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A hybrid (i.e., physics-guided data-driven) feedforward tracking controlleris proposed for systems with unmodeled linear or nonlinear dynamics. Thecontroller is based on the filtered basis function (FBF) approach, hence it iscalled a hybrid FBF controller. It formulates the feedforward control input toa system as a linear combination of a set of basis functions whose coefficientsare selected to minimize tracking errors. The basis functions are filteredusing a combination of two linear models to predict and minimize the trackingerrors. The first model is physics-based and remains unaltered during theexecution of the controller, while the second is data-driven and iscontinuously updated during the execution of the controller. To ensure itspracticality and safe learning, the proposed hybrid FBF controller is equippedwith the ability to handle delays in data acquisition and to detect impendinginstability due to its inherent data-driven feedback loop. Its effectiveness isdemonstrated via application to vibration compensation of a 3D printer withunmodeled linear and nonlinear dynamics. Thanks to the proposed hybrid FBFcontroller, the tracking accuracy of the 3D printer is significantly improvedin experiments involving high-speed printing, compared to a standard FBFcontroller that does not incorporate a data-driven model. Furthermore, theability of the hybrid FBF controller to detect and, hence, potentially avoidimpending instability is demonstrated offline using data collected online fromexperiments.

A physics-guided data-driven feedforward tracking controller for systems with unmodeled dynamics -- applied to 3D printing