Trajectory tracking for a class of switched nonlinear systems: Application to PMSM

This paper proposes a state-dependent switching control for a class of switched nonlinear systems, whose model describes a permanent magnet synchronous machine (PMSM) fed by a three-phase voltage source inverter. Due to its high torque density, high efficiency and wide velocity range, this electrical drive is widely used for traction and several applications in robotics, aerospace, electric vehicles among others. The proposed design conditions are based on a non-quadratic Lyapunov function, dependent on the machine shaft displacement, and assure asymptotic tracking of a pre-specified time-varying rotational velocity profile with guaranteed performance. Properties of the nonlinear system under consideration are used to derive design conditions expressed in terms of linear matrix inequalities that can be solved efficiently. Special cases involving asymptotic stability toward step and ramp velocity profiles are presented. Experimental results are used to validate the proposed technique.