Sojourn-Probability-Based Robust L2 - L∞ Control for Uncertain SS-IPT System With Time-Varying Delays

This paper investigates the
${L}_{2} - {L}_{\infty }$
robust control problem for the series-series-inductive power transfer system with parameter uncertainties, external disturbances, and time-varying delays. To describe the randomness of large-scale parameter variation more precisely, a switched model is skillfully built by dividing the varying ranges of circuit parameters into several subintervals. Considering that the sojourn probabilities related to all subsystems of the switched model are much more easier to be obtained, a closed-loop switched control framework with known sojourn probabilities is designed for practical inductive power transfer systems. With the help of the robust mean-square stabilization and
${L}_{2} - {L}_{\infty }$
disturbance suppression performance indexes, the proposed
${L}_{2} - {L}_{\infty }$
controller with sojourn probabilities can solve the problems of large-scale parameter uncertainties, time-varying delays, and external disturbances much better. Finally, a simulation example of the series-series-inductive power transfer system is utilized to verify that the effectiveness of the designed control method in this paper.Note to Practitioners—For inductive power transfer systems, parameter uncertainties unavoidably affect their desired performance and thus the corresponding robust controller design has brought wide attention in the power transmission research. The proposed robust control strategies have been utilized to suppress the negative influence caused by parameter uncertainties, whereas it is difficult for these strategies to ensure the robustness and the stabilization under large-scale parameter uncertainties. To deal with this problem, this paper is devoted to design a robust
${L}_{2} - {L}_{\infty }$
control strategy with sojourn probabilities to guarantee the stabilization of practical inductive power transfer systems. It is worth mentioning that the proposed robust control strategy is proposed based on a sojourn-probability-based switched inductive power transfer systems with time-varying delays and external disturbances, which is relatively practical in real applications. In this paper, load variation and coil misalignment are considered as parameter uncertainties in the system, but some hostile environment still result in capacitance drift in practice. Therefore, we will take the capacitance drift phenomenon into account in the future research.