On intriguing effects of closed-loop commutation delay in stepper motor control with application to parameter estimation

The purpose of this paper is to call attention to a phenomenon that is observed when a closed-loop commutation delay is present in stepper motor control applications. Commutation is a popular technique used to feedback linearize the mechanical dynamics of a stepper motor by generating phase currents based on the sine and cosine of the relative position within a toothpitch. In the presence of a time delay in the closed loop, the feedback linearization is not exact and a residual term depending on incremental position remains in the closed-loop dynamics. In this paper, we show that a time delay in the closed loop results in two dynamical phenomena, viz, introduction of multiple solution trajectories with sensitive dependence on initial conditions (possibly yielding steady state velocities with opposite signs) and saturation of velocity. We also show that these phenomena can be exploited to estimate parameters such as closed-loop delay, sensor offset, and toothpitch of the motor.