This article presents the design, dynamic analysis, and control of a flywheel energy storage system. At the heart of the system is a hybrid magnetic bearing. The bearing consists of ring and disk shaped permanent magnets, and a synthetic ruby sphere on a sapphire plate. The bearing is shown to be stable without active control. Equations of motion for the flywheel are derived in a sensor based coordinate system. The resulting equations are non-singular around the nominal operating condition and are feedback linearizable without the need for a coordinate transformation. A method of modeling rotor imbalance as a set of sinusoidal disturbances of magnitudes that do not depend on rotational speed is also presented. To reject large external disturbances active control is applied to the flywheel. Two nonlinear control laws are applied and are shown to improve the initial condition response of the inherently stable system.
Analysis and Control of a Flywheel Energy Storage System With a Hybrid Magnetic Bearing
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Stienmier, J. D., Thielman, S. C., and Fabien, B. C. (December 1, 1997). "Analysis and Control of a Flywheel Energy Storage System With a Hybrid Magnetic Bearing." ASME. J. Dyn. Sys., Meas., Control. December 1997; 119(4): 650–656. https://doi.org/10.1115/1.2802374
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