Lyapunov-based microstepping control of Sawyer motors with PID control

Proportional-integral-derivative (PID) controls have been widely used for Sawyer motors. The electrical dynamics are generally neglected in general PIDs control since the electrical dynamics are faster than the mechanical dynamics. However, when the current control is used, the phase currents are reduced by back-emf and have the phase lags due to inductances. Thus, the electrical dynamics should be considered to improve the performance of PID control. In this paper, Lyapunov-based microstepping control of Sawyer motors with PID control is developed for improved performance of PID control. The proposed method consists of PID and Lyapunov-based controller. PID controllers make the desired forces and torque to track the position profiles of x and y with regulation of yaw. And the commutation scheme from the desired forces and torque to the desired phase currents are used. For the design of Lyapunov-based control, the stabilities of the equilibrium points are studied using Lyapunov method. Then, Lyapunov-based control is designed to compensate back-emfs and phase lags. Furthermore, the proposed method guarantees the exponential stabilities of desired currents for PID control. And, the closed-loop system is analyzed. The proposed method considering the electrical dynamics is designed without any coordinate transformation. Therefore, it could reduce the commutation delay. Simulation results show that the tracking performance of PID controller is improved by the proposed method.