A Multiscale Model of Cantilever Arrays with a Semi-decentralized Approximation of an Optimal Control

In this paper, we present a two-scale model including an optimal active control for a one dimensional cantilever array with regularly spaced actuators and sensors. With the purpose of implementing the control in real time, we propose an approximation that may be realized by an analog distributed electronic circuit. More precisely, our analog processor is made by Periodic Network of Resistances (PNR). The control approximation method is based on two general concepts, namely functions of operators and on the Dunford-Schwartz representation formula. We conducted careful validations of the control approximation method as well as of its effect in the complete control loop.