A lagrangian flight simulator for airborne wind energy systems

Gonzalo Sánchez-Arriaga, Alejandro Pastor-Rodríguez, Manuel Sanjurjo-Rivo, Roland Schmehl

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12 Citations (Scopus)
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A parallelized flight simulator for the dynamic analysis of airborne wind energy (AWE) systems for ground- and fly-generation configurations is presented. The mechanical system comprises a kite or fixed-wing drone equipped with rotors and linked to the ground by a flexible tether. The time-dependent control vector of the simulator mimics real AWE systems and it includes the length of the main tether, the geometry of the bridle, the torque of the motor controllers of the rotors, and the deflections of ailerons, rudder and elevator. The use of a lagrangian formulation with a minimal coordinate approach and discretizing the main tether as a chain of inelastic straight rods linked by ideal (dissipative-less) rotational joints, yielded a non-stiff set of ordinary differential equations free of algebraic constraints. Several verification tests, including a reel-in maneuver that admits an analytical solution, are presented. The efficiency of the parallelization with the number of tether segments, and trade-off analysis of the lagrangian and hamiltonian formulations are also considered. The versatility of the simulator is highlighted by analyzing two maneuvers that are relevant for AWE scenarios. First, the simulator is used to compute periodic figure-of-eight trajectories with an open-loop control law that varies the geometry of the kite’s bridle, as frequently done in ground-generation AWE systems. Second, an unstable equilibrium state of a tethered drone equipped with two rotors for energy harvesting is stabilized by implementing a closed-loop control strategy for the deflection of the control aerodynamic surfaces.
Original languageEnglish
Pages (from-to)665-684
Number of pages20
JournalApplied Mathematical Modelling: simulation and computation for engineering and environmental systems
Publication statusPublished - 1 May 2019

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Kite modeling
  • Lagrangian systems
  • Kite control


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