## 6 Conclusions and Outlook on Future Research  
In this study, four different controllers for the power control of an SOFC were designed and compared with each other. A PI controller, an internal model control, a sliding-mode controller, and a linear state-feedback controller were chosen. Here, the real system was approximated by a transfer function of sixth-order (Equation (2)) using measured data from a real-life test rig. To develop each control law, this basic system was then reduced in its order by different linear time-invariant transfer functions for each case, which were transferred into controllable canonical form. All controllers were additionally modified with appropriate feedforward actions. In addition, the control law for the sliding-mode controller was modified by a stationary offset correction. A dynamic gain compensation for the linear state-feedback controller was further implemented. However, the simulation of the sliding-mode control and the linear state-feedback controller show a tracking error caused by model uncertainties, which cannot be handled by those controllers without further disturbance observer techniques. Furthermore, sliding-mode controllers and for the linear state-feedback, the time derivatives of the measured electric power were needed, so that a Luenberger observer was implemented to provide these estimates. The trajectories of each controller were simulated with the analyzed system of sixth order. To check the sensitivity numerically, white noise was added to the measured values. As a result, the IMC has the best trajectory tracking, closely followed by the PI controller. Both controllers were implemented at the test rig to perform an experimental validation. Although a temporal variation of the gain of factors up to two occurs as a model uncertainty during each of the experiments, the two controllers are able to follow the desired trajectory and confirm the results of the simulation.  
In this study, the real SOFC system was approximated with the black-box transfer function estimator, which includes only the input-output behavior. The presented controllers were, hence, based on this model. This means that in future work the model should be refined, in the form of explicit current or thermal dependencies. Furthermore, the sliding-mode controller and the state-feedback controller could be improved with a compensation of the gain error. Here, it is assumed that the gain and time constants are the same in each part of the desired trajectory. However, it is possible to estimate these two parameters in real time, e.g., to implement an adaptive control. In addition, the sliding-mode controller and the state-feedback controller can be optimized with an IQR design or an H\({}_{\infty}\) norm minimization, as mentioned in Section 4. However, this is not necessary for the IMC and PI controller, which are--in their current form--suitable for industrial practice. Here, the time constants of the PI controller are intentionally chosen very large to prevent the wind-up effect. This makes the designed PI controller quite slow. For future work, other anti-wind-up methods could be chosen to enhance the dynamics of the PI controller further.  
Original algorithm design, implementation, and numerical and experimental validation were performed by [PERSON] and [PERSON] under the supervision of [PERSON]. The experiments were performed by [PERSON] and [PERSON]. [PERSON] devised the test rig used for the experiments and contributed to the control methodology. The paper was jointly written by [PERSON], [PERSON], and [PERSON] All authors have read and agreed to the published version of the manuscript.  
This research was partially funded by the European Union within the European Fund for Regional Development (TBI-V-1-256-VBW-090).  
The authors declare no conflict of interest.