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Although brushless DC motors have been preferably used in wide industrial applications on the basis of superior properties and stable operation, the stability of brushless DC motors is found to be dependent on their chaotic characteristics and initial operating conditions. Owing to such characteristics, this article presents the chaos control and chaotic characteristics of brushless DC motors through newly defined mathematical techniques, so-called fractal-fractional differentiations. Mathematical modeling of the governing equations of the brushless DC motor has been developed by means of Caputo, Caputo-Fabrizio and Atangana-Baleanu fractal-fractional differential operators. The sensitive initial conditions and vibrant parameters have been analyzed for the comparative performance and assessment of the brushless DC motor. The numerical simulations of fractal-fractionalized governing equations of the brushless DC motor have been performed by means of the Adams-Bashforth-Moulton method using MATLAB package. Finally, the graphical illustrations have been underlined for the proposed Caputo, Caputo-Fabrizio and Atangana-Baleanu fractal-fractional differential operators subject to the chaotic behaviors investigated for the brushless DC motor.

Chaos control and characterization of brushless DC motor via integral and differential fractal-fractional techniques