Iterative learning control (ILC) is an open-loop control strategy that learns the system input to track a desired trajectory from previous executions. A major limitation of ILC is that for every new trajectory, the ILC is reinitiated and thus takes a number of iterations to learn the new optimal system input. This paper presents a novel methodology for linear time-invariant systems to calculate a better initialization of an ILC based on a previously learned similar trajectory and a disturbance model. To illustrate the potential of the developed method, it is applied to a permanent magnet linear motor and compared to a model-based feedforward control scheme. The experimental results show that the proposed method outperforms the model-based feedforward control scheme in the case of similar motion trajectories, yielding a better initialization of an ILC.