$H_{\infty}$ Control Method of LLC Resonant Converter Based on Loop Shaping

This paper proposes an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> loop shaping control <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left(H_{\infty-}\right.$</tex> LSC) method that enhances dynamic response and robustness of LLC resonant converter. The simple equivalent circuit model is derived based on modification and simplification of extended describing function method. Applying robust control theory, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex>-LSC controller is derived by designing correction compensator and generating a loop shaping controller. The proposed controller enhances the dynamic response and robustness of the system, without the need for additional sensors. Finally, experimental and simulation results demonstrate the effectiveness of the proposed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex>-LSC method.