$H_{\infty}$ Tracking Control for the T-S Fuzzy-Based SS-IPT System with Coil Misalignment

To cope with the coil misalignment problem existing in the inductive power transfer (IPT) system, an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> tracking control strategy for the practical series-series (SS)- IPT system is put forward in this paper. For this purpose, an augmented Takagi-Sugeno (T-S) fuzzy modeling methodology is successfully constructed by introducing an integrator of the error between the actual and the reference system output signals first. Then an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}^{-}$</tex> parallel distributed compensation (PDC) fuzzy control framework is designed to ensure desired tracking control performance. Subsequently, sufficient conditions based on extended Lyapunov functional method are employed to achieve the asymptotic stability of the augmented T-S fuzzy-based SS-IPT system and the disturbance suppression index. Finally, a simulation example with regard to the SS- IPT system is developed, which demonstrates that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> PDC fuzzy control strategy proposed in this paper can maintain the constant output voltage of the SS- IPT system.