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Identification and Modeling of the Airbrake of an Experimental Unmanned Aircraft

Abstract

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 New, unpublished measurements with gradually increasing servo load as the servo moves are also considered to verify the model in more realistic circumstances.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.

References

  1. Flight phase adaptive aero-servo-elastic aircraft design methods. cordis.europa.eu/project/id/815058

  2. Flutter Free Flight Envelope Expansion for Economical Performance Improvement (2015). https://flexop.eu/

  3. Adam, E., Guestrin, E.: Identification and robust control of an experimental servo motor. ISA Transactions 41 (2), 225–234 (2002). https://doi.org/10.1016/S0019-0578(07)60082-2. http://www.sciencedirect.com/science/article/pii/S0019057807600822

    Article  Google Scholar 

  4. Anastasopoulos, L., Hornung, M.: Design of a real-time test bench for UAV servo actuators. AIAA AVIATION Forum. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2018-3735(2018)

  5. Batista, J., Sousa, K., Nunes, J.L., Sousa, R.S., Thé, G.A.P.: Identification of the parameters of a ac servomotor using genetic algorithm. https://doi.org/10.5281/zenodo.1100140 (2015)

  6. Davies, H, Kirk, F.: A resume of aerodynamic data on airbrakes. Tech. Rep., Aeronautical Research Council, Ministry of Supply (1951)

  7. Grote, K.H., Feldhusen, J.: Dubbel: Taschenbuch Für Den Maschinenbau, Auflage, vol. 22. Springer, Berlin (2007)

    Book  Google Scholar 

  8. Ishak, N., Abdullah, N.I., Rahiman, M.H.F., Samad, A.M., Adnan, R.: Model identification and controller design for servomotor. In: 2010 6th International Colloquium on Signal Processing and its Applications. https://doi.org/10.1109/CSPA.2010.5545294, pp 1–4 (2010)

  9. Koerner, D.: Experimental System Identification of an Electric Actuated Airbrake System for the FLEXOP Research UAV. Bachelor Thesis, Institute of Aircraft Design Technical University of Munich (2018)

  10. KST: X30-12-1500 Technical Specification (2018)

  11. Ljung, L.: System Identification: Theory for the User. Prentice Hall information and system sciences series. Prentice Hall PTR. https://books.google.hu/books?id=nHFoQgAACAAJ (1999)

  12. Ortiz, X., Rival, D.E., Wood, D.W.: Forces and moments on flat plates of small aspect ratio with application to PV wind loads and small wind turbine blades. Energies 8(4), 1–16 (2015)

    Article  Google Scholar 

  13. Piatek, M.: Identification of the servo motor used in the walking robot. AUTOMATYKA 14(1) (2010)

  14. Pusch, M., Ossmann, D., Luspay, T.: Structured control design for a highly flexible flutter demonstrator. Aerospace 6(3). https://doi.org/10.3390/aerospace6030027. https://www.mdpi.com/2226-4310/6/3/27 (2019)

  15. Sendner, F.M., Stahl, P., Roessler, C., Hornung, M.: Designing an uav propulsion system for dedicated acceleration and deceleration requirements. AIAA AVIATION Forum. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2017-4105 (2017)

  16. Sendner, F.M., Stahl, P., Roessler, C., Hornung, M.: Design and testing of an electric actuated airbrake for dynamic airspeed control of an unmanned aeroelastic research vehicle. AIAA AVIATION Forum. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2018-3194 (2018)

  17. Takarics, B., Patartics, B., Luspay, T., Vanek, B., Roessler, C., Bartasevicius, J., Koeberle, S.J., Hornung, M., Teubl, D., Pusch, M., Wustenhagen, M., Kier, T.M., Looye, G., Bauer, P., Meddaikar, Y.M., Waitman, S., Marcos, A.: Active flutter mitigation testing on the FLEXOP demonstrator aircraft. In: AIAA Scitech 2020 Forum. https://doi.org/10.2514/6.2020-1970. https://arc.aiaa.org/doi/abs/10.2514/6.2020-1970(2020)

  18. Wada, T., Ishikawa, M., Kitayoshi, R., Maruta, I., Sugie, T.: Practical modeling and system identification of R/C servo motors. In: 2009 IEEE Control Applications, (CCA) Intelligent Control, (ISIC). https://doi.org/10.1109/CCA.2009.5280987, pp 1378–1383 (2009)

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Acknowledgements

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.

Funding

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).

Appendix

Appendix

ϕcD fit:

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

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

$$ \begin{array}{@{}rcl@{}} {c}_{N_{L}}^{\prime}(\phi) &=& \phi^{2} [rad^2] + 1.8706\phi [rad] \ \ if \ 0 \leq \phi < 0.6962rad\\ {c}_{N_{H}}^{\prime}(\phi)&=&0.0514\phi [rad] +1.7512 \ \ if \ 0.6962rad\leq\phi \end{array} $$
(1)

ϕsa fit:

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

αϕ curve:

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

ϕα curve:

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

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). https://doi.org/10.1007/s10846-020-01204-1

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  • DOI: https://doi.org/10.1007/s10846-020-01204-1

Keywords

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