after control with Mamdani FIS ($\omega=10\pi$)

    Figure 6.  Velocity before and after control with Mamdani FIS ($\omega=10\pi$)

    Figure 7.  External and Control forces with Mamdani FIS ($\omega=10\pi$)

    Figure 8.  Clusters of input 1 (Displacement)

    Figure 9.  Clusters of input 2 (Velocity)

    Figure 10.  Displacement before and after control with Sugeno FIS ($\omega=10\pi$)

    Figure 11.  Velocity before and after control with Sugeno FIS ($\omega=10\pi$)

    Figure 12.  External and Control forces with Sugeno FIS ($\omega=10\pi$)

    Figure 13.  Displacement before and after control with Sugeno FIS ($\omega=5\pi$)

    Figure 14.  Velocity before and after control with Sugenoi FIS ($\omega=5\pi$)

    Figure 15.  External and Control forces with Sugenoi FIS ($\omega=5\pi$)

    Figure 16.  Displacement before and after ANFIS with $\omega=10$, $D=10$ (the linear problem)

    Figure 20.  Displacement before and after ANFIS with $\omega=10$, $D=50$ (the linear problem)

    Figure 17.  Displacement before and after using LQR with $\omega=10$, $D=10$

    Figure 21.  Displacement before and after using LQR with $\omega=10$, $D=50$

    Figure 18.  Loading and control forces with ANFIS with $\omega=10$, $D=10$ (the linear problem)

    Figure 22.  Loading and control forces with ANFIS with $\omega=10$, $D=50$ (the linear problem)

    Figure 19.  Loading and control forces with using LQR with $\omega=10$, $D=10$

    Figure 23.  Loading and control forces with using LQR with $\omega=10$, $D=50$

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