Chaotic synchronization of permanent magnet synchronous motors with non-smooth-air-gap up to an arbitrary scaling matrix

This paper introduces a synchronization control method for the chaotic system of the permanent-magnet synchronous motor (PMSM) with non-smooth-air-gap. Firstly, the model of the PMSM based on d-q axis is transformed into a simple dimensionless form via the multi-time-scale transformation, and then the chaotic behavior of the PMSM is analyzed. Secondly, by linear system stability theory and the pole placement technique, the theorem that guarantees synchronization can be achieved for any arbitrary scaling matrix is introduced. Finally, numerical simulation results confirm the correctness of the theoretical analysis and validity of the proposed method.