Parameter Reduction for Disturbance Attenuation with a Discrete-Time LPV Controller

This paper considers the application of a discrete-time LPV controller technique to active noise and vibration control (ANC/AVC) based on dilated LMIs. The goal of the controller design is to reduce the excitations induced by the combustion engine and transmitted through the chassis into the passenger compartment. These vibration disturbances are quite specific and consist of a varying nominal frequency and several multiples of it. The main contribution of this paper focuses in the modeling of the multisine disturbance. A parametrization of the cosine-function is proposed requiring only two parameters for L different frequencies. This reduction is based on a least square approximation. By separating the Lyapunov matrix and the system matrix in the controller design it is possible to use a Lyapunov function with dependent Lyapunov matrices leading to less conservative results. Simulations show the benefit of this method by attenuating six predefined frequencies with only two varying parameters.