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Identification and Modeling of the Airbrake of an Experimental Unmanned Aircraft


This paper presents the modeling, system identification, simulation and flight testing of the airbrake of an unmanned experimental aircraft in frame of the FLEXOP H2020 EU project. As the aircraft is equipped with a jet engine with slow response an airbrake is required to increase deceleration after speeding up the aircraft for flutter testing in order to remain inside the limited airspace granted by authorities for flight testing. The airbrake consists of a servo motor, an opening mechanism and the airbrake control surface itself. After briefly introducing the demonstrator aircraft, the airbrake design and the experimental test benches the article gives in depth description of the modeling and system identification referencing also previous work. System identification consists of the determination of the highly nonlinear (saturated and load dependent) servo actuator dynamics and the nonlinear aerodynamic and mechanical characteristics including stiffness and inertia effects. New contributions relative to the previous work are a unified servo angular velocity limit model considering opening against the load or closing with it, the detailed construction and evaluation of airbrake normal and drag force models considering the whole deflection and aircraft airspeed range, the presentation of a unified aerodynamic - mechanic nonlinearity model giving direct relation between airbrake angle, dynamic pressure and servo torque and the transfer function-based modeling of stiffness and inertial effects in the mechanism. The identified servo dynamical model includes system delay, inner saturation, the aforementioned load dependent angular velocity limit model and a transfer function model. The servo model was verified based-on test bench measurements considering the whole opening angle and dynamic load range of the airbrake. New, unpublished measurements with gradually increasing servo load as the servo moves are also considered to verify the model in more realistic circumstances. Then the full airbrake model is constructed and tested in simulation to check realistic behavior. In the next step the airbrake model integrated into the nonlinear simulation model of the FLEXOP aircraft is tested by flying simulated test trajectories with the baseline controller of the aircraft in software-in-the-loop (SIL) Matlab simulation. First, the standalone airbrake simulation is compared to the SIL results to verify flawless integration of airbrake model into the nonlinear aircraft simulation. Then deceleration times with and without airbrake are compared underlining the usefulness of the airbrake in the test mission. Finally, real flight data is used to verify and update the airbrake model and show the effectiveness of the airbrake.


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The authors gratefully acknowledge the contribution of Matthias Wuestenhagen at Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR) Institut für Systemdynamik und Regelungstechnik (RMC-SR-FLS) who integrated the airbrake simulation model into the nonlinear model of the FLEXOP aircraft.

The authors gratefully acknowledge the help of Tamas Luspay (senior research fellow, SZTAKI) in simulating the airbrake dynamics together with the baseline controller.

The authors gratefully acknowledge the contribution of Institute of Aircraft Design, Department of Mechanical Engineering, Technical University of Munich flight test team (Christian Roessler, Fabian Wiedemann, Sebastian Koeberle, Julius Bartasevicius and Daniel Teubl) with executing the flight tests.


Open Access funding provided by ELKH Institute for Computer Science and Control.

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Correspondence to Peter Bauer.

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The research leading to these results is part of the FLEXOP project. This project has received funding from the European Unions Horizon 2020 research and innovation program under grant agreement No 636307. Part of this research has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 815058 (FLiPASED project).



ϕcD fit:

$$ c_{D}(\phi)=0.88\cdot \phi [rad] $$

\(\phi -{c}_{N}^{\prime }\) fit:

$$ \begin{array}{@{}rcl@{}} {c}_{N_{L}}^{\prime}(\phi) &=& \phi^{2} [rad^2] + 1.8706\phi [rad] \ \ if \ 0 \leq \phi < 0.6962rad\\ {c}_{N_{H}}^{\prime}(\phi)&=&0.0514\phi [rad] +1.7512 \ \ if \ 0.6962rad\leq\phi \end{array} $$

ϕsa fit:

$$ \begin{array}{@{}rcl@{}} s_a(\phi) [m]&=&-0.02735\phi^5 [rad^{5}]+0.09069\phi^4 [rad^4]-0.11428\phi^{3} [rad^{3}]\\ &&+0.071245\phi^{2} [rad^2]-0.02437\phi [rad]+0.006 \end{array} $$

αϕ curve:

$$ \phi(\alpha) [rad]=-0.01864\alpha^{3} [rad^{3}]+0.213425\alpha^{2} [rad^{2}]+0.20056\alpha [rad] $$

ϕα curve:

$$ \begin{array}{@{}rcl@{}} \alpha(\phi) [rad]&=&-1.83448\phi^4 [rad^4]+5.03271\phi^{3} [rad^{3}]\\ &&- 5.28037\phi^{2} [rad^2]+3.9602\phi [rad] \end{array} $$

Stiffness formula:

$$ k_{\phi}=1383.097\phi^{3} [rad^{3}]-3028.264\phi^{2} [rad^{2}]+1764.837\phi [rad]+45.722 $$

System dynamics from angular velocity reference to angular velocity:

$$ G_{sys}(z)=\frac{1.039}{1+0.0149z^{-1}+0.238z^{-2}-0.2361z^{-3}} $$

System dynamics from delayed load to angle:

$$ G_{T_{L}}(z)=\frac{-0.002181}{1-0.5267z^{-1}} $$

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Bauer, P., Anastasopoulos, L., Sendner, FM. et al. Identification and Modeling of the Airbrake of an Experimental Unmanned Aircraft. J Intell Robot Syst 100, 259–287 (2020).

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  • Aircraft airbrake
  • Dynamic test bench
  • System identification
  • Simulation
  • Flight test results