Phase space singularities in speed field oriented control of PMSM

The existence and the stability of phase space singularities namely equilibrium points and limit cycles are discussed. The coexistence of many stable behaviors for a given set of system parameters and for different initial conditions is presented putting evidence into the most exciting phenomena in nonlinear dynamics, referred to as multistability. A classical method of speed control of synchronous motor is applied in order to obtain numerical coordinates of equilibrium points. Their stability is analyzed by mean of Eigenvalues derived from Jacobian matrix of the system. The sets of initial conditions leading to such or such equilibrium point known as attraction basins are traced for different sets of system parameters whether that was close or far from critical points or bifurcation.