Optimal control of a MEMS gyroscope based on the Koopman theory

Mehran Rahmani; Sangram Redkar

doi:10.1007/s40435-022-01110-4

Optimal control of a MEMS gyroscope based on the Koopman theory

Mehran Rahmani, Sangram Redkar

Engineering, Ira A. Fulton Schools of (IAFSE)

Research output: Contribution to journal › Article › peer-review

Abstract

Microelectromechanical (MEMS) gyroscopes are small devices used in different industries such as automotive and robotics systems due to their small size and low costs. The MEMS gyroscopes constantly encounter external disturbances, which introduce some mechanical and electromechanical nonlinearity in those systems. In this paper, the Koopman theory is applied to the nonlinear dynamic model of MEMS gyroscope to the linear dynamics model. Dynamic mode decomposition (DMD) is used to obtain eigenfunctions using Koopman’s theory to linearize the system. Then, a linear quadratic regulator (LQR) controller is used to control the MEMS gyroscope. The simulation results verify the performance of the proposed controller in terms of high-tracking performance.

Original language	English (US)
Journal	International Journal of Dynamics and Control
DOIs	https://doi.org/10.1007/s40435-022-01110-4
State	Accepted/In press - 2023

Keywords

Dynamic mode decomposition
Koopman theory
LQR controller
MEMS gyroscope
Nonlinearity

ASJC Scopus subject areas

Control and Systems Engineering
Civil and Structural Engineering
Modeling and Simulation
Mechanical Engineering
Control and Optimization
Electrical and Electronic Engineering

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10.1007/s40435-022-01110-4

Cite this

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title = "Optimal control of a MEMS gyroscope based on the Koopman theory",

abstract = "Microelectromechanical (MEMS) gyroscopes are small devices used in different industries such as automotive and robotics systems due to their small size and low costs. The MEMS gyroscopes constantly encounter external disturbances, which introduce some mechanical and electromechanical nonlinearity in those systems. In this paper, the Koopman theory is applied to the nonlinear dynamic model of MEMS gyroscope to the linear dynamics model. Dynamic mode decomposition (DMD) is used to obtain eigenfunctions using Koopman{\textquoteright}s theory to linearize the system. Then, a linear quadratic regulator (LQR) controller is used to control the MEMS gyroscope. The simulation results verify the performance of the proposed controller in terms of high-tracking performance.",

keywords = "Dynamic mode decomposition, Koopman theory, LQR controller, MEMS gyroscope, Nonlinearity",

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AU - Rahmani, Mehran

AU - Redkar, Sangram

N1 - Funding Information: This article is based upon work supported by the National Science Foundation (Grant No. 1828010). Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - Microelectromechanical (MEMS) gyroscopes are small devices used in different industries such as automotive and robotics systems due to their small size and low costs. The MEMS gyroscopes constantly encounter external disturbances, which introduce some mechanical and electromechanical nonlinearity in those systems. In this paper, the Koopman theory is applied to the nonlinear dynamic model of MEMS gyroscope to the linear dynamics model. Dynamic mode decomposition (DMD) is used to obtain eigenfunctions using Koopman’s theory to linearize the system. Then, a linear quadratic regulator (LQR) controller is used to control the MEMS gyroscope. The simulation results verify the performance of the proposed controller in terms of high-tracking performance.

AB - Microelectromechanical (MEMS) gyroscopes are small devices used in different industries such as automotive and robotics systems due to their small size and low costs. The MEMS gyroscopes constantly encounter external disturbances, which introduce some mechanical and electromechanical nonlinearity in those systems. In this paper, the Koopman theory is applied to the nonlinear dynamic model of MEMS gyroscope to the linear dynamics model. Dynamic mode decomposition (DMD) is used to obtain eigenfunctions using Koopman’s theory to linearize the system. Then, a linear quadratic regulator (LQR) controller is used to control the MEMS gyroscope. The simulation results verify the performance of the proposed controller in terms of high-tracking performance.

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KW - Nonlinearity

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Optimal control of a MEMS gyroscope based on the Koopman theory

Abstract

Keywords

ASJC Scopus subject areas

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