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A Robust Filtered Basis Functions Approach for Feedforward Tracking Control—With Application to a Vibration-Prone 3-D Printer

The filtered basis functions (FBF) approach is gaining interest for feedforward tracking control of linear, especially, nonminimum phase systems. It expresses the control input to the plant as a linear combination of basis functions with unknown coefficients. The basis functions are forward filtered through the plant dynamics and the coefficients are selected such that the tracking error is minimized. This article proposes a robust FBF approach for tracking control of linear time invariant systems with known uncertainty. A robust filter is formulated as the inverse of an optimal controller that minimizes a frequency-domain cost function over the known uncertainty. The proposed robust FBF approach filters the basis functions using the robust filter in lieu of the nominal plant dynamics. Stability issues associated with the robust filter are discussed, as are the incorporation of dynamic uncertainty into the robust filter. Applied to a vibration-prone desktop 3-D printer with dynamic uncertainty, significant improvements in tracking accuracy are demonstrated using the robust FBF approach compared to the standard FBF approach.