Design of an optimal and robust controller for a free-electron laser exploiting symmetries of the RF-system

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.