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. ... Read more

Simulation, state estimation, and aerodynamic parameter identification from in-flight data are actual research topics in AWE [1,2]. This work summarizes the status of four infrastructures developed at Universidad Carlos III de Madrid that are related with them: (i) a portable experimental rig for the acquisition of flight data like kite position, velocity, Euler angles, angular velocity, aerodynamic speed, angle of attack and sideslip angles, tether tensions, and wind velocity, (ii) an estimator of the state of the system, including the aerodynamic force and torque (iii) an optimization algorithm to compute the aerodynamic parameters from the estimated state variables, and (iv) the open-source simulator LAKSA, that contains modules aimed at the dynamic simulation and control of fly-gen and ground-gen generation systems, 2- line acrobatic kites, four-line kitesurf kites, and a train of N stacked kites. ... Read more

A flight-path reconstruction algorithm for tethered aircraft, which is based on an extended Kalman filter, is presented. The algorithm is fed by the measurements of a set of onboard and ground-based instruments and provides the optimal estimation of the system state-space trajectory, which includes typical aircraft variables such as position and velocity, as well as an estimation of the aerodynamic force and torque. Therefore, it can be applied to closed-loop control in airborne wind energy systems and it is a first step toward aerodynamic parameter identification of tethered aircraft using flight-test data. The performance of the algorithm is investigated by feeding it with real flight data obtained from a low-cost and highly portable experimental setup with a four-line kite. Several flight tests, which include pullup and lateral-directional steering maneuvers with two kites of different areas, are conducted. The coherence of the estimations provided by the filter, such as the kite state-space trajectory and aerodynamic forces and torques, is analyzed. For some standard variables, such as kite Euler angles and position, the results are also compared with a second independent onboard estimator.
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A mathematical model of a kite connected to the ground by two straight tethers of varying lengths is presented and used to study the traction force generated by kites flying in cross-wind conditions. The equations of motion are obtained by using a Lagrangian formulation, which yields a low-order system of ordinary differential equations free of constraint forces. Two parameters are chosen for the analysis. The first parameter is the wind velocity. The second parameter is one of the stability derivatives of the aerodynamic model: the roll response to the sideslip angle, known also as effective dihedral. This parameter affects significantly the lateral dynamics of the kite. It has been found that when the effective dihedral is below a certain threshold, the kite follows stable periodic trajectories, and naturally flies in cross-wind conditions while generating a high tension along both tethers. This result indicates that kite-based propulsion systems could operate without controlling tether lengths if kite design, including the dihedral and sweep angles, is done appropriately. If both tether lengths are varied out-of-phase and periodically, then kite dynamics can be very complex. The trajectories are chaotic and intermittent for values of the effective dihedral below a certain negative threshold. It is found that tether tensions can be very similar with and without tether length modulation if the parameters of the model are well-chosen. The use of the model for pure traction applications of kites is discussed. ... Read more

Analytical mechanics techniques are applied to the construction of three kite flight simulators with applications to airborne wind energy generation and sport uses. All of themwere developed under a minimal coordinate formulation approach. This choice has the main advantage of yielding a set of ordinary differential equations free of algebraic constraints, a feature that distinguishes the simulators from codes based on classical mechanics formulation and improves their robustness and efficiency. The first simulator involves a kite with a flexible tether, a bridle of variable geometry, and several on-board wind turbines. Such a simulator, which models the tether by a set of rigid bars linked with ideal joints, can be used to study the on-ground generation of electrical energy through yo-yo pumping maneuvers and also the onboard generation by the wind turbines. The second simulator models a kite linked to the ground by two rigid control lines. This numerical tool is aimed at the study of the dynamics of acrobatic kites and the traction analysis of giant kites to propel cargo ships. The third and last simulator of this work considers a kite with four control lines similar to the ones used in kitesurf applications. Two of them are rigid tethers of constant length that connect the leading edge of the kite with a fixed point at the ground. The other two tethers are elastic and they link a control bar with the trailing edge of the kite. The performances of the simulators in terms of computational cost and parallelization efficiency are discussed. Their architectures and user interfaces are similar, and appropriate to carry out trade-off and optimization analyses for airborne wind energy generation. ... Read more

The aerodynamic characterization of kites is of paramount importance in the analysis of kites applied to wind energy generation because it is a key component of flight simulators. However, due to flexibility effects of the kite structure and the typically large sideslip and attack angles, severe difficulties arise. This work applies a Estimation-Before-Modeling (EBM) method, a widespread technique in aerospace engineering that makes use of data obtained during flight testing, to the aerodynamic characterization of power kites with four control lines. The procedure includes two main steps: an estimation phase and a modelling phase. The estimation phase involves a Kite Estimator (KE) that receives a comprehensive set of measurements and provides the time history of the state vector of the system. In this phase, aerodynamic forces andmoments are components of the extended state vector of the kite and they are estimated fromthemeasurements by using stochastic filtering and smoothing techniques. The KE has been fed with experimental data obtained during a test campaign with two different power kites (10m2 and 13m2). In the modelling phase, a multivariable regression algorithm has been used to determine the nonlinear coefficients of the aerodynamic model. The regression algorithm compares the aerodynamic forces and torques provided by the KE and the one computed theoretically with a flight simulator of a four-line kite. The accuracy of the aerodynamic model obtained with the EBM technique was assessed by comparing time histories of the experimental trajectories and the one provided by the kite simulator updated with the new aerodynamic model. ... Read more