High-accuracy Motion Estimation for MEMS Devices with Capacitive Sensors

With the development of micro-electro-mechanical system (MEMS) technologies, emerging MEMS applications such as in-situ MEMS IMU calibration, medical imaging via endomicroscopy, and feedback control for nano-positioning and laser scanning impose needs for especially accurate measurements of motion using on-chip sensors. Due to their advantages of simple fabrication and integration within system level architectures, capacitive sensors are a primary choice for motion tracking in those applications. However, challenges arise as often the capacitive sensing scheme in those applications is unconventional due to the nature of the application and/or the design and fabrication restrictions imposed, and MEMS sensors are traditionally susceptible to accuracy errors, as from nonlinear sensor behavior, gain and bias drift, feedthrough disturbances, etc. Those challenges prevent traditional sensing and estimation techniques from fulfilling the accuracy requirements of the candidate applications. The goal of this dissertation is to provide a framework for such MEMS devices to achieve high-accuracy motion estimation, and specifically to focus on innovative sensing and estimation techniques that leverage unconventional capacitive sensing schemes to improve estimation accuracy. Several research studies with this specific aim have been conducted, and the methodologies, results and findings are presented in the context of three applications. The general procedure of the study includes proposing and devising the capacitive sensing scheme, deriving a sensor model based on first principles of capacitor configuration and sensing circuit, analyzing the sensor’s characteristics in simulation with tuning of key parameters, conducting experimental investigations by constructing testbeds and identifying actuation and sensing models, formulating estimation schemes is to include identified actuation dynamics and sensor models, and validating the estimation schemes and evaluating their performance against ground truth measurements. The studies show that the proposed techniques are valid and effective, as the estimation schemes adopted either fulfill the requirements imposed or improve the overall estimation performance. Highlighted results presented in this dissertation include a scale factor calibration accuracy of 286 ppm for a MEMS gyroscope (Chapter 3), an improvement of 15.1% of angular displacement estimation accuracy by adopting a threshold sensing technique for a scanning micro-mirror (Chapter 4), and a phase shift prediction error of 0.39 degree for a electrostatic micro-scanner using shared electrodes for actuation and sensing (Chapter 5).PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147568/1/davidsky_1.pd

Energy efficient control of electrostatically actuated MEMS

Plenty of Micro-electro-mechanical Systems (MEMS) devices are actuated using electrostatic forces, and specially, parallel-plate actuators are extensively used, due to the simplicity of their design. Nevertheless, parallel-plate actuators have some limitations due to the nonlinearity of the generated force. The dissertation analyzes the dynamics of the lumped electrostatically actuated nonlinear system, in order to obtain insight on its characteristics, define desired performance goals and implement a controller for energy efficient robustly stable actuation of MEMS resonators. In the first part of the dissertation, the modeling of the electromechanical lumped system is developed. From a complete distributed parameters model for MEMS devices which rely on electrostatic actuation, a concentrated parameters simplification is derived to be used for analysis and control design. Based on the model, energy analysis of the pull-in instability is performed. The classic approach is revisited to extend the results to models with a nonlinear springs. Analysis of the effect of dynamics is studied as an important factor for the stability of the system. From this study, the Resonant Pull-in Condition for parallel-plate electrostatically actuated MEMS resonators is defined and experimentally validated. Given the importance of the nonlinear dynamics and its richness in behaviors, Harmonic Balance is chosen as a tool to characterize the steady-state oscillation of the resonators. This characterization leads to the understanding of the key factors for large and stable oscillation of resonators. An important conclusion is reached, Harmonic Balance predicts that any oscillation amplitude is possible for any desired frequency if the appropriate voltage is applied to the resonator. And the energy consumption is dependent on this chosen oscillation frequency. Based on Harmonic Balance results, four main goals are defined for the control strategy: Stable oscillation with large amplitudes of motion; Robust oscillation independently of MEMS imperfections; Pure sinus-like oscillation for high-grade sensing; and Low energy consumption. The second part of the dissertation deals with the controller selection, design and verification. A survey of prior work on MEMS control confirms that existing control approaches cannot provide the desired performance. Consequently, a new three-stage controller is proposed to obtain the desired oscillation with the expected stability and energy efficiency. The controller has three different control loops. The first control loop includes a Robust controller designed using on µ-synthesis, to deal with MEMS resonators uncertainties. The second control loop includes an Internal-Model-Principle Resonant controller, to generate the desired control action to obtain the desired oscillation. And the third control loop handles the energy consumption minimization through an Extremum Seeking Controller, which selects the most efficient working frequency for the desired oscillation. The proposed controller is able to automatically generate the needed control voltage, as predicted by the Harmonic Balance analysis, to operate the parallel-plate electrostatically actuated MEMS resonator at the desired oscillation. Performance verification of stability, robustness, sinus-like oscillation and energy efficiency is carried out through simulation. Finally, the needed steps for a real implementation are analyzed. Independent two-sided actuation for full-range amplitude oscillation is introduced to overcome the limitations of one-sided actuation. And a modification of standard Electromechanical Amplitude Modulation is analyzed and validated for position feedback implementation. With these improvements, a MEMS resonator with the desired specifications for testing the proposed control is designed for fabrication. Based on this design, testing procedure is discussed as future work.Molts microsistemes (MEMS) són actuats amb forces electrostàtiques, i especialment, els actuadors electrostàtics de plaques paral.leles són molt usats, degut a la simplicitat del seu disseny. Tot i això, aquests actuadors tenen limitacions degut a la no-linealitat de les forces generades. La tesi analitza el sistema mecànic no-lineal actuat electrostàticament que forma el MEMS, per tal d'entendre'n les característiques, definir objectius de control de l'oscil.lació, i implementar un controlador robust, estable i eficient energèticament. A la primera part de la tesi es desenvolupa el modelat del sistema electromecànic complert. A partir de la formulació de paràmetres distribuïts aplicada a dispositius MEMS amb actuació electrostàtica, es deriva una formulació de paràmetres concentrats per a l'anàlisi i el disseny del control. Basat en aquest model, s'analitza energèticament la inestabilitat anomenada Pull-in, ampliant els resultats de l'enfocament clàssic al model amb motlles no-lineals. Dins de l'anàlisi, l'evolució dinàmica s'estudia per ser un factor important per a l'estabilitat. D'aquest estudi, la Resonant Pull-in Condition per a actuadors electrostàtics de plaques paral.leles es defineix i es valida experimentalment. Donada la importància de la dinàmica no-lineal del sistema i la seva riquesa de comportaments, s'utilitza Balanç d'Harmònics per tal de caracteritzar les oscil.lacions en estacionari. Aquesta caracterització permet entendre els factors claus per a obtenir oscil.lacions estables i d'amplitud elevada. El Balanç d'Harmònics dóna una conclusió important: qualsevol amplitud d'oscil.lació és possible per a qualsevol freqüència desitjada si s'aplica el voltatge adequat al ressonador. I el consum energètic associat a aquesta oscil.lació depèn de la freqüència triada. Llavors, basat en aquests resultats, quatre objectius es plantegen per a l'estratègia de control: oscil.lació estable amb amplituds elevades; robustesa de l'oscil.lació independentment de les imperfeccions dels MEMS; oscil.lació sinusoïdal sense harmònics per a aplicacions d'alta precisió; i baix consum energètic. La segona part de la tesi tracta la selecció, disseny i verificació dun controlador adequat per a aquests objectius. La revisió dels treballs existents en control de MEMS confirma que cap dels enfocaments actuals permet obtenir els objectius desitjats. En conseqüència, es proposa el disseny d'un nou controlador amb tres etapes per tal d'obtenir l'oscil.lació desitjada amb estabilitat i eficiència energètica. El controlador té tres llaços de control. Al primer llaç, un controlador robust dissenyat amb µ-síntesis gestiona les incertes es dels MEMS. El segon llaç inclou un controlador Ressonant, basat en el Principi del Model Intern, per a generar l'acció de control necessària per a obtenir l'oscil.lació desitjada. I el tercer llaç de control gestiona la minimització de l'energia consumida mitjançant un controlador basat en Extremum Seeking, el qual selecciona la freqüència de treball més eficient energèticament per a l'oscil.lació triada. El controlador proposat és capaç de generar automàticament el voltatge necessari, igual al previst pel Balanç d'Harmònics, per tal d'operar electrostàticament amb plaques paral.leles els ressonadors MEMS. Mitjançant simulació se'n verifica l'estabilitat, robustesa, inexistència d'harmònics i eficiència energètica de l'oscil.lació. Finalment, la implementació real és analitzada. En primer lloc, un nou esquema d'actuació per dos costats amb voltatges independents es proposa per aconseguir l'oscil.lació del ressonador en tot el rang d'amplituds. I en segon lloc, una modificació del sensat amb Modulació d'Amplitud Electromecànica s'utilitza per tancar el llaç de control de posició. Amb aquestes millores, un ressonador MEMS es dissenya per a ser fabricat i validar el control. Basat en aquest disseny, es proposa un procediment de test plantejat com a treball futur.Postprint (published version

Parametric Resonance of a Repulsive Force MEMS Electrostatic Mirror

We investigate the nonlinear dynamic behavior of an electrostatic MEMS mirror. The MEMS mirror is driven by repulsive force actuators, which avoid pull-in instability and enable large travel ranges. In parallel-plate actuators, the force on the structure is toward the substrate limiting the range of motion to the capacitor gap. Unlike parallel-plate, repulsive force actuators push the mirror away from the substrate not limiting the motion. The highly nonlinear nature of the repulsive force and the large motions create unique characteristics that dier from parallel-plate actuators. Repulsive force actuators show linear natural frequency hardening with increased DC voltages unlike parallel-plate ones that have frequency softening. A large parametric resonance is another attribute of repulsive force actuators as the limitations of a small gap and pull-in instability are eliminated. To simulate the system response, we use a lumped parameter model with linear and cubic stiness modulated by the excitation voltage that causes parametric resonances. Using the shooting technique, we obtained simulations that agree well with the nonlinear responses observed in our experiments. As the limitation of a small gap is overcome, the electrostatic force triggers large principal parametric resonances with amplitudes as large as the primary resonance. The parametric resonance is more pronounced at low DC excitation levels when geometric nonlinearities are not significant (axial stress is low). While the initial gap is only 2 microns, under parametric resonance, our one-millimeter diameter mirror reaches 43 m at 1.2 KHz when the excitation level is as low as VDC = 40 V; VAC = 1 V in a vacuum. The ability to achieve parametric resonances with repulsive force actuation can serve and improve the signal-to-noise ratio and speed in various applications such as confocal microscopy

Low-Voltage Closed Loop MEMS Actuators

An efficient electrostatic resonator is designed by adding a low voltage controller to an electrostatic actuator. The closedloop actuator shows stable, and bi-sable behaviors with bounded chaotic oscillations as large as 117% of the capacitor gap. The controller voltage is decreased from a previously designed resonator to less than 9 V thereby reducing the load on the controller circuit components. Bifurcation diagrams are obtained showing the frequency and magnitude of AC voltage required for chaotic oscillations to develop. The information entropy, a measure of chaotic characteristic, is calculated for the micro-resonator and is found to be 0.732

Model identification for impact dynamics of a piezoelectric microactuator

A parameterized model for the impact dynamics of a piezoelectric microactuator is proposed, and a system-identification procedure for quantifying model parameters is presented. The proposed model incorporates squeeze-film damping, adhesion and coefficient-of-restitution effects. Following parameter quantification from sample data of bouncing impacts and progressive ramped-square-wave inputs, the model is found to be effective in predicting the time response of the actuator to a range of square-wave and sinusoidal inputs. The main contributions of this paper are to show that the dynamic response to micro-scale contact can be predicted using simple lumped-parameter modeling after a proposed system-identification procedure is performed and that certain small-scale forces can be quantified. For example, for motions where bounce of the cantilever tip may occur, the range of adhesion is found to be time dependent and vary between approximately 20 and 520 nN, while the range of squeeze-film damping is estimated to be between 50 and 130 nN, depending on the input signal frequency and amplitude. The presence, absence and quantity of bounces upon impact are predicted very accurately, while oscillation amplitudes and contact durations are predicted to be between 1% and 30% error for the majority of many test cases of periodic inputs between 5 and 100 Hz.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98611/1/0960-1317_22_11_115002.pd

Dynamics of a Close-Loop Controlled MEMS Resonator

The dynamics of a close-loop electrostatic MEMS resonator, proposed as a platform for ultra sensitive mass sensors, is investigated. The parameter space of the resonator actuation voltage is investigated to determine the optimal operating regions. Bifurcation diagrams of the resonator response are obtained at five different actuation voltage levels. The resonator exhibits bi-stability with two coexisting stable equilibrium points located inside a lower and an upper potential wells. Steady-state chaotic attractors develop inside each of the potential wells and around both wells. The optimal region in the parameter space for mass sensing purposes is determined. In that region, steady-state chaotic attractors develop and spend most of the time in the safe lower well while occasionally visiting the upper well. The robustness of the chaotic attractors in that region is demonstrated by studying their basins of attraction. Further, regions of large dynamic amplification are also identified in the parameter space. In these regions, the resonator can be used as an efficient long-stroke actuator

Review on the Modeling of Electrostatic MEMS

Electrostatic-driven microelectromechanical systems devices, in most cases, consist of couplings of such energy domains as electromechanics, optical electricity, thermoelectricity, and electromagnetism. Their nonlinear working state makes their analysis complex and complicated. This article introduces the physical model of pull-in voltage, dynamic characteristic analysis, air damping effect, reliability, numerical modeling method, and application of electrostatic-driven MEMS devices

Micro-Resonators: The Quest for Superior Performance

Microelectromechanical resonators are no longer solely a subject of research in university and government labs; they have found a variety of applications at industrial scale, where their market is predicted to grow steadily. Nevertheless, many barriers to enhance their performance and further spread their application remain to be overcome. In this Special Issue, we will focus our attention to some of the persistent challenges of micro-/nano-resonators such as nonlinearity, temperature stability, acceleration sensitivity, limits of quality factor, and failure modes that require a more in-depth understanding of the physics of vibration at small scale. The goal is to seek innovative solutions that take advantage of unique material properties and original designs to push the performance of micro-resonators beyond what is conventionally achievable. Contributions from academia discussing less-known characteristics of micro-resonators and from industry depicting the challenges of large-scale implementation of resonators are encouraged with the hopes of further stimulating the growth of this field, which is rich with fascinating physics and challenging problems

Combined Electrostatic/Electromagnetic MEMS Actuators

In this work, one and two degrees of freedom (DOF) lumped mass models of Micro- Electro-Mechanical System (MEMS) actuators are introduced, investigated, and compared to experimental results. A one degree of freedom system representing the actuators out-of plane bending motion under the electrostatic excitation is demonstrated. The capacitive gap between the movable plate and stationary electrode decreases when the microplate inclination angle is accounted for in the model. We investigate experimentally the primary, superharmonic of order two, and subharmonic of order one-half resonances of an electrostatic MEMS actuator under direct excitation. We identify the parameters of a 1-DOF generalized Duffing oscillator, model that represents it. The experiments were conducted in soft vacuum in order to reduce squeeze- film damping and the actuator response was measured optically using a laser vibrometer. The predictions of the identified model were found to be in close agreement with the experimental results. We also identified the power level of process (actuation voltage) and measurement noise. A one DOF model of the actuator's torsional motion under the electrostatic torque is also introduced. It was found that utilizing electrostatic actuation in torsional motion is not e ffective. The maximum angle obtained was 0.04 degrees at high voltage. Finally, a novel two DOF model of the MEMS actuator's torsion and bending under electrostatic and electromagnetic excitation was demonstrated analytically and compared to experimental results. Torsional motions were driven by a torque arising from a Lorentz force. It succeeded in generating a large torsion angle, 1 degree at 1.35 T magnetic field density, and a current of 3.3 mA

Robust free space board-to-board optical interconnect with closed loop MEMS tracking

We present a free-space optical interconnect system capable of dynamic closed-loop optical alignment using a microlens scanner with a proportional integral and derivative controller. Electrostatic microlens scanners based on combdrive actuators are designed and characterized with vertical cavity surface emitting lasers (VCSELs) for adaptive optical beam tracking in the midst of mechanical vibration noise. The microlens scanners are fabricated on silicon-on-insulator wafers with a bulk micromachining process using deep reactive ion etching. We demonstrate dynamic optical beam positioning with a 700 Hz bandwidth and a maximum noise reduction of approximately 40 dB. Eye diagrams with a 1 Gb/s modulation rate are presented to demonstrate the improved optical link in the presence of mechanical noise