This paper includes two main parts: the first part investigates the coexistence and the bifurcation of equilibrium points in the dynamics of permanent magnet sychronous motor (PMSM). Some critical points are detected for a set of system parameters and initial condition, namely Hopf and saddle Node bifurcations. The second part deals with the synchronization of chaos by using a PI regulator. The role of Largest Lyapunov exponents and their computation are among the main issues discussed in this part.