Robust H ∞ Control for ICPT Process With Coil Misalignment and Time Delay: A Sojourn-Probability-Based Switching Case

Abstract

In this paper, the robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem is studied for the inductively coupled power transfer (ICPT) process with coil misalignment, energy bounded interference and time-varying delay. The problem of coil misalignment between the primary and secondary coils are considered, and the time varying coupling coefficient are described in a sojourn-probability-based switch model. A set of random variables are utilized to describe the sojourn probabilities of the finite modes of the coil misalignment. It should be pointed out that the sojourn probability of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> th subsystem is obtained by the off-line statistical test instead of prescribed by hand, which is of more closer physical significance due to its engineering practice. Corresponding to the proposed switching systems, a set of controllers with time-varying delays are constructed. By resorting to the Lyapunov stability theory, the matrix analysis, and the stochastic analysis tools, the delay-dependent sufficient criteria with less conservatism are derived to guarantee the mean square stability of the ICPT system and the given interference attenuation level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> . The feedback gains of the desired controller can be readily obtained by using the control toolbox in Matlab software. Three cases of the illustrative examples without exception verify the effectiveness of the suggested modeling method and control scheme.