Model Predictive Control of Rigid-Airfoil Airborne Wind Energy Systems

  • Mario ZanonEmail author
  • Sébastien Gros
  • Moritz Diehl
Part of the Green Energy and Technology book series (GREEN)


In order to allow for a reliable and lasting operation of Airborne Wind Energy systems, several problems need to be addressed. One of the most important challenges regards the control of the tethered airfoil during power generation. Tethered flight of rigid airfoils is a fast, strongly nonlinear, unstable and constrained process, and one promising way to address the control challenge is the use of Nonlinear Model Predictive Control (NMPC) together with online parameter and state estimation based on Moving Horizon Estimation (MHE). In this paper, these techniques are introduced and their performance demonstrated in simulations of a 30 m wingspan tethered airplane with power generation in pumping mode.


Optimal Control Problem Model Predictive Control Linear Quadratic Regulator Prediction Horizon Turbulent Wind 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This research was supported by Research Council KUL: PFV/10/002 Optimization in Engineering Center OPTEC, GOA/10/09 MaNet and GOA/10/11 Global real-time optimal control of autonomous robots and mechatronic systems. Flemish Government: IOF/KP/SCORES4CHEM, FWO: PhD/postdoc grants and projects: G.0320.08 (convex MPC), G.0377.09 (Mechatronics MPC); IWT: PhD Grants, projects: SBO LeCoPro; Belgian Federal Science Policy Office: IUAP P7 (DYSCO, Dynamical systems, control and optimization, 2012-2017); EU: FP7-EMBOCON (ICT-248940), FP7-SADCO (MC ITN-264735), ERC ST HIGHWIND (259 166), Eurostars SMART, ACCM.


  1. 1.
    Burton, T., Sharpe, D., Jenkins, N., Bossanyi, E.:Wind Energy Handbook. John Wiley & Sons, Ltd, Chichester (2001). doi:  10.1002/0470846062
  2. 2.
    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
  3. 3.
    Daum, F.: Nonlinear Filters: Beyond the Kalman Filter. IEEE Aerospace and Electronic Systems Magazine 20(8), 57–69 (2005). doi:  10.1109/MAES.2005.1499276
  4. 4.
    Diehl, M., Bock, H., Schl¨oder, J.: A real-time iteration scheme for nonlinear optimization in optimal feedback control. SIAM Journal on Control and Optimization 43(5), 1714–1736 (2005). doi:  10.1137/S0363012902400713 Google Scholar
  5. 5.
    Diehl, M., Bock, H., Schl¨oder, J., Findeisen, R., Nagy, Z., Allg¨ower, F.: Real-time optimization and Nonlinear Model Predictive Control of Processes governed by differential-algebraic equations. Journal of Process Control 12(4), 577–585 (2002). doi:  10.1016/S0959-1524(01)00023-3 Google Scholar
  6. 6.
    Diehl, M., Magni, L., Nicolao, G. D.: Efficient NMPC of unstable periodic systems using approximate infinite horizon closed loop costing. Annual Reviews in Control 28(1), 37–45 (2004). doi:  10.1016/j.arcontrol.2004.01.011.
  7. 7.
    Ferreau, H. J.: Model predictive control algorithms for applications with millisecond timescales. Ph.D. Thesis, KU Leuven, 2011. ferreau.pdf
  8. 8.
    Ferreau, H. J., Bock, H. G., Diehl, M.: An online active set strategy to overcome the limitations of explicit MPC. International Journal of Robust and Nonlinear Control 18(8), 816–830 (2008). doi:  10.1002/rnc.1251 Google Scholar
  9. 9.
    Ferreau, H. J., Kraus, T., Vukov, M., Saeys,W., Diehl, M.: High-speed moving horizon estimation based on automatic code generation. In: Proceedings of the 51st IEEE Annual Conference on Decision and Control, pp. 687–692, Maui, HI, USA, 10–13 Dec 2012. doi:  10.1109/CDC. 2012.6426428
  10. 10.
    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
  11. 11.
    Gros, S., Zanon, M., Diehl, M.: Orbit Control for a Power Generating Airfoil Based on Non- linear MPC. In: Proceedings of the 2012 American Control Conference, pp. 137–142, Montr´eal, Canada, 27–29 June 2012. all.jsp?arnumber = 6315367
  12. 12.
    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
  13. 13.
    Gr¨une, L.: NMPC Without Terminal Constraints. In: Proceedings of the IFAC Conference on Nonlinear Model Predictive Control, pp. 1–13, Leeuwenhorst, Netherlands, 23–27 Aug 2012. doi:  10.3182/20120823-5-NL-3013.00030
  14. 14.
    Houska, B., Ferreau, H., Diehl, M.: An Auto-Generated Real-Time Iteration Algorithm for Nonlinear MPC in the Microsecond Range. Automatica 47(10), 2279–2285 (2011). doi:  10.1016/j.automatica.2011.08.020
  15. 15.
    Houska, B., Diehl, M.: Optimal control of towing kites. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 2693–2697, San Diego, CA, USA, 13–15 Dec 2006. doi:  10.1109/CDC.2006.377210
  16. 16.
    Ilzh¨ofer, A., Houska, B., Diehl, M.: Nonlinear MPC of kites under varying wind conditions for a new class of large-scale wind power generators. International Journal of Robust and Nonlinear Control 17(17), 1590–1599 (2007). doi:  10.1002/rnc.1210
  17. 17.
    K¨uhl, P., Diehl, M., Kraus, T., Schl¨oder, J., Bock, H.: A real-time algorithm for moving horizon state and parameter estimation. Computers & Chemical Engineering 35(1), 71–83 (2011). doi:  10.1016/j.compchemeng.2010.07.012.
  18. 18.
    Leineweber, D. B., Bauer, I., Bock, H. G., Schl¨oder, J. P.: An Efficient Multiple Shooting Based Reduced SQP Strategy for Large-Scale Dynamic Process Optimization. Part 1: theoretical aspects. Computers & Chemical Engineering 27(2), 157–166 (2003). doi:  10.1016/S0098-1354(02)00158-8
  19. 19.
    Leineweber, D. B., Sch¨afer, A., Bock, H. G., Schl¨oder, J. P.: An Efficient Multiple Shooting Based Reduced SQP Strategy for Large-Scale Dynamic Process Optimization: Part II: Soft ware aspects and applications. Computers & Chemical Engineering 27(2), 167–174 (2003). doi:  10.1016/S0098-1354(02)00195-3
  20. 20.
    Manwell, J. F., McGowan, J. G., Rogers, A. L.: Wind Energy Explained: Theory, Design and Application. 2nd ed. John Wiley & Sons, Ltd., Chichester (2009). doi:  10.1002/9781119994367
  21. 21.
    Mayne, D., Rawlings, J., Rao, C., Scokaert, P.: Constrained model predictive control, stability and optimality. Automatica 26(6), 789–814 (2000). doi:  10.1016/S0005-1098(99)00214-9 Google Scholar
  22. 22.
    Quirynen, R.: Automatic code generation of Implicit Runge-Kutta integrators with continuous output for fast embedded optimization. M.Sc.Thesis, KU Leuven, 2012. Scholar
  23. 23.
    Quirynen, R., Vukov, M., Diehl, M.: Auto Generation of Implicit Integrators for Embedded NMPC with Microsecond Sampling Times. In: Proceedings of the 4th IFAC Nonlinear Model Predictive Control Conference, pp. 175–180, Leeuwenhorst, Netherlands, 23–27 Aug 2012. doi:  10.3182/20120823-5-NL-3013.00013
  24. 24.
    Rao, C. V.: Moving Horizon Estimation of Constrained and Nonlinear Systems. Ph.D. Thesis, University of Wisconsin–Madison, 2000.
  25. 25.
    Rawlings, J., Bakshi, B.: Particle filtering and moving horizon estimation. Computers and Chemical Engineering 30(10–12), 1529–1541 (2006). doi:  10.1016/j.compchemeng.2006.05.031

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentKU LeuvenLeuvenBelgium

Personalised recommendations