A Composite Hysteresis Model in Self-Sensing Feedback Control of Fully Integrated $\mathrm{VO_2}$ Microactuators

In this paper, a composite hysteresis model is proposed for self-sensing feedback control of vanadium dioxide (
$\mathrm{VO_2}$
)-integrated microactuators. The deflection of the microactuator is estimated with the resistance measurement through the proposed model. To capture the complicated hysteresis between the resistance and the deflection, we exploit the physical understanding that both the resistance and the deflection are determined by hysteretic relationships with the temperature. Since direct temperature measurement is not available, the concept of temperature surrogate, representing the constant current value in Joule heating that would result in a given temperature at the steady state, is explored in the modeling. In particular, the hysteresis between the deflection and the temperature surrogate and the hysteresis between the resistance and the temperature surrogate are captured with a generalized Prandtl–Ishlinskii (GPI) model and an extended GPI (EGPI) model, respectively. The composite self-sensing model is obtained by cascading the EGPI model with the inverse GPI model. For comparison purposes, two algorithms, based on a Preisach model and an EGPI model, respectively, are also used to estimate the deflection based on the resistance measurement directly. The proposed self-sensing scheme is evaluated with proportional-integral control of the microactuator under step and sinusoidal references, and its superiority over the other schemes is demonstrated by experimental results.