In this work, we propose a new learning-based iterative control (IC) framework that enables a complex softrobotic arm to track trajectories accurately. Compared to traditional iterative learning control (ILC), which operates on a single fixed reference trajectory, we use a deep learning approach to generalize across various reference trajectories. The resulting nonlinear mapping computes feedforward actions and is used in a two degrees of freedom control design. Our method incorporates prior knowledge about the system dynamics and by learning only feedforward actions, it mitigates the risk of instability. We demonstrate a low sample complexity and an excellent tracking performance in real-world experiments. The experiments are carried out on a custom-made robot arm with four degrees of freedom that is actuated with pneumatic artificial muscles. The experiments include high acceleration and high velocity motion.