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Fuzzy-enhanced robust fault-tolerant control of IFOC motor with matched and mismatched disturbances

  • * Corresponding author: Alain Soup Tewa Kammogne

    * Corresponding author: Alain Soup Tewa Kammogne 
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  • This paper focuses on the dynamical analysis of the permanent magnet asynchronous motor with the aim of subsequently designing effective robust control laws for the indirect field-oriented control (IFOC) devices. We first perform some tasks which demonstrate the existence of chaos phenomenon in the IFOC using relevant indicators such as phase portraits, bifurcations diagrams and Lyapunov exponents. Chaotic signature and some striking transitions are revealed such as period-doubling, torus, period-adding and chaos when an accessible parameter of the IFOC motor is changed. More interestingly, a certain range of the parameter space corresponds to the transient chaos. This behavior was not reported previously and can be considered as an enriching contribution. Secondly, due to the great interest to reduce the upper bound of uncertainties and interference, conventional sliding mode control (SMC) has been abundantly investigated for fault-tolerant control (FTC) systems. However, this approach presents several drawbacks in terms of overshoot, less robustness, transient state error, large chattering and speed of convergence that limit its use for industrial applications. For these reasons, the integral sliding mode control (ISMC) and the fuzzy sliding mode control (FISMC) are proposed to keep the IFOC motor in the regular operation zone. The optimal feedback gains and a sufficient condition are proposed for the stability of the overall IFOC system is drawn based on the linear quadratic regulator (LQR) method. To highlight the effectiveness and applicability of the proposed control scheme, numerical simulation results are presented. This analysis allows us a great knowledge of engineers for interpreting the operation of the IFOC motor. To highlight the effectiveness and the applicability of the proposed control scheme, numerical simulations results are presented and clearly demonstrated the feasibility of these techniques.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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  • Figure 1.  Phase portraits of system (2) in the plane $ (x_{2},x_{1}) $ obtained for some value of $ k $ : (a) $ k=1.2 $, (b) $ k=1.5 $, (c) $ k=3.2 $, (d) $ k=3.56 $, (e) $ k=3.6 $ and (f) $ k=3.67 $

    Figure 2.  Bifurcation diagram (a) and Lyapunov exponent (b)

    Figure 3.  Time evolution of the trajectory $ x3(t) $ of the IFOC and the corresponding phase portrait in the plane $ (x1, x3) $

    Figure 4.  Input membership functions of the fuzzy system

    Figure 5.  External disturbance

    Figure 6.  Histogram of external disturbance

    Figure 7.  State trajectories of the IFOC when the controller is deactivated; (a) the direct axis of the rotor flux, (b) quadrature axis component of the rotor flux, (c) rotor speed error, (d) quadratic axis stator current

    Figure 8.  Time evolution. (a) quadratic, (b) direct flux rotor, (c) speed of the rotor, (d) quadratic stator current under the ISMC

    Figure 9.  The evolution of the $ u(t) $ under the ISMC

    Figure 10.  Time evolution. (a) quadratic, (b) direct flux rotor, (c) speed of the rotor, (d) quadratic stator current under the FISMC

    Figure 11.  Fuzzy integral sliding mode controller

    Figure 12.  Performance index of the ISMC and FISMC

    Figure 13.  IAE of ISMC and FISMC

    Table 1.  Fuzzy rules extracted for the TS fuzzy logic system

    $\dot s$
    NL -1 -1 -1 -1 -0.66 -0.33 0
    NM -1 -1 -1 -0.66 -0.33 0 0.33
    NS -1 -1 -0.66 -0.33 0 0.33 0.66
    Z -1 -0.66 -0.33 0 0.33 0.33 1
    PS -0.66 -0.33 0 0.33 0.66 1 1
    PM -0.33 0 0.33 0.66 1 1 1
    PL 0 0.33 0.66 1 1 1 1
     | Show Table
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