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 `2-stability of the overall system; secondly, from the second repetitive trajectory and onwards, a trajectory-periodic adaptive compensator is designed to stabilize the system; and 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 the actual PMLM model based simulation. Index Terms Cogging force, Coulomb friction force, state-dependent disturbance, adaptive control, trajectory-periodic adaptation.