Approximate inversion of hysteresis: Theory and numerical results

In previous work, we had proposed a low (6) dimensional model for a thin magnetostrictive actuator that was suitable for real-time control. One of the main results of this modeling effort was the separation of the rate-independent hysteretic effects from the rate-dependent linear effects. The hysteresis phenomenon may also be captured by a (modified) Preisach operator with the average magnetic field as the input. If one can find an inverse for the Preisach operator, then the composite system can be approximately linearized. In this paper, we propose a new algorithm for computation of the inverse for the classical Preisach model. Prior approaches depended on the linearization of the operator at the operating point. As numerical differentiation is involved, this approach can cause divergence. Our algorithm does not linearize the Preisach operator, but makes use of its strictly incrementally increasing property. Convergence of the algorithm is proved using the contraction mapping principle.