$\mu$-Synthesis for Frequency Uncertainty of the ICPT System

Abstract

A μ-controller is designed based on the structured singular value with regard to the frequency uncertainty of a real inductively coupled power transfer (ICPT) system. Due to system-parameter variations (such as system load) and nonlinear features of ICPT systems, the operating frequency will be perturbed accordingly. Uncertainty in the operating frequency will contribute to electromagnetic interference and power losses, and even instability of ICPT systems. To fulfill a robust stability and robust performance (RSRP) design, a generalized state-space averaging model for a nominal ICPT system is established by developing the equivalent circuit equations and expanding the related circuit variables as the Fourier series. A linear fractional transformation of this nominal model and its uncertainty is discussed to generate a standard configuration for μ-synthesis. The D-K iteration method is proposed for the “optimal” RSRP design. Computer simulation and a practical experiment are conducted to verify the RSRP of the μ-synthesis control system to ensure that the μ-synthesis algorithm is effective for ICPT systems.