Adaptive observer-based nonlinear control in microstepping for permanent magnet stepper motors

This paper presents an adaptive observer-based nonlinear controller. Due to the resistance difference between phases A and B, the Lissajou curve of the desired phase currents is an ellipse. Therefore, a position error exists in the steady-state, and a ripple of position error appears during operation. To remedy this problem, the desired voltage inputs are modified so that the Lissajou curve of the desired phase currents should be a circle. For guarantees of the desired currents, a nonlinear controller is developed. The adaptive observer is designed to estimate the velocity and the phase resistances. In the stability analysis, the closed-loop is transformed into a time-varying cascade form, and its stability is proven. Simulation results show that the position error in the steady-state is avoided with the proposed method if the persistent excitation conditions are satisfied. Furthermore, the position ripple is reduced, and the Lissajou curve of the phase currents is a circle.