Abstract—This study investigates a repetitive-control plug-in integrated with a Proportional–Integral–Derivative (PID) controller for a two-degree-of-freedom lower-limb robotic system consisting of hip and knee joints. All experiments were conducted in a MATLAB-based discrete-time simulation using periodic reference trajectories. The proposed plug-in incorporates a Finite-Impulse-Response (FIR) time window and a ring-buffer structure to reuse previously learned control signals, while a phase-lead compensation term is introduced to improve tracking response. System performance was evaluated using the Root Mean Square Error (RMSE) of joint angle tracking during iterative learning cycles and under steady-state conditions. A systematic analysis was performed by varying the lead compensation parameter (rcLead = 0, 2, 4, and 6) and the FIR window length (winLen = 3, 5, and 7), with an additional steady-state evaluation at winLen = 9. Simulation results show that the controller rapidly reduces tracking errors and achieves stable convergence across all tested configurations. The best performance was obtained with rcLead = 2 and winLen = 5, which yielded the lowest steady-state RMSE values of 0.014510 degrees for the hip joint and 0.004741 degrees for the knee joint, while also providing the fastest practical convergence. Larger lead values increased residual tracking errors, whereas excessively short or long window lengths either amplified noise or introduced additional response delays. The results demonstrate that combining moderate phase-lead compensation with an intermediate FIR window length provides an effective and computationally efficient approach for periodic trajectory tracking in multi-joint robotic systems. Future work will focus on experimental validation using a physical platform, evaluation under more diverse motion conditions, and the development of adaptive strategies for automatic parameter tuning.

Index Terms—Finite-Impulse-Response (FIR) window, lower‑limb exoskeleton, phase compensation, Proportional–Integral–Derivative (PID), Q‑filter, repetitive control, trajectory tracking

Cite: Panya Minyong, Phichitphon Chotikunnan, Rawiphon Chotikunnan, Nuntachai Thongpance, Yutthana Pititheeraphab, Songtham Deewanichsakul, Udomsak Jantontapo, and Surachat Chantarachit, "FIR Window and Phase Lead Effects in Repetitive Control for Exoskeleton Tracking," International Journal of Electrical and Electronic Engineering & Telecommunications, vol. 15, no. 3, pp. 221-232, 2026. doi: 10.18178/ijeetc.15.3.221-232

Copyright © 2026 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).