In this work, we apply the recent framework of sparsity invariance to a large-scale facility, the European XFEL. With the sparsity invariance framework, the most general known class of convex approximations of distributed controller design problems is characterized. It is shown in previous work that this convex restriction can perform at least as well as all existing approximations for the possibly NP-hard problem of distributed controller design. The optical synchronization system at the European XFEL can be modeled as a distributed system with a tree or chain topology. Whereas in previous work based on the spatial invariance framework either static state feedback or high-order dynamic output feedback controller design is presented, we extend it in this work to static or fixed-order output feedback control and apply it to the system at hand. We show simulation results motivated by the real application and demonstrate that the convex approximation can outperform a local baseline tuning.