Input-shaping control of nonlinear MEMS

Mohammed Daqaq, C. K. Reddy, A. H. Nayfeh

Research output: Contribution to journalArticle

Abstract

We develop a new technique for preshaping input commands to control microelectromechanical systems (MEMS). In general, MEMS are excited using an electrostatic field which is a nonlinear function of the states and the input voltage. Due to the nonlinearity, the frequency of the device response to a step input depends on the input magnitude. Therefore, traditional shaping techniques which are based on linear theory fail to provide good performance over the whole input range. The technique we propose combines the equations describing the static response of the device, an energy balance argument, and an approximate nonlinear analytical solution of the device response to preshape the voltage commands. As an example, we consider set-point stabilization of an electrostatically actuated torsional micromirror. The shaped commands are applied to drive the micromirror to a desired tilt angle with zero residual vibrations. Simulations show that fast mirror switching operation with almost zero overshoot can be realized using this technique. The proposed methodology accounts for the energy of the significant higher modes and can be used to shape input commands applied to other nonlinear micro- and macro-systems.

Original languageEnglish (US)
Pages (from-to)167-179
Number of pages13
JournalNonlinear Dynamics
Volume54
Issue number1-2
DOIs
StatePublished - Oct 1 2008

Fingerprint

Micro-electro-mechanical Systems
MEMS
Nonlinear Systems
Micromirror
Electric potential
Energy balance
Macros
Mirrors
Stabilization
Voltage
Electric fields
Electrostatic Field
Microsystems
Overshoot
Energy Balance
Zero
Tilt
Nonlinear Function
Point Sets
Mirror

Keywords

  • Input-shaping control
  • MEMS
  • Reduced-order modeling
  • Torsional micromirror

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Input-shaping control of nonlinear MEMS. / Daqaq, Mohammed; Reddy, C. K.; Nayfeh, A. H.

In: Nonlinear Dynamics, Vol. 54, No. 1-2, 01.10.2008, p. 167-179.

Research output: Contribution to journalArticle

Daqaq, Mohammed ; Reddy, C. K. ; Nayfeh, A. H. / Input-shaping control of nonlinear MEMS. In: Nonlinear Dynamics. 2008 ; Vol. 54, No. 1-2. pp. 167-179.
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