Synthesis and Analysis of Multirate Repetitive Control for Fractional-order Periodic Disturbance Rejection in Powder Bed Fusion

This paper studies control approaches to advance the quality of repetitive energy deposition in powder bed fusion (PBF) additive manufacturing. A key pattern in the nascent manufacturing process, the repetitive scanning of the laser or elec- tron beam can be fundamentally improved by repetitive control (RC) algorithms. An intrinsic limitation, however, appears in discrete-time RC when the exogenous signal frequency cannot divide the sampling frequency. In other words, N in the internal model 1/ 􏰊1 − z−N 􏰋 is not an integer. Such a challenge hampers high-performance applications of RC to PBF because periodicity of the exogenous signal has no guarantees to comply with the sampling rate of molten-pool sensors. This paper develops a new multirate RC and a closed-loop analysis method to address such fractional-order RC cases by generating high-gain control signals exactly at the fundamental and harmonic frequencies. The proposed analysis method exhibits the detailed disturbance- attenuation properties of the multirate RC in a new design space. Numerical verification on a galvo scanner in laser PBF reveals fundamental benefits of the proposed multirate RC.

Conference paper