### 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 language | English (US) |
---|---|

Pages (from-to) | 167-179 |

Number of pages | 13 |

Journal | Nonlinear Dynamics |

Volume | 54 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1 2008 |

### Fingerprint

### 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

*Nonlinear Dynamics*,

*54*(1-2), 167-179. https://doi.org/10.1007/s11071-007-9246-x

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

Research output: Contribution to journal › Article

*Nonlinear Dynamics*, vol. 54, no. 1-2, pp. 167-179. https://doi.org/10.1007/s11071-007-9246-x

}

TY - JOUR

T1 - Input-shaping control of nonlinear MEMS

AU - Daqaq, Mohammed

AU - Reddy, C. K.

AU - Nayfeh, A. H.

PY - 2008/10/1

Y1 - 2008/10/1

N2 - 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.

AB - 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.

KW - Input-shaping control

KW - MEMS

KW - Reduced-order modeling

KW - Torsional micromirror

UR - http://www.scopus.com/inward/record.url?scp=50249163874&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50249163874&partnerID=8YFLogxK

U2 - 10.1007/s11071-007-9246-x

DO - 10.1007/s11071-007-9246-x

M3 - Article

AN - SCOPUS:50249163874

VL - 54

SP - 167

EP - 179

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 1-2

ER -