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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Optimal control of a MEMS gyroscope based on the Koopman theory
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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- Award ID(s):
- 1828010
- NSF-PAR ID:
- 10433577
- Date Published:
- Journal Name:
- International Journal of Dynamics and Control
- ISSN:
- 2195-268X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s40435-022-01110-4
