## 1 Introduction
Although the ILCC can effectively reduce the contour errors of feed drive axes while performing repeated positional command paths, the motion control design of each feed drive axis must mitigate the adverse influence of model uncertainty and external disturbance variation. In addition, feed drive axes must have similar motion dynamics and external disturbance properties to match multi-axis motions and increase contour accuracy. Moreover, an ILCC that combines contour error estimation and iterative learning control must have an easy-to-implement control structure and must not excessively increase the computational burden of motion control systems to facilitate the realization of ILCC in industrial applications. During thread milling operations, the three feed drive axes of a CNC machine tool perform synchronous motions along a helical path so that the thread milling tool can move along the helical path for thread cutting. Therefore, the cutting force in milling operations and the motion dynamics and friction disturbance of each feed drive axis affect the contour motion accuracy of feed drive axes while performing helical paths. Existing ILCC methods can improve the contour motion accuracy of feed drive axes; however, motion control systems were required to record and process a large amount of collected data, requiring longer data processing and computing time that usually increases the computational burden. In addition, before the convergence of the applied iterative learning processes, the existing ILCC could produce a few defective products due to the low contour control accuracy, which waste materials and increase manufacturing costs. A helical path consists of multiple pitch cycles, and, thus, feed drive axes perform repeated synchronous motions in pitch cycles. Moreover, during the motions of pitch cycles in a thread milling operation, feed drive axes possess the same motion dynamics and influence of the cutting force and friction disturbance. Therefore, this study developed a pitch cycle-based ILCC (PCB-ILCC) to address the control system and thread manufacturing problems caused by applying the ILCC to thread milling operations. The PCB-ILCC applied the ILCC to pitch cycles so that the contour error produced by feed drive axes while performing synchronous motions in the previous pitch cycle can be used to compute and modify the positional commands of synchronous motions in the current pitch cycle. Thus, the PCB-ILCC, pitch by pitch, gradually improves the contour motion accuracy of feed drive axes while performing helical paths. To achieve the design goal, the PCB-ILCC must integrate with the contour error vector (CEV) estimation method without excessive computational burden, the ILCC design with a simple and easy-to-implement structure, and the driving control design of the feed drive axis with robust motion properties. Therefore, this study estimated the CEV by referring to the interpolated positions on the helical cycle and the response positions on the response cycle produced by the feed drive axes. The ILCC design with the previous cycle learning method was modified and applied to generate a command cycle for the feed drive axes. This study also considered the dynamic characteristics of the feed drive axis actuated by a permanent magnet synchronous motor (PMSM) and applied the robust control with friction and dynamic compensations to design a PMSM driving control so that the feed drive axes can have robust motion performance. To evaluate and validate the feasibility and performance of the PCB-ILCC design, this study performed a PMSM motion control experiment on a PMSM testbench and a machine tool thread milling experiment on a five-axis CNC machining center. The results of this experiment showed that in comparison to the proportional-proportional-integral control extensively used in commercialized PMSM driving control, the rate of reduction achieved by the PCB-ILCC is significant.