Macro-modelling of a double-gimballed electrostatic torsional micromirror

Zhou, Guangya; Tay, Francis Eng Hock; Chau, Fook Siong

doi:10.1088/0960-1317/13/5/303

Cited by 13 publications

(5 citation statements)

References 18 publications

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“…In recent years, optical MEMS mirrors have found many applications such as optical cross-connects, optical switches and variable attenuators [1,2], etc. The double-gimballed torsional micromirror [3,4] is considered to be one of the key components in the realization of three-dimensional MEMS that can be scaled into hundreds or thousands of ports with low loss and high uniformity.…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical model for squeeze-film damping including rarefaction in a MEMS torsion mirror with complex geometry

Pandey

Pratap

2008

J. Micromech. Microeng.

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A semi-analytical approach is presented to model the effects of complicated boundary conditions and rarefaction on the squeeze-film damping dependent quality factor in a double-gimballed MEMS torsion mirror. To compute squeeze-film damping in a rectangular torsion mirror with simple boundaries, compact models derived by solving the conventional Reynolds equation with zero pressure boundary conditions on the edges of the plate are generally used. These models are not applicable if the air-gap thickness is comparable to the length of the plate. To extend the validity of the existing models in devices with large air-gap thickness and complicated boundaries, we present a procedure that requires the computation of the effective length of the structure and uses this length for the computation of damping in all flow regimes using a modified effective viscosity model. The effective length is computed by comparing the damping obtained from a numerical solution of Navier-Stokes equations with that obtained from a Reynolds-equation-based compact model. To capture the effect of rarefaction in different flow regimes, we use two different approaches: the effective viscosity approach which is valid for continuum, slip, transition and molecular flow regimes, and an approach based on the free molecular model which is valid only in a molecular flow regime. We show that the effective length obtained for complicated structures in the continuum regime may still be used to capture the rarefaction effect in the slip, transition and molecular regimes. On comparing different empirical models based on the effective viscosity approach with experimental results, we find some anomaly in the region between the molecular regime and the intrinsic regime where non-fluid damping dominates. To improve modelling in the rarified regimes, we modify the best model among the existing models by minimizing error obtained with respect to the experimental results. We find that the proposed model captures the rarefaction effect not only in the slip, transition and molecular regimes but also couples well with the non-fluid damping in the intrinsic regime and captures the transition to purely intrinsic losses.

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Section: Introductionmentioning

confidence: 99%

A semi-analytical model for squeeze-film damping including rarefaction in a MEMS torsion mirror with complex geometry

Pandey

Pratap

2008

J. Micromech. Microeng.

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“…Modeling and analysis of the electrostatically actuated torsional micromirror have been reported [7][8][9][10][11][12][13]. The wellknown pull-in phenomenon exists in electrostatic actuation techniques, which limits the stable operational range of the electrostatically actuated torsional micromirror.…”

Section: Introductionmentioning

confidence: 99%

Second-order sliding mode control of a 2D torsional MEMS micromirror with sidewall electrodes

Chen

Sun

et al. 2012

J. Micromech. Microeng.

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A second-order sliding mode control (2-SMC) scheme with a proportional integral derivative (PID) sliding surface, to achieve enhanced transient response, accurate positioning and precise tracking performance of a 2-degree-of-freedom (2D) torsional MEMS micromirror with sidewall electrodes, is developed in this paper. The PID sliding surface is chosen to achieve a zero steady-state error of the closed-loop system. The 2-SMC is able to reduce the chattering phenomena, which comprises of an equivalent control and switching control to dominate model uncertainty and external disturbances leading to an enhanced performance of the controlled system. Finite-time convergence of the closed-loop system in the presence of bounded parameter uncertainties and external disturbances is guaranteed through Lyapunov stability analysis. The proposed 2-SMC is programmed in a LABVIEW environment and implemented based on National Instrument (NI) field-programmable gate array hardware to verify the effectiveness and robustness. The experimental results of set-point regulation and sinusoidal trajectory tacking demonstrate that the closed-loop system with the proposed control scheme significantly improves the transient performance, accurate positioning and trajectory tracking with robustness against external disturbance. The 95% settling time is shortened from 70 to 3 ms for the X-axis and from 60 to 3 ms for the Y-axis respectively, the overshoots and steady-state errors are eliminated in both axes, and less than 5% maximum positioning error is achieved in the presence of external disturbance.

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“…Matlab/Simulink is one of such simulation packages [12][13][14][15][16][17][18]. It can handle nonlinearity of electrostatic actuator and realize circuit blocks by the high level implementation.…”

Section: Introductionmentioning

confidence: 99%

The dynamic model of electrostatic torsion mirror with pull-in consideration for multiphysics behavior anticipation

Fujita

Toshiyoshi

2009

EuroSimE 2009 - 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelect

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This study presents a newly developed dynamic model established by MATLAB Simulink that can handle post pull-in behavior of MEMS electrostatic torsional mirror. In addition to the conventional MATLAB Simulink model of the quadratic oscillation system, a mathematical model of displacement limiter has been inserted to represent the pull-in effect in dynamic analysis. Due to the modification, the model has become applicable to both pre-and post pull-in region of electrostatic actuators. Electrical circuits from the MAT-LAB Simulink libarary can be combined with the mechanical model and simulated to see multiphysics behavior. The new model has been integrated in the simulation model of self-oscillating MEMS system which has CMOS logics, and the versatility in the behaviorlevel simulation has been verified.

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Macro-modelling of a double-gimballed electrostatic torsional micromirror

Cited by 13 publications

References 18 publications

A semi-analytical model for squeeze-film damping including rarefaction in a MEMS torsion mirror with complex geometry

A semi-analytical model for squeeze-film damping including rarefaction in a MEMS torsion mirror with complex geometry

Second-order sliding mode control of a 2D torsional MEMS micromirror with sidewall electrodes

The dynamic model of electrostatic torsion mirror with pull-in consideration for multiphysics behavior anticipation

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