Dual-high-order periodic adaptive learning compensation for state-dependant periodic disturbance

State-periodic disturbances are frequently found in motion control systems. Examples include cogging in permanent magnetic linear motor, eccentricity in rotary machines and etc. This paper considers general form of state-dependent periodic disturbance and proposes a new high-order periodic adaptive learning compensation (HO-PALC) method for state-dependent periodic disturbance where the stored information of more than one previous periods is used. The information includes composite tracking error as well as the estimate of the periodic disturbance. This dual HO-PALC (DHO-PALC) scheme offers potential to achieve faster learning convergence. In particular, when the reference signal is also periodically changing, the proposed DHO can achieve much better convergence performance in terms of both convergence speed and final error bound. Asymptotical stability proof of the proposed DHO-PALC is presented. Extensive lab experimental results are presented to illustrate the effectiveness of the proposed DHO-PALC scheme over the first order periodic adaptive learning compensation (FO-PALC).