Theory and Experimental Validation of a Simple Comprehensible Model of Tethered Kite Dynamics Used for Controller Design

  • Michael ErhardEmail author
  • Hans Strauch
Part of the Green Energy and Technology book series (GREEN)


We present a simple model for the dynamics and aerodynamics of a tethered kite system and validate it by experimental flight data. After introduction of system setup and model assumptions, the equations of motion for the kinematics are derived and discussed. Then the turn rate law for the kite response to a steering deflection is introduced. The tutorial introduction of the model is finalized by an extension for varying tether lengths, which is the regular operation mode of certain classes of airborne wind energy setups. The second part starts with a summary of the sensor setup. Then, the turn rate law, as distinguishing feature of the model, is illustrated and validated by experimental data. Subsequently, we discuss the kinematics of the kite by comparing model based prediction to experiment. Conclusively, we briefly summarize controller design considerations and discuss the flight controller performance, which further proves the validity of the model as it is based on a feed forward term which in turn, is build on the presented model.


Controller Design Circular Orbit Outer Loop Model Predictive Control Inertial Measurement Unit 
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  1. 1.
    Baayen, J. H., Ockels, W. J.: Tracking control with adaption of kites. IET Control Theory and Applications 6(2), 182–191 (2012). doi:  10.1049/iet-cta.2011.0037
  2. 2.
    Dadd, G. M., Hudson, D. A., Shenoi, R. A.: Determination of kite forces using three dimensional flight trajectories for ship propulsion. Renewable Energy 36(10), 2667–2678 (2011). doi:  10.1016/j.renene.2011.01.027 Google Scholar
  3. 3.
    Diehl, M.: Real-time optimization for large scale nonlinear processes. Ph.D. Thesis, University of Heidelberg, 2001.
  4. 4.
    Erhard, M., Strauch, H.: Control of Towing Kites for Seagoing Vessels. IEEE Transactions on Control Systems Technology (2012). doi:  10.1109/TCST.2012.2221093.arXiv:1202.3641 [cs.DS]
  5. 5.
    Erhard, M., Strauch, H.: Sensors and Navigation Algorithms for Flight Control of Tethered Kites. In: Proceedings of the European Control Conference (ECC13), Zurich, Switzerland, 17–19 July 2013. arXiv:1304.2233 [cs.SY]Google Scholar
  6. 6.
    Fagiano, L.: Control of tethered airfoils for high-altitude wind energy generation. Ph.D. Thesis, Politecnico di Torino, 2009. thesis_Fagiano_Final.pdf
  7. 7.
    Fagiano, L., Zgraggen, A. U., Morari, M., Khammash, M.: Automatic crosswind flight of tethered wings for airborne wind energy: modeling, control design and experimental results. Submitted to IEEE Transactions on Control System Technology (2013). arXiv:1301. 1064 [cs.DS]Google Scholar
  8. 8.
    Houska, B., Diehl, M.: Robustness and Stability Optimization of Power Generating Kite Systems in a Periodic Pumping Mode. In: Proceedings of the IEEE Multi-Conference on Systems and Control, pp. 2172–2177, Yokohama, Japan, 8–10 Sept 2010. doi:  10.1109/CCA.2010.5611288
  9. 9.
    Ilzhöfer, 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
  10. 10.
    Lingard, J. S.: The aerodynamics of gliding Parachutes. AIAA Paper 86-2427-CP. In: Proceedings of the 9th Aerodynamic Decelerator and Balloon Technology Conference, Albuquerque, NM, USA, 7–9 Oct 1986. doi:  10.2514/6.1986-2427
  11. 11.
    Ljung, L.: System Identification—Theory for the User. 2nd ed. PTR Prentice Hall, Upper Saddle River, NJ (1999)Google Scholar
  12. 12.
    Williams, P., Lansdorp, B., Ockels, W.: Optimal Crosswind Towing and Power Generation with Tethered Kites. AIAA Journal of Guidance, Control, and Dynamics 31(1), 81–93 (2008). doi:  10.2514/1.30089
  13. 13.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.SkySails GmbHHamburgGermany

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