An Analysis of the Effects of Closed-Loop Commutation Delay on Stepper Motor Control and Application to Parameter Estimation

The purpose of this brief is to call attention to a phenomenon that is observed when a closed-loop commutation delay is present in stepper motor control applications especially involving high-speed precision motors, e.g., precision assembly, wafer probing, coordinate measuring machines. 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 brief, 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.