Robust $\mu$ -Synthesis Control of Dual LCL Type IPT System Considering Load and Mutual Inductance Uncertainty

The output voltage of a dual LCL inductive power transfer (IPT) system varies with the load and mutual inductance, which can affect the system performance, e.g., the charging speed of electrical equipment. This paper proposes a robust controller to maintain constant output voltage against the load and mutual inductance variations. A <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synthesis method is proposed based on structured singular value to design the dual LCL IPT closed-loop system. The frequency-domain nominal model of the system is established by using the generalized state-space averaging (GSSA) method. A standard M-<inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> configuration is generalized through separating the nominal and uncertain block by upper linear fractional transformation (LFT). The <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-controller is finally obtained by <inline-formula> <tex-math notation="LaTeX">${D}$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> iteration. The robust performance analysis and time-domain performance analysis are also carried out. The simulation and experimental results verified the effectiveness of the proposed modeling and controller design, and demonstrated the robust stability and robust performance of the dual LCL IPT system.