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Optimal control of a MEMS gyroscope based on the Koopman theory

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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.

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Funding

This article is based upon work supported by the National Science Foundation (Grant No. 1828010).

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Authors and Affiliations

  1. The Polytechnic School, Ira Fulton School of Engineering, Arizona State University, Mesa, AZ, 85212, USA

    Mehran Rahmani & Sangram Redkar

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  1. Mehran Rahmani
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  2. Sangram Redkar
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by MR and Dr. SR. The first draft of the manuscript was written by MR and Dr. SR commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Mehran Rahmani.

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Ethical Statement

I hereby declare that this manuscript is the result of my independent creation under the reviewer’s comments. Except for the quoted contents, this manuscript does not contain any research achievements that have been published or written by other individuals or groups. Mehran Rahmani and Sangram Redkar are the only authors of this manuscript. The legal responsibility of this statement shall be borne by me.

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Rahmani, M., Redkar, S. Optimal control of a MEMS gyroscope based on the Koopman theory. Int. J. Dynam. Control 11, 2256–2264 (2023). https://doi.org/10.1007/s40435-022-01110-4

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  • DOI: https://doi.org/10.1007/s40435-022-01110-4

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