Compensation for hysteresis using bivariate Preisach models

The accurate control of a system that exhibits hysteresis requires a control strategy that incorporates some form of compensation for the hysteresis. One approach is to develop a compensator based on an inverse hysteresis operator. If this can be accomplished, the composite operation will produce a linear relationship between the input and output. Thus, an open loop control can be developed in which the inverse operation adjusts the system input to compensate for the hysteresis in the physical system. One difficulty lies in developing a model of the hysteresis for which an inverse operator can be obtained. In this work, a system with hysteresis in modeled by a classical Preisach Model. We show that in the case of certain bivariate distributions, a closed-form formula for the inverse operator can be obtained. The concept is illustrated by a computer simulation.