Modeling and Inverse Compensation of Nonmonotonic Hysteresis in VO $_2$ -Coated Microactuators

Vanadium dioxide ( VO₂) undergoes a thermally induced solid-to-solid phase transition, which can be exploited for actuation purposes. VO₂-coated silicon cantilevers demonstrate abrupt curvature changes when their temperature is varied across the phase transition. Unlike the monotonic hysteresis phenomena observed in many other smart materials, the curvature-temperature hysteresis of VO₂ actuators is nonmonotonic due to competing mechanisms associated with the material´s phase transition and the different thermal expansion coefficients of the materials that form the bilayered cantilever. Motivated by the underlying physics, a novel model for the nonmonotonic hysteresis that combines a monotonic Preisach hysteresis operator and a quadratic operator is presented. A constrained least-squares scheme is proposed for model identification, and an effective inverse control scheme is presented for hysteresis compensation. For comparison purposes, a Preisach operator with a signed density function and a single-valued polynomial model are considered. Experimental results show that, for a 300- μm -long actuator, the largest modeling errors with the proposed model, the signed Preisach operator, and the polynomial approximation are 46.8, 80.3, and 483 m^-1, respectively, over the actuated curvature range of [ -104, 1846] m^-1. In addition, both the largest tracking error and root-mean-square error under the proposed inversion scheme are only around 10% of those under the polynomial-based inversion scheme.