Many control applications are nonlinear and have to perform a range of different tasks. Iterative Learning Control (ILC) enables high performance for a single task, but is highly sensitive to task variations. The aim of this paper is to develop an ILC framework for Linear Parameter Varying (LPV) systems, which encompasses a large class of nonlinear systems, which allows for trial-varying reference signals. This is achieved by exploiting parameter varying basis functions, such that perfect tracking is enabled for LPV systems. The proposed approach is applied to a printer sheet positioning unit, thereby validating that the tracking performance is significantly enhanced with respect to existing approaches.