Closed-Loop Tracking of Large Displacements in Electro-Thermally Actuated ${\rm VO}_{2}$ -Based MEMS

The large displacements produced by vanadium dioxide (VO
₂
) integrated microelectromechanical systems (MEMS)-based actuators have been precisely controlled through the use of a simple proportional-integral-derivative (PID) controller and an integrated heater. A complete device characterization is performed, including quasi-static response, frequency response, creep, repeatability, and rate dependency. These characterization results are used to design, simulate, and implement two PID controllers for closed-loop device actuation optimized for different control specifications. To validate the performance of the designed controllers, step and sinusoidal reference tracking experiments are performed. Highly accurate deflection control is obtained for each case with a displacement range of 80 μm. Zero average steady-state error and fast actuation, up to 0.34 ms, are observed for the step reference tracking experiment with some signal oscillations resulting from the limit cycles produced by the VO
₂
hysteresis. The root-mean-square error obtained for the sinusoidal reference tracking was found to increase for increasing frequencies due to the phase lag. A comparison between open- and closed-loop control is also performed, which shows the far superior stability and performance of the latter when the sample temperature is varied. The obtained results show that the VO
₂
-based MEMS actuators, although characterized by a complicated hysteretic and nonmonotonic deflection-to-heater current behavior, can be accurately controlled with a simple PID controller.