Safe Periodic Tracking via a Repetitive Controller with Control Barrier Function Constraints: A Servomotor Simulation Study

In many control applications, achieving precise tracking and rejecting periodic disturbances remain persistent challenges. A widely adopted solution is repetitive control (RC), which provides excellent steady-state performance for periodic reference tracking but often exhibits large overshoots during transients and offers only asymptotic stability guarantees. To overcome these limitations, this study integrates a Control Barrier Function (CBF) into an output-feedback RC framework to enforce safety while maintaining tracking accuracy. In the proposed structure, the CBF operates as a safety filter that modifies the RC–PD control input only when needed to prevent potential violations of predefined output states. This ensures that system trajectories remain within a prescribed safe region throughout operation. The framework is validated through a servomotor simulation study, including a case with periodic disturbance to demonstrate consistent tracking behavior under non-nominal operating condition. The simulation results show that the RC–CBF controller eliminates overshoot, ensuring transient safety while preserving the key benefits of RC in achieving accurate steady-state periodic tracking. Although the integration of the CBF introduces a slight increase in steady-state error compared with standalone RC, the error remains negligible for all tested conditions. By contrast, a PD controller with or without a CBF yields safer transients than standalone RC but does not achieve the steady-state accuracy of RC-based methods. Overall, combining RC with CBF offers a practical way to enforce transient safety while preserving accurate periodic tracking, making the approach promising for precise reference tracking and disturbance rejection in industrial applications.