Electrostatic Torsional Micromirror Research Articles

Twisting sliding mode control of an electrostatic MEMS micromirror for a laser scanning system

In this paper, we present a twisting control scheme with proportional-integral-derivative &#x0028 PID &#x0029 sliding surface for a two-axis electrostatic torsional micromirror, and the utilization of the proposed scheme in a laser scanning system. The experimental results of set-point regulation verify that the proposed scheme provides enhanced transient response and positioning performance as compared to traditional sliding mode control. To evaluate the tracking performance of the closed-loop system, triangular waves with different frequencies are used as desired traces. With the proposed scheme the experimental results verified that the closed-loop controlled micromirror follows the given triangular trajectories precisely. A micromirror-based laser scanning system is developed to obtain images. When compared with open-loop control, the experimental results demonstrated that the proposed scheme is able to reduce the distortion of the raster scan, and improve the imaging performance in the presence of cross-coupling effect.

Active Disturbance Rejection Control of a 2D MEMS Micromirror with Sidewall Electrodes

This study proposes the active disturbance rejection control (ADRC) for a second degree of freedom (2D) electrostatic torsional micromirror with sidewall electrodes. The main idea is to use the linear extended state observer (LESO) to estimate the external disturbance and the angular velocity of the micromirror, and a feedback controller is further applied to achieve the position control of the micromirror. The effectiveness of the LESO in the estimation of the external disturbance and angular velocity is demonstrated. The proposed novel control scheme provides the micromirror with high positioning accuracy and disturbance rejection.

Robust control of the electrostatic torsional micromirrors

In order to simplify the sensors subsystems of the electrostatic torsional micromirrors (ETMs), the output feedback control for the ETM systems is investigated in this paper. The dynamics of the systems is established by combining the dynamics of both the mechanical and electronic subsystems, and it is proved that the dynamics of the overall system with uncertainties in electrical parameters can be exactly transformed into the third order linear system. Then an output feedback finite-time stabilizing (FTS) controller is presented by composing of a full state FTS observer and a state feedback FTS controller for the third order linear systems, such that the ETM systems can be stabilized in its full travel range by merely measuring the tilt angle. Some numerical simulations demonstrate the stability of the proposed output feedback FTS controller.

Enhancing tilt range of electrostatic torsional micromirrors using robust adaptive critic-based neurofuzzy control

Electrostatic torsional micromirrors, as instances of Micro Electro Mechanical Systems (MEMS), have many optical network applications; such as optical wavelength-selective switches, optical cross-connects, etc. For all these applications, the micromirror needs to have minimal overshoot and settling time in order to minimize the time between two successive switching operations. Moreover, the controllability and stability of a torsional micromirror are major challenges due to high nonlinearities in its dynamic characteristics.In this paper, a robust adaptive critic-based neurofuzzy controller is proposed for electrostatic torsional micromirrors, which can improve the performance of the mirror tilting and enhance the robustness of the system to any stochastic perturbations. Furthermore, utilizing this adaptive neurofuzzy controller, which is based on a proportional and derivative (PD) critic, the micromirror “pull-in” phenomenon is crucially eliminated. Thus, the mirror tilting range is significantly expanded. Moreover, the stability of the closed-loop system is guaranteed via the Lyapunov theorem.The robust adaptive critic-based neurofuzzy controller is simulated for a 1-DOF electrostatic torsional micromirror and the results show the effectiveness of this approach for various tilt ranges and conditions. In addition, the robustness of this controller is examined in the presence of input noises and parameter uncertainties.

Constraint adaptive output regulation of output feedback systems with application to electrostatic torsional micromirror

SummaryThis paper studies a constraint adaptive output regulation design for a class of nonlinear systems with an unknown exosystem by output feedback control. First, by introducing an internal model with some known design parameter, our concerned problem may be formulated as a specific regulation problem with output constraint. Then, the barrier Lyapunov function technique is further integrated to approach the problem. It is shown that such a constraint adaptive output regulation problem is solvable without constraint violation. In particular, the constructed regulator cannot only keep the boundedness of the closed‐loop system signals but also guarantees the parameter convergence for the unknown parameter vector in the exosystem. As an application, it is illustrated that our result is applicable in tracking the control of an electrostatic torsional micromirror with physical geometry constraint. Copyright © 2013 John Wiley & Sons, Ltd.

Design and Simulation of a MEMS Torsional Micromirror

In this paper, we designed an electrostatic driving MEMS torsional micromirror. The operation principle of the torsional micromirror is analyzed. Based on the analysis, a set of optimized design parameters of the micromirror is suggested. The design optimization of the micromirror is also performed with MathCAD software. At last an ANSYS simulation is achieved in the paper, which proves that the micromirror can provide a maximum workable torsional angle rotation of ±0.55º with corresponding driving voltage of 17.5V.

Modeling and Active Control of Circular Electrostatic Torsional Micromirror

Three main obstacles in modeling electrostatic torsional micromirror are hard to calculate – damping coefficient, mechanical spring constant and electrostatic torsion accurately. Because that parameter variations and model uncertainty of the torsional micromirror resulting from fabrication imperfections are inevitable, it is another problem to seek a control scheme for achieving accurate positioning and trajectory tracking of an electrostatic torsional micromirror. In this paper, aimed at a real prototype of circular electrostatic torsional micromirrorr, both static and dynamic behaviors are modeled and studied. A novel nonlinear Proportional, Integral and Derivative (PID) control are proposed in succession. Simulation results show that the system model derived is more accurate to the micromirror and the nonlinear PID can eliminate the static deviation.

Gas-damped double-gimbaled electrostatic torsional micromirror modeling and simulation

In this paper, the modeling and simulation of the gas-damped double-gimbaled electrostatic torsional micromirror are presented. The model is represented as a system of coupled equations, and combines both the distributed and lumped parameter description. It involves electrostatics, solid mechanics and gas dynamics. The bending effect of the micromirror suspensions is also considered. Based on the model, the micromirror behavior has been simulated and the simulation results are presented. The model is applicable for wide class of electrostatic MEMS actuators. Moreover, the great advantage of the presented model is enormous reduction in computational time in comparison with the model completely based on the finite element analysis.

Nonlinear vibrations and chaos in electrostatic torsional actuators

Electrostatic torsional micro-mirrors have wide spread use in different industries for diverse purposes. This paper investigates the development of superharmonics and chaotic responses in electrostatic torsional micro-mirrors near the pull-in condition. Appearance of nonlinear phenomena is investigated in models accounting for and disregarding the coupling of torsional and flexural deflections. Analysis of the system response to step and harmonic excitation reveals the appearance of DC and AC symmetry breaking. Increasing the amplitude of harmonic excitation, the response in the form of distinct superharmonics changes to a broad band response, where there is loss of periodicity and the response becomes chaotic. Accounting for flexural deflections in coupled model reduces the voltage thresholds corresponding to symmetry breaking and chaotic responses. It is also shown that damping has a regularizing effect and introduction of damping changes the chaotic undamped response into quasi-periodic one.

Switching Time Reduction for Electrostatic Torsional Micromirrors Using Input Shaping

We have demonstrated switching time reduction for microfabricated, vertical comb-based electrostatic torsional micromirror actuators by suppressing residual vibration using pre-shaped command inputs. The step input is pre-shaped by pulse–impulse convolution method, one of the impulse shaping filters. The micromirror actuators tested in experiment are made of single-crystal silicon and driven by vertical comb sets in torsional direction. Before shaping the input signal, the measured 2% settling time is 25 ms with percent overshoot of 58% for a step voltage input to induce the angular motion in micromirror actuator. The improved settling time is observed to be 8 ms with 5.8% overshoot when the pre-shaped input is applied. The input-shaping technique is applied to two types of microactuators with different dynamic characteristics in order to verify its feasibility on various systems, and it is experimentally shown that the pre-shaped input command successfully suppresses the residual vibration for both highly underdamped microactuators.

Modeling of an electrostatic torsional micromirror for laser projection system

This paper presents the Simulink™ model of a new 2D torsional scanning micromirror. This Micro-Opto-Electro-Mechanical-System (MOEMS) is very important towards the integration into a system on a package of a complete laser projection system. Modeling and simulation of the MOEMS is a key point for the development of the proper micromirror electronic conditioning interface thus reducing time to market and production costs. In literature there are not exhaustive examples of complete characterizations of 2D torsional scanning micromirrors. The aim of this work is to develop a Simulink™ model which incorporates the main mechanical and electrostatic parameters of the sensor such as the resonance frequency, the torsional constant and capacitance versus rotation angle characteristic. This model has been successfully verified via experimental measurements and it proved his effectiveness in the development of the relevant electronic conditioning circuitry.

Torque Multiplication and Singularity Avoidance in the Control of Electrostatic Torsional Micro-Mirrors

The present work addresses the control of torsional micro-mirrors assisted by a constant bias voltage. It is shown that such a configuration will have an effect of torque multiplication and hence, it will reduce the dynamic range of actuation signal. A nonlinear controller using backstepping and barrier functions is developed, which can guarantee closed-loop stability in a restricted range covering a big portion of the physically allowable one, while eliminating the singularities due to uncontrollability and contact dynamics. In this study, the actuation voltage is taken as a state variable. This would further simplify the implementation of experimental systems. The development of the control algorithm has been demonstrated through a rectangular micro-mirror and the performance of the system is verified by numerical simulations. As a generic model is used in the design, the control algorithm developed can be applied to any device with the same structure regardless of the geometric shape.

Investigation of the torsion and bending effects on static stability of electrostatic torsional micromirrors

In this paper the electromechanical behavior of a torsional micromirror was investigated using of a static model with considering torsion and bending characteristics of micro-beams. A set of nonlinear equations based on the parallel plate capacitor model was derived to represent the relationships between the applied voltage, torsion angle, and vertical displacement of the torsional micromirror. Step by step linearization method (Newton’s method) was used to calculate the rotation angle and vertical displacement of the micromirror due to the applied voltage. This method is fast and gave acceptable and accurate results which were in good agreement with the experimental data.

A Design Approach to 2-D Electrostatic Torsional Micromirrors With Z-Axis Displacement Compensation

We report a new method for maintaining constant z-axis displacement of an electrostatic torsional micromirror driven by quadrant electrodes, by adding an additional control electrode. The voltage applied to the control electrode is theoretically related to the voltages applied to the quadrant electrodes. The mathematical model is presented and validated through finite-element analysis

Design, modeling, fabrication and testing of a high aspect ratio electrostatic torsional MEMS micromirror

As an essential part of an optical imager project, there was the need for a very high aspect ratio MEMS optical scanning mirror (5 mm × 150 µm clear aperture), capable of a ±2° sweep at 1 kHz with an applied voltage less than 200 V. This paper reports on the design, fabrication, modeling and testing of such an electrostatically actuated MEMS mirror. Fabrication involves using a ⟨1 0 0⟩ n-type double side polished silicon wafer, along with surface and bulk micromachining techniques, to produce a mirror with nickel torsion springs and nickel electrostatic actuators. There were 8 masks and 20 processing steps required. The performance of these devices was measured and found to be within the required specifications. Analysis involved developing models to predict the dynamic behavior of these MEMS micromirrors. A basic parallel plate capacitor model was adjusted with finite element analysis to account for fringing fields. Young's modulus of the electroplated nickel was determined to be 110 GPa from a comparison of the model with the results of dynamic testing, and the residual strain test structures led to a value of 0.0029 for the residual strain. Each of these values is within the rather wide range of published values. Once these values were determined, the model agreed very well with the measurements of the dynamic angular response of the mirror.

Bouncing mode electrostatically actuated scanning micromirror for video applications

We present a design and operation concept of a scanning device based on an electrostatictorsional micromirror that is aimed to fulfil the requirements of motion linearity, highoperational frequency and low actuation voltages imposed by laser display applications.The operational mode incorporates a contact event between the mirror and an elasticconstraint followed by a bouncing and an inversion of motion. A triangular response signalis obtained by the application of an actuation voltage which is piecewise constant in time.The tuning of the resonant frequency through the control of the applied voltage permitsthe synchronization of the response of the microfabricated device with a videosignal.

A study on the coupled dynamic characteristics for a torsional micromirror

A nonlinear dynamic model of an electrostatic torsional micromirror considering the coupled effect of the torsion and vertical bending motion of its torsional beam simultaneously is presented. The effect of the vertical deformation of the mirror plate and the distributed mass of the torsion beam are also considered in this model. The validity of the model is verified by a finite element simulation with ANSYS. Undamped and damped responses of the torsional and vertical vibration of the micromirror are analyzed by the model given here. The results of the simulation indicate that this model can simulate the dynamic behaviors of the micromirror fast and accurately.

Neural Network Approach for Linearization of the Electrostatically Actuated Double-Gimballed Micromirror

In this paper, a hierarchical circuit based approach is used for the development of a reduced-order macro-model for a double-gimballed electrostatic torsional micromirror. The nonlinearity and cross-axis coupling of the micromirror subjected to the differential driving scheme are investigated using the proposed macro-model. The simulation results are used to train a feed-forward neural network which carries out a function approximation of the relation between the desired location and the required driving voltages. The trained neural network is then coded into MAST AHDL. System-level simulation of the micromirror together with the neural network is performed in the SABER™ simulator. It is found that using a feed-forward neural network, the linearity of the micromirror is greatly improved, the steady state of the cross-axis coupling is reduced to a negligible level and the transient response of the cross-axis coupling is also suppressed. This implies that introducing a feed-forward neural network would be useful to simplify the design of the feedback control system for the double-gimballed electrostatic torsional micromirror.

An approach to the coupling effect between torsion and bending for electrostatic torsional micromirrors

A general theoretical model using the coupling effect between the torsion and bending is presented in this paper, which characterizes the static properties of the electrostatic torsional micromirror, especially its pull-in effect. A set of normalized equations governing the static actuation properties of the torsional micromirror based on the parallel plate capacitor model is derived to demonstrate the relationships between the parameters of static characteristics, such as torsion angle, vertical displacement, and applied voltage. Thereafter, the pull-in effect is investigated specifically to predict pull-in voltage, pull-in angle, and pull-in displacement, which highly depend on the electrode size and position, and ratio of the bending and torsion effect of the torsion beam. The ratio of the bending and torsion effect plays a key role in the pull-in phenomena. It also determines the instability mode of torsional micromirrors dominated by either the torsion or bending effect. Then, a group of torsional micromirrors is fabricated using three-layer-polysilicon micromachining process and measured using an optical projection method to verify the static actuation relation and pull-in effect respectively. The experimental data are processed and analyzed, and the theoretical analysis is in good agreement with the experimental results.

MODELING OF A TWO-AXIS TORSIONAL MICROMIRROR USING AHDL

This paper presents the development of a reduced-order macro-model for a two-axis electrostatic torsional micromirror using analog hardware description language (AHDL). The proposed macro-model permits extremely fast simulation while providing nearly FEM accuracy. This enables the user to investigate the close-loop controlled global system level performances at acceptable computational cost.