Position-Dependent Motion Feedforward via Gaussian Processes: Applied to Snap and Force Ripple in Semiconductor Equipment

The requirements for high accuracy and throughput in next-generation data-intensive motion systems lead to situations where position-dependent feedforward is essential. This article aims to develop a framework for interpretable and task-flexible position-dependent feedforward through systematic learning with automated experimental design. A data-driven and interpretable framework is developed by employing Gaussian process (GP) regression, enabling accurate modeling of feedforward parameters as a continuous function of position. The data is efficiently collected and illustrated through an iterative learning control (ILC) algorithm. Moreover, a framework for experimental design in the sense of automatically determining the training positions is presented by exploiting the uncertainty estimates of the GP and the specified first-principles knowledge. Two relevant case studies show the importance and significant performance improvement of the approach for position-dependent snap feedforward for a simplified 1-D wafer stage simulation and experimental application to position-dependent motor force constant compensation in an industrial wirebonder.