Emmanuelle Merced

Phase transition behavior in microcantilevers coated with M1-phase VO2 and M2-phase VO2:Cr thin films

Silicon microcantilevers were coated by pulsed laser deposition with vanadium dioxide (VO2) (monoclinic M1 phase) and V1−xCrxO2 with x near 0.024 (monoclinic M2 phase), and their mechanical characteristics were studied as a function of temperature through the films’ insulator-to-metal transition (IMT). The undoped VO2 films grew with (011)M1 planes parallel to the substrate, while Cr-doped VO2 films grew oriented with (201)M2 and (2¯01)M2 planes parallel to the substrate. In both cases, the films transformed reversibly through the IMT to the tetragonal (rutile, R) phase, with film (110)R planes oriented parallel to the substrate. The fundamental resonant frequencies of the cantilevers were measured as the temperature was cycled from ambient temperature, through the IMT, and up to 100  °C. Very high resonant frequency changes were observed through the transition for both types of samples, with increases during heating of over 11% and over 15% for the cantilevers coated with pure and Cr-doped VO2, respectiv...

Performance of Electro-Thermally Driven

The integration of VO2 thin films in a MEMS actuator device is presented. The structural phase transition of VO2 was induced electro-thermally by resistive heaters monolithically integrated in the MEMS actuator. The drastic mechanical displacements generated by the large stress induced during the VO2 thin film phase transition have been characterized for static and time-dependent current pulses to the resistive heater, for air and vacuum environments. A comprehensive and simplified finite element model is developed and validated with experimental data. It was found that the cut-off frequency of the 300 μm-long VO2-based MEMS actuator operated in vacuum (f3dB=29 Hz) was mostly limited by conductive heat loss through the anchor, whereas convection losses were more dominant in air (f3dB=541 Hz). The cut-off frequency is found to be strongly dependent on the dimensions of the cantilever when operated in air but far less dependent when operated in vacuum. Total deflections of 68.7 and 28.5 μm were observed for 300 and 200 μm-long MEMS cantilevers, respectively. Full actuation in air required ~ 16 times more power than in vacuum.

{\rm VO}_{2}

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 materials 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.

-Based MEMS Actuators

The dynamic response of VO2-coated silicon microcantilevers thermally driven over the film’s insulator-to-metal transition was studied using laser light pulses directly incident on the cantilevers. The measured photothermal response revealed very high curvature changes of approximately 2500 m−1 up to pulse frequencies greater than 100 Hz and readily observable vibrations up to frequencies of a few kHz with no amplitude degradation after tens of thousands of pulses. Maximum tip amplitudes for 300-μm-long, 1-μm-thick cantilevers used in these experiments were nearly 120 μm and correspondingly less for 2-μm-thick cantilevers. The main mechanism limiting oscillation amplitude was found to be heat transport response during heating and cooling, which depends mainly on thermal conduction through the cantilever itself to the massive anchor and chip body, which acted as a heat sink at room temperature. For the laser-driven oscillations studied, damping by the surrounding air is unimportant in the range of frequencies probed. Large-curvature response is expected to extend to higher pulse frequencies for cantilevers with smaller dimensions.

Modeling and Inverse Compensation of Nonmonotonic Hysteresis in VO

Prandtl-Ishlinskii (PI) hysteresis models have been used widely in magnetic and smart material-based systems. A generalized PI model, consisting of a weighted superposition of generalized play operators, is capable of characterizing saturated and asymmetric hysteresis. The fidelity of the model hinges on accurate representation of the envelope functions, play operator radii, and corresponding weights. Existing work has typically adopted some predefined play radii, the performance of which could be far from optimal. In this paper, novel schemes are proposed for optimally compressing generalized PI models, subject to a complexity constraint characterized by the number of play operators. An information-theoretic tool, entropy, is adopted to capture the information loss in replacing a group of weighted play operators with a single play operator. The optimal compression algorithm is reformulated as an optimal control problem and solved with dynamic programming, the computational complexity of which is shown to be much lower than that of exhaustive search. Simulation results are first presented to examine the performance of the proposed approach in approximating a PI model consisting of a large number of play operators, where cases with different types of weight distributions are explored. The approach is further applied to compress an experimentally identified generalized PI model for the complex hysteresis behavior between the resistance and temperature of vanadium dioxide, a promising multifunctional material. Both simulation and experimental results demonstrate that the proposed algorithms in general yield far more superior performance than a typically adopted scheme where the play radii are assigned uniformly.

_2

Vanadium dioxide (VO ) 2 , a promising multifunctional smart material, has shown strong promise in microactuation, memory, and optical applications. During thermally induced insulator-tometal phase transition of VO2, the changes of its electrical, mechanical, and optical properties demonstrate pronounced, complex hysteresis with respect to the temperature, which presents a challenge in the utilization of this material. In this paper, an extended generalized Prandtl– Ishlinskii model is proposed to model the hysteresis in VO2, where a nonlinear memoryless function is introduced to improve its modeling capability. A novel inverse compensation algorithm for this hysteresis model is developed based on fixed-point iteration with which the convergence conditions of the algorithm are derived. The proposed approach is shown to be effective for modeling and compensating the asymmetric and non-monotonic hysteresis with saturation between the curvature output and the temperature input of a VO2-coated microactuator, as well as the asymmetric hysteresis with partial saturation between the resistance output and the temperature input of a VO2 film.

-Coated Microactuators

A self-sensing approach is used to accurately control the large displacements observed in VO2-based microelectromechanical systems actuators. The device is operated electrothermally using integrated resistive heaters. The coupling of the abrupt electrical and mechanical changes in VO2 films across its phase transition allow for the estimation of the devices deflection by monitoring the films resistance. Furthermore, the typical hysteretic behavior observed in VO2 films is significantly reduced in the present device and the need for optical testing equipment is eliminated. The displacement-resistance relationship is modeled by a memoryless Boltzmann function consisting of four parameters, which are optimized to fit the experimental data with an average error of 1.1 μm throughout the complete actuation range of 95 μm. The estimated deflection is used as feedback to achieve closed-loop micropositioning control of the device, which is designed from the system dynamics obtained experimentally. Closed-loop sinusoidal and step reference response experiments are performed in order to show the effectiveness of the self-sensing feedback technique used. In the closed-loop sinusoidal frequency response, a cutoff frequency of 43 Hz is observed with a maximum actual deflection error of 0.19 dB up to the phase margin frequency of 30 Hz. In the step response, an average actual displacement steady-state error of ±1.15 μm is obtained with response times ranging from 5 to 12 ms.

Dynamics of photothermally driven VO2-coated microcantilevers

Photo-thermal actuation has been used to program the resonant frequency of a VO2-coated SiO2 micro-bridge. The SiO2 micro-bridge had nominal length, width, and thickness of 300, 45, and 4.15??m, respectively. The thickness of the VO2 coating was 150?nm. The changes in resonant frequency are caused by stress changes on the bimorph structure during the coating?s insulator-to-metal-transition. A total of 13 resonant frequency memory states ranging from 215.5 to 222.7?kHz were programmed by laser pulses of increasing energy in steps of 0.7??J, focused on the micro-bridge structure. The device was maintained at 60??C during programming experiments, and the memory was reset by driving the temperature outside the hysteresis loop. After programming the device to a particular resonant frequency, the memory state was stored for more than 24?h as long as the sample was maintained at the pre-heating temperature of 60??C.

Optimal compression of generalized Prandtl-Ishlinskii hysteresis models

The large displacements produced by vanadium dioxide (VO2) 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 VO2 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 VO2-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.

Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model

The Preisach operator is a popular hysteresis model that has been widely applied in magnetic and smart material systems. Fidelity of the model hinges on accurate representation of the Preisach density function on the Preisach plane, which weighs basic hysteretic elements comprising the operator. Parameter identification and control methods for Preisach operators involve the discretization of the Preisach density function, and existing work has typically adopted some predefined discretization scheme, the performance of which could be far from optimal. In this paper we propose a novel scheme for optimal compression of a Preisach operator. The Kullback-Leibler (KL) divergence is utilized to measure the information loss in approximating the Preisach density as piecewise-constant functions. The proposed approach is applied to the modeling of the hysteretic relationship between resistance and temperature of a vanadium dioxide (VO2) film, and its effectiveness is further examined in open-loop inverse compensation experiments. In particular, under the same complexity constraint, the KL-divergence based Preisach density function discretization scheme results in an inversion error that is only 40% of that under a scheme.