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In this study, a simulation model of permanent magnet synchronous motor (PMSM) position servo system is presented briefly first, then, a dynamic high order periodic adaptive learning compensation (HO-PALC) scheme is proposed for cogging effect on PMSM position and velocity servo tasks. The cogging torque is considered as a position-dependent disturbance that is periodic. The key idea of the implemented cogging disturbance compensation method is to use past information of more than one position period along the state axis to update the current adaptation learning law. Simulation results illustrate the effectiveness of the proposed high order PALC method. Furthermore, the dynamic item in the HO-PALC can guarantee the stability in the real experimental system with unexpected noise and unmodelled dynamics. Experimental validation is presented to show the performance with proposed dynamic high order periodic adaptive cogging compensation scheme. The advantage of the dynamic HO-PALC is demonstrated through the comparison with the first order periodic adaptive learning compensation.