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Dynamics and Control of Single-Line Kites

Published online by Cambridge University Press:  03 February 2016

G. Sánchez
G. Sánchez*
Affiliation:
Dept Física Aplicada, ETSI Aeronáuticos, Universidad Politécnica, Madrid, Spain
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Abstract

This paper presents a dynamic analysis of a single-line kite with two degrees of freedom. A Lagrangian formulation is used to write convenient equations of motion. The equilibrium states of the system and their stability are studied; Eigenvalues and eigenmodes are calculated by using linear theory. The stability in the parametric plane δ – W0 is discussed, where δ defines the bridle geometry and W0 is wind velocity. The system goes through a Hopf bifurcation and periodic branches of solutions appear. The orbits and their stability have been calculated numerically using Floquet theory and wind velocity seems to play an important role in their existence. Finally the kite response against gusts is considered and an open loop control system developed to keep the flight altitude invariant under changing atmospheric conditions. Modifying the bridle’s geometry seems to be a convenient way to control a kite’s performance.

Type
Research Article
Information
The Aeronautical Journal , Volume 110 , Issue 1111 , September 2006 , pp. 615 - 621
Copyright
Copyright © Royal Aeronautical Society 2006 

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References

1. Glauert, H., The stability of a body towed by a light wire, RM, 1930, 1312, Aeronautical Research Council, UK.Google Scholar
2. Bairstow, L., Relf, E.F. and Jones, R., The stability of kite ballons: mathematical investigation, RM, December 1915, 208, Aeronautical Research Council, UK.Google Scholar
3. Bryant, L.W., Brown, W.S. and Sweeting, N.E., Collected research on the stability of kites and towed gliders, RM, February 1942, 2303, Aeronautical Research Council, National Physical Lab, Teddington Middlesex, UK.Google Scholar
4. Adomaitis, R.A., Kites and bifurcation theory, SIAM Review, September 1989, 31, (3), pp 478–483.Google Scholar
5. Alexander, K. and Stevenson, J., Kite equilibrium and bridle length, Aeronaut J, September 2001, pp 535–541.Google Scholar
6. Veldman, S., Bersee, H., Vermeeren, C. and Bergsma, O., Conceptual design of a high altitude kite, 2002, 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, Colorado, 22-25 April, 2002.Google Scholar
7. Diehl, M., Magni, L. and De Nicolao, G., Efficient NMPC of unstable periodic systems using approximate infinite horizon closed loop costing, Annual Review in Control, 2004, 28, pp 37–45.Google Scholar
8. Delaurier, J.D., Influence of ballonet motions on the longitudinal stability of tethered aerostats, J Aircr, May 1980, 17, (5), pp 305–312.Google Scholar
9. Fluid forces and moments on flat plates, September 1970, ESDU International, Engineering Science Data Unit 70015.Google Scholar
10. Doedel, E.J., Champmeys, A.R., Fairgrieve, T.F., Kuznetsov, Y., Sanstede, B., Wang, X.J., AUTO 97: Continuation and bifurcation software for ordinary differential equations, 1997, pub/doedel/auto at ftp.cs.concordia.ca.Google Scholar
11. Ermentrout, B. Xppaut, Dynamical systems software with continuation and bifurcation capabilities, 2000, /pub/bardware at ftp.math.pit.edu.Google Scholar