Robust Filtered Basis Functions Approach for Feedforward Tracking Control

This paper proposes a robust filtered basis functions approach for feedforward tracking of linear time invariant systems with dynamic uncertainties. Identical to the standard filtered basis functions (FBF) approach, the robust FBF approach expresses the control trajectory as a linear combination of user-defined basis functions with unknown coefficients. The basis functions are forward filtered using a model of the plant and their coefficients are selected to minimize tracking errors. The standard FBF and robust FBF approaches differ in the filtering process. The robust FBF approach uses an optimal robust filter which is based on minimization of a frequency domain based error cost function over the dynamic uncertainty, whereas, the standard FBF approach uses the nominal model. Simulation examples and experiments on a desktop 3D printer are used to demonstrate significantly more accurate tracking of uncertain plants using robust FBF compared with the standard FBF.