This invention discloses an adaptive chaos control method of the fractional-order brushless DC motor system whichcovers the following steps:(1) firstly build the fractional-order mathematicalmodel of the brushless DC motorsystem, use the estimated values of state variables to substitute real statevariables of the observed system whereinthe fractional-order high-gain observer is designed, (2)define the errorvector and employ the Chebyshev neuralnetwork to approximate nonlinear function with a small error, then design thefractional-order Levanttracking-differentiator to solve the repeated derivative associated withbackstepping, (3)use the fractional-orderLyapunov function to obtain virtual and real control inputs, and deal with thestability analysis, meanwhile establishan adaptive chaos controller by the aid of the continuous frequencydistributed model in the framework ofbackstepping. This invention not only guarantees the transient and steadystate performance of the fractional-orderbrushless DC motor system, but also suppresses the chaotic oscillation.
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