A lagrangian flight simulator for airborne wind energy systems

Abstract

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 (dissipativeless) 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.

Modeling and Natural Mode Analysis of Tethered Multi-Aircraft Systems

“…It implements a Lagrangian formulation with an approach based on minimal coordinates. Such a methodology has been commonly adopted for AWE systems because the fast longitudinal oscillations of the tethers are removed and the resulting set of ordinary dierential equations is not coupled with algebraic constraints [15,19,22,24,27].…”

Flight trajectory optimization of Fly-Gen airborne wind energy systems through a harmonic balance method

“…Higher-fidelity, but still computationally efficient, dynamic models are developed by Sánchez-Arriaga et al (2017, 2019; Sánchez-Arriaga and Serrano-Iglesias (2021) as a part of the Lagrangian Kite Flight Simulators (LAKSA) package based on minimal coordinates and by to study the dynamics of multiple AWES configurations. Moreover, thorough Newtonian dynamic models are used to compute reference flight paths and the consequent flight path control for soft-wing AWESs (Fechner et al, 2015;Fechner and Schmehl, 2016) and for fixed-wing AWESs (Licitra et al, 2019;Malz et al, 2019;Eijkelhof and Schmehl, 2022).…”

Identification of kite aerodynamic characteristics using the estimation before modeling technique

“…Reaching high lift coefficients is important to maximize the performance. High‐fidelity models and flight simulators 7‐12 also play an important role during the design and optimization phases of the machines. Pioneering aerodynamic models 13‐15 have been followed by studies with viscous‐inviscid interaction methods, 16 Reynolds averaged Navier–Stokes simulations, 17,18 and large eddy simulations 19 .…”

“…Reaching high lift coefficients is important to maximize the performance. High-fidelity models and flight simulators [7][8][9][10][11][12] also play an important role during the design and optimization phases of the machines.…”