Two-Stage Robust Tracking Controller for Linear Systems With Known Uncertainty Using Filtered Basis Functions

There is growing interest in the use of the filtered basis functions (FBF) approach to track linear systems, especially nonminimum phase (NMP) plants, because of the distinct advantages it presents as compared to other popular methods in the literature. The FBF approach expresses the control input to the plant as a linear combination of basis functions. The basis functions are forward filtered through the plant dynamics and the coefficients of the linear combination are selected such that the tracking error is minimized. This paper proposes a two-stage robust filtered basis functions approach for tracking control of linear systems in the presence of known uncertainty. In the first stage, the nominal model for filtering the basis functions is selected such that a Frobenius norm metric which considers the known uncertainty is minimized. In the second stage, an optimal set of basis functions is selected such that the effect of uncertainty is minimized for the nominal model selected in the first stage. Experiments on a 3D printer, demonstrate up to 7 times improvement in tracking performance using the proposed method as compared to the standard FBF approach.