Fractional-order Adaptive Control of Permanent Magnet Synchronous Motor

In order to achieve the chaotic control of permanent magnet synchronous motor, a new method of fractional order adaptive controller design is put forward. First, the mathematical model of fractional-order permanent magnet synchronous motor was built, the chaotic behaviors of which was investigated by using fractional-order predictor-corrector approach. Then, a new simple fractional-order adaptive feedback controller was designed to implement the chaotic control for the fractional-order permanent magnet synchronous motor system. By constructing an appropriate Lyapunov function and utilizing a new fractional inequality, Mittag-Leffler function, and Laplace transform, a sufficient criterion was derived for the global asymptotical stabilization by using the designed adaptive controller. Finally, numerical simulations were given to demonstrate the effectiveness and the robust of the proposed method to the external disturbances, such as random sinusoidal signals.