Control of Bifurcation and Chaos in the Model of the Permanent-magnet Synchronous Motor

This paper addresses the problem of control bifurcation and chaos in the model of permanent-magnet synchronous motors in the unforced mode. By constructing the bifurcation diagram and calculating the largest Lyapunov exponent, we found that the permanent-magnet synchronous motor can undergo Pitchfork and Hopf bifurcations as well as exhibit chaotic behavior when its parameter lies in a certain area. Also, the paper proposes a dynamic feedback control to relocate a Hopf bifurcation point to a new desired position. As a result of the control action, the stable range of equilibria can be extended as well as the chaotic behavior can be avoided in the desired range of the motor's parameter