ORIGINAL PAPER Model-based control of the flying helicopter simulator: evaluating and optimizing the feedback controller Johannes Hofmann • Antje Dittmer Received: 2 April 2011 / Revised: 1 August 2011 / Accepted: 1 August 2011 / Published online: 24 August 2011 Ó Deutsches Zentrum fu ¨r Luft- und Raumfahrt e.V. 2011 Abstract 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 pre- sented. 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 Rat- ing’’, 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 fre- quency. Apart from the Simulink Ò model, a ground-based simulator is used to evaluate the standard and the optimized controllers. Keywords Model-based control  Two-degree-of-freedom control  Flying helicopter simulator  In-flight simulation  Genetic algorithm  Nelder–Mead simplex Abbreviations AC, RC, TC Attitude, rate, translational rate command DLR Deutsches Zentrum fu ¨r 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 DR , J DROv Delta Rating objective function in time domain, without and with additional overshoot criterion This paper is based on a presentation at the German Aerospace Congress, September 27–29, 2011, Bremen, Germany. J. Hofmann (&)  A. Dittmer German Aerospace Center, DLR, Institute of Flight Systems, Lilienthalplatz 7, 38108 Braunschweig, Germany e-mail: johannes.hofmann@dlr.de A. Dittmer e-mail: antje.dittmer@dlr.de 123 CEAS Aeronaut J (2011) 2:43–56 DOI 10.1007/s13272-011-0008-6