A limited-preview filtered B-spline approach to tracking control - With application to vibration-induced error compensation of a 3D printer

A limited-preview filtered B-spline (FBS) approach for minimizing errors in tracking a desired trajectory is presented. In the full-preview FBS approach, the feedforward control input to a stable linear system, with or without non-minimum phase zeros, is decomposed into B-spline basis functions with unknown coefficients; the basis functions are forward filtered using the (modeled) dynamics of the system, and their coefficients selected to minimize tracking errors of the entire trajectory in one batch. Instead, this paper proposes the use of a receding horizon to recursively compute unknown coefficients that minimize tracking errors for small batches (subsets) of the trajectory at a time, by exploiting the local property of B-splines. This allows optimal control signals to be determined at much lower computational cost compared to full-preview FBS, thus enabling online implementation on real-time controllers. The adverse effects of limited preview on tracking accuracy, relative to full preview, are analyzed, and limited-preview FBS is shown in numerical examples to preserve the versatility of full-preview FBS in tracking systems irrespective of their zero locations. The practicality and effectiveness of the limited-preview FBS approach are demonstrated by employing it for online feedforward compensation of tracking errors caused by structural vibrations of a stepper-motor-driven 3D printer. Alleviation of vibration-induced surface waviness and layer-to-layer registration errors, without sacrificing print speed, are demonstrated. (C) 2017 Elsevier Ltd. All rights reserved.