Advertisement

Modeling of Airborne Wind Energy Systems in Natural Coordinates

  • Sébastien GrosEmail author
  • Moritz Diehl
Chapter
Part of the Green Energy and Technology book series (GREEN)

Abstract

This paper presents a modeling approach for AWE systems that allows for developing models of low symbolic complexity and low nonlinearity. The approach is based on multi-body modeling, using natural coordinates and algebraic constraints as a representation of the system evolution. This paper shows how to build such models for AWE systems in the Lagrangian framework and how to efficiently incorporate a non-singular representation of the pose (i.e. 3D orientation) of the wing. The proposed modeling technique is illustrated on a single-wing AWE system for power generation and rotating start-up, and for a dual-wing AWE system.

Keywords

Multibody System Model Predictive Control Aerodynamic Force Nonlinear Model Predictive Control Propose Modeling Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersson, J., Åkesson, J., Diehl, M.: CasADi – A symbolic package for automatic differentiation and optimal control. In: Forth, S., Hovland, P., Phipps, E., Utke, J., Walther, A. (eds.) Recent Advances in Algorithmic Differentiation, Vol. 87, Lecture Notes in Computational Science and Engineering, pp. 297–307. Springer, Berlin (2012). doi: 10.1007/978-3-642-30023-327 Google Scholar
  2. Ascher, U. M., Petzold, L. R.: Computer Methods for Ordinary Differential Equations and Differential–Algebraic Equations. SIAM Press, Philadelphia (1998)Google Scholar
  3. Canale, M., Fagiano, L., Milanese, M.: High Altitude Wind Energy Generation Using Controlled Power Kites. IEEE Transactions on Control Systems Technology 18(2), 279–293 (2010). doi:  10.1109/TCST.2009.2017933
  4. Fagiano, L., Milanese, M., Piga, D.: Optimization of airborne wind energy generators. International Journal of Robust and Nonlinear Control 22(18), 2055–2083 (2011). doi:  10.1002/rnc.1808 Google Scholar
  5. Fagiano, L., Milanese, M., Piga, D.: High-altitude wind power generation. IEEE Transactions on Energy Conversion 25(1), 168–180 (2010). doi:  10.1109/TEC.2009.2032582 Google Scholar
  6. Groot, S. G. C. de, Breukels, J., Schmehl, R., Ockels, W. J.: Modeling Kite Flight Dynamics Using a Multibody Reduction Approach. AIAA Journal of Guidance, Control and Dynamics 34(6), 1671–1682 (2011). doi:  10.2514/1.52686 Google Scholar
  7. Gros, S., Zanon, M., Diehl, M.: Control of AirborneWind Energy Systems Based on Nonlinear Model Predictive Control & Moving Horizon Estimation. In: Proceedings of the European Control Conference (ECC13), Zurich, Switzerland, 17–19 July 2013Google Scholar
  8. Gros, S., Zanon, M., Vukov, M., Diehl, M.: Nonlinear MPC and MHE for Mechanical Multi-Body Systems with Application to Fast Tethered Airplanes. In: Proceedings of the 4th IFAC Nonlinear Model Predictive Control Conference, pp. 86–93, Leeuwenhorst, Netherlands, 23–27 Aug 2012. doi:  10.3182/20120823-5-NL-3013.00061
  9. Gros, S., Ahmad, H., Geebelen, K., Swevers, J., Diehl, M.: In-flight Estimation of the Aerodynamic Roll Damping and Trim Angle for a Tethered Aircraft based on Multiple-shooting. In: Proceedings of the 16th IFAC Symposium on System Identification, pp. 1407–1412, Brussels,Belgium, 11–13 July 2012. doi:  10.3182/20120711-3-BE-2027.00342
  10. Houska, B.: Robustness and Stability Optimization of Open-Loop Controlled Power Generating Kites. M.Sc.Thesis, Ruprecht-Karls-Universit¨at, Heidelberg, 2007. http://www.kuleuven.be/optec/files/Houska2007a.pdf
  11. Joshi, A. W.: Elements of Group Theory for Physicists. 4th ed. New Age International Publishers,New Delhi (1997)Google Scholar
  12. Pantelides, C. C., Sargent, R. W. H., Vassiliadis, V. S.: Optimal control of multistage systems described by high-index differential-algebraic equations. In: Bulirsch, R., Kraft, D. (eds.) Computational Optimal Control, ISNM International Series of Numerical Mathematics Vol. 115, pp. 177–191. Birkh¨auser, Basel (1994). doi: Google Scholar
  13. Papastavridis, J. G.: Analytical Mechanics. Oxford University Press, New York (2002)Google Scholar
  14. Schulz, V. H., Bock, H. G., Steinbach, M. C.: Exploiting invariants in the numerical solution of multipoint boundary value problems for DAEs. SIAM Journal on Scientific Computing 19(2), 440–467 (1998). doi:  10.1137/S1064827594261917 Google Scholar
  15. Shabana, A. A.: Dynamics of Multibody Systems. 3rd ed. Cambridge University Press, Cambridge (2005)Google Scholar
  16. Terink, E. J., Breukels, J., Schmehl, R., Ockels, W. J.: Flight Dynamics and Stability of a Tethered Inflatable Kiteplane. AIAA Journal of Aircraft 48(2), 503–513 (2011). doi:  10.2514/1.C031108 Google Scholar
  17. Williams, P., Lansdorp, B., Ockels,W. J.: Modeling and Control of a Kite on a Variable Length Flexible Inelastic Tether. AIAA Paper 2007-6705. In: Proceedings of the AIAA Modelling and Simulation Technologies Conference and Exhibit, Hilton Head, SC, USA, 20–23 Aug 2007. doi:  10.2514/6.2007-6705
  18. Williams, P., Lansdorp, B., Ockels, W. J.: Nonlinear Control and Estimation of a Tethered Kite in Changing Wind Conditions. AIAA Journal of Guidance, Control and Dynamics 31(3) (2008). doi:  10.2514/1.31604
  19. Williams, P., Lansdorp, B., Ruiterkamp, R., Ockels, W.: Modeling, Simulation, and Testing of Surf Kites for Power Generation. AIAA Paper 2008-6693. In: Proceedings of the AIAA Modeling and Simulation Technologies Conference and Exhibit, Honolulu, HI, USA, 18–21 Aug 2008. doi:  10.2514/6.2008-6693
  20. Zanon, M., Gros, S., Andersson, J., Diehl, M.: Airborne Wind Energy Based on Dual Airfoils. IEEE Transactions on Control Systems Technology 21(4), 1215–1222 (2013). doi:  10.1109/TCST.2013.2257781 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentKU LeuvenLeuvenBelgium

Personalised recommendations