title: Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation.
abstract: High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror's nonlinear dynamics under such excitation is analyzed in a Hill's equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror's frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies.
authors.affiliation: Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48105 USA.
authors.forename: Wajiha
authors.initials: W
authors.lastname: Shahid
authors.affiliation: Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109 USA.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Qiu
authors.affiliation: Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109 USA.
authors.forename: Xiyu
authors.initials: X
authors.lastname: Duan
authors.affiliation: Department of Internal Medicine-Gastroenterology Division, University of Michigan, Ann Arbor, MI 48109 USA.
authors.forename: Haijun
authors.initials: H
authors.lastname: Li
authors.affiliation: Department of Biomedical Engineering, Department of Internal Medicine-Gastroenterology Division, University of Michigan, Ann Arbor, MI 48109 USA.
authors.forename: Thomas D
authors.initials: TD
authors.lastname: Wang
authors.affiliation: Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48105 USA.
authors.forename: Kenn R
authors.initials: KR
authors.lastname: Oldham
keywords: Hill’s equation; MEMS; micro-mirror; nonlinear dynamics; parametric resonance