Inverse compensation for hysteresis in magnetostrictive transducers

This paper addresses the development of inverse compensation techniques for a class of ferromagnetic transducers including magnetostrictive actuators. If unaccommodated, the hysteresis and nonlinear dynamics can produce severe loss of control authority and potential instabilities when the actuators are incorporated in control design. In this work, hysteresis is modeled through the domain wall theory originally proposed by Jiles and Atherton [1]. This model is based on the quantification of the energy required to translate domain walls pinned at inclusions in the material with the magnetization at a given field level specified through the solution of an ordinary differential equation. A complementary differential equation is then employed to compute the inverse which can be used to compensate for hysteresis and nonlinear dynamics in control design. The performance of the inverse compensator and its employment in LQR control design are illustrated through numerical examples.