The numerical evaluation and optimization of the feedback controller parameters of the model-based control implemented in the flying helicopter simulator is subject of this paper. The German Aerospace Center operates this helicopter as a flying testbed for numerous applications, e.g., pilot assistance and in-flight simulation. Initially, the elements of the model-based control are presented. A genetic algorithm and the Nelder-Mead simplex method used for optimization are described. Two simple objective functions to rate parameter sets in the time domain are presented, and a Simulink Ò model of the helicopter dynamics and the controller structure are used to find optimized sets. The first function, called ''Delta Rating'', consists of a normalized integral of the absolute error between commanded and measured states. The second function incorporates the Delta Rating, but is enhanced by a penalty on overshoots. The controllers found are further evaluated using a frequency domain approach consisting of a weighted sum of the differences in amplitude and phase, also considering the coherence at the corresponding frequency. Apart from the Simulink Ò model, a ground-based simulator is used to evaluate the standard and the optimized controllers.Keywords Model-based control Á Two-degree-of-freedom control Á Flying helicopter simulator Á In-flight simulation Á Genetic algorithm Á Nelder-Mead simplex Abbreviations AC, RC, TC Attitude, rate, translational rate command DLR Deutsches Zentrum für Luft-und Raumfahrt/German Aerospace Center DR Delta Rating FB, FF Feedback, feedforward controller FHS Flying helicopter simulator IAE Integrated absolute error MBCS Model-based control system MIMO Multiple input multiple output SISO Single input single output A, B, C, D State-space representation matrices (standard form) b Sideslip angle [°] C(s) Transfer function matrix of feedback controller d Disturbance vector d p Pilot inputs (% deflection) d lon , d lat Longitudinal, lateral cyclic pilot control (% deflection) d ped , d col Pedal and collective pilot control (% deflection) G(s) Transfer function matrix I Identity matrix J Objective function J ave Objective function in frequency domain, weighting amplitude and phase difference J

This paper explores the use of Autoencoder (AE) models to identify Koopman-based linear representations for designing model predictive control (MPC) for wind farms. Wake interactions in wind farms are challenging to model, previously addressed with Koopman lifted states. In this study we investigate the performance of two AE models: The first AE model estimates the wind speeds acting on the turbines these are affected by changes in turbine control inputs. The wind speeds estimated by this AE model are then used in a second step to calculate the power output via a simple turbine model based on physical equations. The second AE model directly estimates the wind farm output, i.e., both turbine and wake dynamics are modeled. The primary inquiry of this study addresses whether any of these two AE-based models can surpass previously identified Koopman models based on physically motivated lifted states. We find that the first AE model, which estimates the wind speed and hence includes the wake dynamics, but excludes the turbine dynamics outperforms the existing physically motivated Koopman model. However, the second AE model, which estimates the farm power directly, underperforms when the turbines' underlying physical assumptions are correct. We additionally investigate specific conditions under which the second, purely data-driven AE model can excel: Notably, when modeling assumptions, such as the wind turbine power coefficient, are erroneous and remain unchecked within the MPC controller. In such cases, the data-driven AE models, when updated with recent data reflecting changed system dynamics, can outperform physicsbased models operating under outdated assumptions.

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