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To suppress the speed ripple of a permanent magnet synchronous motor in a seeker servo system, we propose an accelerated iterative learning control with an adjustable learning interval. First, according to the error of current iterative learning for the system, we determine the next iterative learning interval and conduct real-time correction on the learning gain. For the learning interval, as the number of iterations increases, the actual interval that needs correction constantly shortens, accelerating the convergence speed. Second, we analyze the specific structure of the controller while applying reasonable assumptions pertaining to its condition. Using the λ-norm, we analyze and apply our mathematical knowledge to obtain a strict mathematical proof on the P-type iterative learning control and obtain the condition of convergence for the controller. Finally, we apply the proposed method for periodic ripple inhibition of the torque rotation speed of the permanent magnet synchronous motor and establish the system model; we use the periodic load torque to simulate the ripple torque of the synchronous motor. The simulation and experimental results indicate the effectiveness of the method. [ABSTRACT FROM AUTHOR]