Scientific experiments conducted with the help of a particle accelerator rely on the stability of the corresponding particle beam. One way of improving this stability is the application of a control method called beam-based feedback. Following this, the control system of the linear accelerator ELBE is planned to be upgraded by this feedback mechanism. This paper exploits the continuous wave operation mode of ELBE in order to reinterpret the given control problem as a disturbance rejection goal. In this context, the paper studies the influence of stochastic disturbances on electron beam arrival time, proposes and designs a control system that is capable of effectively compensating the arrival time fluctuations. Moreover, the prospective hardware implementation is taken into account when choosing the most suitable control strategy for this specific task. Finally, the simulation of the designed regulator on measured disturbance data indicates an improvement in arrival time performance.