Control of Hysteresis: Theory and Experimental Results

Abstract

Hysteresis in smart materials hinders the wider applicability ofsuch materials in actuators. In this paper, a systematic approachfor coping with hysteresis is presented. The method is illustratedthrough the example of controlling a commercially available magnetostrictive actuator.We utilize the low-dimensional model for the magnetostrictive actuator that was developed in earlier work. For low frequency inputs, the model approximates to a rate-independent hysteresis operator, with current as its input and magnetization as its output. Magnetostrictive strain is proportional to the square of the magnetization. In this paper, we use a classical Preisach operator for the rate-independent hysteresis operator. We present the results of experiments conducted on a commercial magnetostrictive actuator, the purpose of which was the control of the displacement/strain output. A constrained least-squares algorithm is employedto identify a discrete approximation to the Preisach measure. We then discussa nonlinear inversion algorithm for the resulting Preisach operator, basedon the theory of strictly-increasing operators. This algorithm yields a control input signal to produce a desired magnetostrictive response.The effectiveness of the inversion scheme is demonstrated via an open-looptrajectory tracking experiment.