A lyapunov method in microstepping control for permanent magnet stepper motors

Abstract

In this paper, the stability of microstepping is investigated via Lyapunov method. A Lyapunov based control is proposed for the position tracking of a Permanent Magnet (PM) stepper motor. Given static inputs to the two phase PM stepper motor, it is proven that the convergence of equilibrium points is guaranteed by LaSalle's theorem. For position tracking, the relationships between the voltage input and current output of each phase for the position tracking are derived. From the relationships, the Lyapunov based controller is developed for the position tracking. Simulation results showed that the rotor angle and speed tracking performance of the proposed controller are good comparison to microstepping with current feedback PI controller.