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

Vanadium dioxide (
${\rm VO_2}$
) undergoes a thermally induced solid-to-solid phase transition, which can be exploited for actuation purposes.
${\rm VO_2}$
-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
${\rm VO_2}$
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-
$\mu \hbox{m}$
-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
${\rm m}^{-1}$
, respectively, over the actuated curvature range of [
${\rm -}$
104,  1846]
${\rm m}^{-1}$
. 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.