Effects of closed-loop commutation delay for various types of motors

In a recent paper [1], we reported the occurrence of interesting phenomena that were observed experimentally during closed-loop commutation experiments with a planar (Sawyer) stepper motor and showed that the phenomena were caused due to time delays in the sensor and actuator. The observed dynamical phenomena included 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 showed that these phenomena can be exploited to estimate parameters such as closed-loop delay, sensor offset, and toothpitch. The analysis in [1] was applicable to a permanent-magnet stepper motor (and any other motor that shares the same form of the mechanical dynamics and torque expression). In this paper, we continue the work of [1] and investigate the effect of closed-loop commutation delay on other types of motors including variable reluctance (VR) stepper motors, brushless DC (BLDC) motors, and three-axis planar Sawyer stepper motors.