In this brief, a fractional order periodic adaptive learning compensation (FO-PALC) method is devised for the general state-dependent periodic disturbance minimization on the position and velocity servo platform. In the first trajectory period of the proposed FO-PALC scheme, a fractional order adaptive compensator is designed which can guarantee the boundedness of the system state, input and output signals. From the second repetitive trajectory period and onward, one period previously stored information along the state axis is used in the current adaptation law. Asymptotical stability proof of the system with the proposed FO-PALC is presented. Experimental validation is demonstrated to show the benefits from using fractional calculus in periodic adaptive learning compensation for the state-dependent periodic disturbance.

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