This article proposes a finite-space repetitive learning control strategy based on the Lyapunov method for the rotating motor system performing spatial repetitive tasks. By introducing spatial differentiation operators, the transformation of rotating motor systems from time domain representation to spatial domain representation is achieved. Convert the rotating motor model with time as the independent variable to a rotating motor model with rotor angular position as the independent variable. On this basis, the uncertainty of the system is separated into inherent spacial periodic and non-periodic parts by considering the periodic repetitive characteristics of rotating motors operating in space. A fully saturated spatial repetitive learning law is constructed to accurately compensate for the spacial periodic uncertainty. Meanwhile, finite spatial control law and robust control law are developed to enable the angular velocity tracking error of the rotating motor to converge to the neighborhood near the origin within a finite range of rotation angles of the motor rotor, achieving fast and high-precision tracking of the angular velocity of the rotating motor to the desired angular velocity trajectory. Finally, the tracking error of the closed-loop system converges to the neighborhood of the origin in a finite space through the Lyapunov stability synthesis, and the experimental results are given to verify the effectiveness of the proposed control method.