Numerical simulation of tethered–wing power systems based on variational integration

Abstract

This paper describes dynamic formulations for a multi-physics system consisting of an electrical generator and a finite element model of a variable-length cable attached at one end to a reeling mechanism and the other to a rigid body that represents a flying wing. Lie group methods are utilized to obtain singularity-free dynamics of the wing. Two different methods are employed for the derivation and integration of the Euler–Lagrange equations. In the first method, the equations of motion are derived in continuous-time and integrated by a general-purpose implicit ODE solver. The second is the application of the discrete analogue of Lagrange–d’Alembert principle that yields a variational integrator. Extensive simulations are carried out to calculate the computational complexity of the discrete integrator and compare the results for CPU time and accuracy to those of the ODE solver. It is shown that the variational integrator has a significant advantage in terms of preservation of the orthogonality of the wing’s attitude matrix and reduction of the CPU time. The descriptions of the implemented aerodynamic models and controllers, along with the results for the simulation of a tethered-wing system operating in a turbulent wind environment are also presented.