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 (PMLM) executing a task repeatedly. The cogging force is considered as a position dependent disturbance and the considered Coulomb friction is non-Lipschitz at zero velocity. The key idea of our disturbance compensation method is to use one trajectory-period past information along the state axis to update the current adaptation law. The new method consists of three different steps: firstly, in the first repetitive trajectory, an adaptive compensator is designed to guarantee the l₂-stability of the overall system. Secondly, from the second repetitive trajectory and onwards, a trajectory-periodic adaptive compensator is designed to stabilize the system. Finally, to make use of the stored past state-dependent cogging information, a search process is utilized for adapting the current cogging coefficient. The validity of our adaptive cogging and friction compensator is illustrated through a simulation example.