A real-time inverse-based hysteresis compensation with adaptation?

This paper presents a novel approach for compensation of hysteresis present for example in piezoelectric actuators. This adverse phenomenon limits seriously their accuracy, especially for large range positioning. The advantage of the proposed method is that it only requires the parametric description of the hysteresis model and does not require modeling its inverse directly. Instead, a combination of Newton and bisection algorithms is incorporated to solve for proper compensation input on-line. A simple polynomial model is chosen to approximate the hysteresis curve. The novelty of the proposed method is based on the adaptation of such a parametric model in real-time. In this way, one avoids modeling both ascending and descending branches of hysteresis separately and/or for different amplitude of the input. In order to track time varying parameters an adaptive estimator with stabilized exponential forgetting in a Bayesian framework is proposed. The optimal value of the forgetting factor is found by solving a maximin problem containing the Kullback-Leibler divergences. The method is validated experimentally on piezoelectric actuator in horizontal axis of some STM-like lab-made nanopositioning platform.