A Multirate Repetitive Control for Fractional-order Servos in Laser-based Additive Manufacturing

This paper studies repetitive control (RC) algorithms to advance the quality of repetitive energy deposition in laser-based additive manufacturing (AM). An intrinsic limitation appears in discrete-time RC when the period of the exogenous signal is not an integer multiple of the sampling time. Such a challenge hampers high-performance applications of RC to laser-based AM because periodicity of the exogenous signal has no guarantees to comply with the sampling rate of molten-pool sensors. This paper investigates three RC algorithms to address such fractional-order RC cases. A wide-band RC and a quasi RC apply the nearest integer approximation of the period, yielding overdetermined and partial attenuation of the periodic disturbance. A new multirate RC generates high-gain control signals exactly at the fundamental frequency and its harmonics. Experimentation on a dual-axis galvo scanner in laser-based AM compares the effectiveness of different algorithms and reveals fundamental benefits of the proposed multirate RC.