PID position regulation in one-degree-of-freedom Euler–Lagrange systems actuated by a PMSM

This paper is concerned with position regulation in one-degree-of-freedom Euler–Lagrange Systems. We consider that the mechanical subsystem is actuated by a permanent magnet synchronous motor (PMSM). Our proposal consists of a Proportional-Integral-Derivative (PID) controller for the mechanical subsystem and a slight variation of field oriented control for the PMSM. We take into account the motor electric dynamics during the stability analysis. We present, for the first time, a global asymptotic stability proof for such a control scheme without requiring the mechanical subsystem to naturally possess viscous friction. Finally, as a corollary of our main result we prove global asymptotic stability for output feedback PID regulation of one-degree-of-freedom Euler–Lagrange systems when generated torque is considered as the system input, i.e. when the electric dynamics of PMSM's is not taken into account.