The registration accuracy of Roll-to-Roll (R2R) printing systems is critical as it determines the product quality. However, the unknown system parameters and couplings of the speed-up phase makes the register control challenging. In this article, a model-based self-tuning fully decoupled (MBSTFD) control method is proposed. In the MBSTFD, a parametric register error model is established for the speed-up phase of R2R printing systems, in which a D-type iterative learning algorithm is adopted for the closed-loop parameters identification. Then, a model-based self-tuning fully decoupled compensation is designed to automatically adjust to completely eliminate the complex couplings in R2R printing systems, thereby reduce the register errors. The effectiveness of the proposed MBSTFD is verified via experiments. The results indicate that the MBSTFD can achieve precise closed-loop parameters identification effect, and reduce the register errors of the speed-up phase into$\pm 7 \times 10^{-5}$m. Moreover, comparisons of the well-tuned PD control, the model-based feed-forward PD control and MBSTFD methods are also carried out, and the results show that the MBSTFD owns higher register precision and less waste material than other two control methods.