Stability and robustness analysis of an adaptive algorithm for quasi-periodic disturbances rejection

Winding and web transport systems are subjected to quasi-periodic disturbances of the web tension due to the eccentricity and the non-circularity of the reel and rolls. The disturbances induced by the non-circularity and eccentricity of the rolls are quasi-periodic with a frequency that varies with their rotation speed. An adaptive method of rejection of these disturbances is proposed. It is based on a phase-locked loop structure that estimates simultaneously the phase and magnitude of the perturbation and then cancels it. This algorithm can be plugged in an existing industrial controller. The stability and robustness of the algorithm are discussed. The ability of the algorithm to reject quasi-periodic disturbances with slowly varying frequencies is shown through simulation results.