The longitudinal intra-train beam-based feedback has been recommissioned after major upgrades on the synchronization system of the FLASH facility. Those upgrades include: new bunch arrival time monitors (BAMs), the optical synchronization system accommodating the latest European XFEL design based on PM fibers, and installation of a small broadband normal conducting RF cavity. The cavity is located prior to the first bunch compressor at FLASH and allows energy modulation bunch-by-bunch (1 μs spacing) on the per mille range. Through the energy dependent path length of the succeeding magnetic chicane the cavity is used for ultimate bunch arrival time corrections. Recently the RF cavity operated 1 kW pulsed solid-state amplifier was successfully commissioned. First tests have been carried out incorporating the fast cavity as actuator together with SRF stations for larger corrections in our intra-train beam-based feedback pushing now arrival time stabilities towards 5 fs (rms). The latest results and observed residual instabilities are presented.

In this paper, the system identification and feedback controller design for a normal conducting standing wave radio frequency cavity operated in pulsed mode of a free electron laser is presented. The system identification, essential to achieve high performance control, is based on a grey box model, with a priori knowledge about the physical behavior. The feedback regulation concept is separated into two basic controller parts. A radio frequency controller design, based on the identified radio frequency model, is followed by a system identification and regulation of the pulse width to overcome the limitation of the underlying temperature regulation. It will be shown by measurements at the free electron laser FLASH at DESY, Germany, that the combination of both cascaded control schemes lead to high radio frequency field performance.

In this paper, a distributed controller design is proposed for a linear accelerator such as the European XFEL. The linear accelerator is modeled as a chain of 25 subsystems, each representing one of the 25 radio frequency stations which form the XFEL plant. A distributed control scheme is presented that exploits the interaction between neighboring stations. A local controller is attached to each station; these local controllers exchange information with neighboring controllers, in order to reduce the error in beam energy at a given station by coordinated control action across neighboring stations. A recently developed framework for distributed control of spatially interconnected systems is employed to design the distributed controllers in a H-infinity mixed sensitivity approach. Simulation studies indicate a significant improvement in performance when the proposed control scheme is applied.

An iterative learning control (ILC) algorithm reduces repetitive control errors to a desired trajectory within the same repeated task. This paper considers an alternative ILC representation based on a tensor representation. Hereby a decoupling of static and dynamic parts of each calculated ILC matrix leads for computational reasons to a reduction by an order of magnitude. Based on such tensor representation the Norm Optimal ILC is compressed to a Norm Optimal Tensor ILC. The reduced number of elements to store the ILC parameter in this approach simplifies the calculation, especially for high sampled datasets and therefore long trajectories. The resulting algorithm is implemented at FLASH, a free electron laser facility, highly suitable for this approach.

This paper shows a mixed sensitivity H∞ controller design, which uses the symmetric radio frequency system structure of a free electron laser. The controller design includes plant decoupling, which is needed for additional feedbacks. Furthermore unwanted additional resonant modes, so-called passband modes are suppressed. This paper shows a strategy by rewriting the multi-input multi-output model as a single-input single-output model applying the two dimensional special orthogonal group symmetry of the plant. The controller design is separated into two steps. An analytical controller design, which is calculated from the single-input single-output representation is mapped back to a multi-input multi-output controller and optimized by discrete-time H∞ fixed-order optimization to guarantee optimality and robustness.