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Fractional robust data-driven control of nonlinear MEMS gyroscope

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Abstract

This research proposes a new fractional robust data-driven control method to control a nonlinear dynamic micro-electromechanical (MEMS) gyroscope model. The Koopman theory is used to linearize the nonlinear dynamic model of MEMS gyroscope, and the Koopman operator is obtained by using the dynamic mode decomposition (DMD) method. However, external disturbances constantly affect the MEMS gyroscope. To compensate for these perturbations, a fractional sliding mode controller (FOSMC) is applied. The FOSMC has several advantages, including high trajectory tracking performance and robustness. However, one of the drawbacks of FOSMC is generating high control inputs. To overcome this limitation, the researchers proposed a compound controller design that applies fractional proportional integral derivative (FOPID) to reduce the control efforts. The simulation results showed that the proposed compound Koopman-FOSMC and FOPID (Koopman-CFOPIDSMC) outperformed two other controllers, including FOSMC and Koopman-FOSMC, in terms of performance. Therefore, this research proposes an effective approach to control the nonlinear dynamic model of MEMS gyroscope.

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Funding

This material is based upon work supported by the National Science Foundation under 261 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

  2. Department at the Polytechnic School, Ira Fulton School of Engineering, Arizona State University, Mesa, AZ, 85212, USA

    Sangram Redkar

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  1. Mehran Rahmani
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Correspondence to Mehran Rahmani.

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Rahmani, M., Redkar, S. Fractional robust data-driven control of nonlinear MEMS gyroscope. Nonlinear Dyn 111, 19901–19910 (2023). https://doi.org/10.1007/s11071-023-08912-x

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