State-periodic adaptive compensation of cogging and Coulomb friction in permanent-magnet linear motors

This paper focuses on the state-periodic adaptive compensation of cogging and Coulomb friction for permanent-magnet linear motors (PMLMs) executing a task repeatedly. The cogging force is considered as a position-dependent disturbance and the Coulomb friction is non-Lipschitz at zero velocity. The key idea of our disturbance compensation method is to use past information for one trajectory period along the state axis to update the current adaptation law. The new method consists of three different steps: 1) in the first repetitive trajectory, an adaptive compensator is designed to guarantee the l₂-stability of the overall system; 2) from the second repetitive trajectory and onward, a trajectory-periodic adaptive compensator stabilizes the system; and 3) to make use of the stored past state-dependent cogging information, a search process is utilized for adapting the current cogging coefficient. We illustrate the validity of our state-periodic adaptive cogging and friction compensator by actual PMLM-model-based simulation.