Adaptive Neural Network Control of Chaotic Fractional-Order Permanent Magnet Synchronous Motors Using Backstepping Technique

The backstepping technique is greatly effective for the integral-order triangular nonlinear systems. Nevertheless, it is dramatically challenging to implement backstepping technique in the manipulation of fractional-order permanent magnet synchronous motors (FOPMSMs), since the fractional derivatives of the composite functions are deeply complex. In this paper, a fuzzy adaptive backstepping-based control scheme for FOPMSMs on the basis of fractional Lyapunov stability criterion is established. First, we propose a novel adaptive synchronous controller for FOPMSMs by coupling with fuzzy logic systems and backstepping technique. Then, we present a detailed stability analysis in terms of FOPMSMs via the proposed controllers. Finally, a simulation example is given to reveal that the proposed controller can effectively eliminate or restrain the chaos of FOPMSMs, and keep the tracking signals synchronous with the reference signals.