Global Asymptotic Stability of PD Control for PM Stepper Motor Servo‐Systems

Commutation is a well-known and successful strategy used in practice to control permanent magnet stepper motors. However, stability analysis has not been presented until now for this simple control strategy. In this note we prove, for the first time, that commutation achieves global asymptotic stability when used to regulate position in Euler–Lagrange systems actuated by permanent magnet stepper motors. Contrary to the traditional design methodology, this is accomplished by taking into account the electrical dynamics of the motors and, hence, we avoid the possibility of either performance degradation or instability due to the neglected electrical dynamics. We include high-gain electric current loops and we introduce a saturated output feedback PD controller as the desired torque, i.e. velocity measurements are not required.