Lyapunov-based Control in Microstepping with a Nonlinear Observer for Permanent Magnet Stepper Motors

In this paper, we propose a Lyapunov-based control with a nonlinear observer in microstepping for permanent magnet stepper motors (PMSMs). Given static inputs to a PMSM, stability of the equilibrium points is studied in the sense of Lyapunov stability and their local asymptotic stability is proved using LaSalle's theorem. From the stability analysis the principle of microstepping is verified. The Lyapunov-based controller was developed to regulate the desired phase current errors. For the implementation of the proposed controller a nonlinear observer is also designed using the Lyapunov method to estimate the full state of PMSM. And we analyze the stability of the closed-loop system. The Lyapunov-based controller and nonlinear observer do not require any transformation so that it could reduce the commutation delay. The proposed method is validated via experiments and its tracking performance was compared with that of the conventional microstepping. We used two position profiles to evaluate the performance of the proposed method. Overall more than a 40% improvement in tracking error was obtained. Furthermore, we achieved improved uniformity in the tracking error during the constant velocity period.