Abstract
Earlier results by the authors showed constructions of Lie algebraic, partial feedback linearizing control methods for pitch and plunge primary control utilizing a single trailing edge actuator. In addition, a globally stable nonlinear adaptive control method was derived for a structurally nonlinear wing section with both a leading and trailing edge actuator. However, the global stability result described in a previous paper by the authors, while highly desirable, relied on the fact that the leading and trailing edge actuators rendered the system exactly feedback linearizable via Lie algebraic methods. In this paper, the authors derive an adaptive, nonlinear feedback control methodology for a structurally nonlinear typical wing section. The technique is advantageous in that the adaptive control is derived utilizing an explicit parameterization of the structural nonlinearity and a partial feedback linearizing control that is parametrically dependent is defined via Lie algebraic methods. The closed loop stability of the system is guaranteed to be stable via application of La Salle's invariance principle.
Similar content being viewed by others
References
Tang, D. M. and Dowell, E. H., ‘Flutter and stall response of a helicopter blade with structural nonlinearity’, Journal of Aircraft 29, 1992, 953–960.
Tang, D. M. and Dowell, E. H., ‘Comparison of theory and experiment for non-linear flutter and stall response of a helicopter blade’, Journal of Sound and Vibration 165, 1993, 251–276.
Conner, M. D., Tang, D. M., Dowell, E. H., and Virgin, L. N., ‘Nonlinear behavior of a typical wing section with control surface freeplay: A numerical and experimental study’, Journal of Fluids and Structures 11, 1997, 89–109.
Price, S. J., Alighanbari, H., and Lee, B. H. K., ‘Postinstability behavior of a two-dimensional airfoil with a structural nonlinearity’, Journal of Aircraft 31, 1994, 1395–1401.
Price, S. J., Alighanbari, H., and Lee, B. H. K., ‘The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities’, Journal of Fluids and Structures 9, 1995, 175–193.
Lee, B. H. K. and LeBlanc, P., ‘Flutter analysis of a two-dimensional airfoil with cubic nonlinear restoring force’, National Aeronautical Establishment, Aeronautical Note 36, National Research Council (Canada) No. 25438, Ottawa, Canada, 1986.
Zhao, L. C. and Yang, Z. C., ‘Chaotic motions of an airfoil with non-linear stiffness in incompressible flow’, Journal of Sound and Vibration 138, 1990, 245–254.
Chen, P., Sarhaddi, D., and Liu, D., ‘Limit-cycle-oscillation studies of a fighter with external stores’, AIAA Paper No. 98–1727, in Proceedings of the 39th AIAA Structures, Structural Dynamics and Materials Conference, Long Beach, CA, April 20–23, 1998, pp. 258–266.
Stearman, R. O., Powers, E. J., Schwartz, J., and Yurkovich, R., ‘Aeroelastic identification of advanced technology aircraft through higher order signal processing’, in Proceedings of the 9th International Modal Analysis Conference, Florence, Italy, April 15–18, 1991, pp. 1607–1616.
O'Neil, T. and Strganac, T. W., ‘Nonlinear aeroelastic response – Analyses and experiments’, AIAA Paper No. 96–0014, in AIAA 34th Aerospace Sciences Meeting & Exhibit, Reno, NV, January 15–18, 1996.
O'Neil, T., Gilliatt, H. C., and Strganac, T. W., ‘Investigations of aeroelastic response for a system with continuous structural nonlinearities’, AIAA Paper 96–1390, in Proceedings of the 37th AIAA Structures, Structural Dynamics, and Materials Conference, Salt Lake City, UT, April 15–17, 1996.
Ko, J., Kurdila, A. J., and Strganac, T. W., ‘Nonlinear control of a prototypical wing section with torsional nonlinearity’, Journal of Guidance, Control, and Dynamics 20, 1997, 1181–1189.
Block, J. J. and Strganac, T. W., ‘Applied active control for a nonlinear aeroelastic structure’, Journal of Guidance, Control, and Dynamics, 1998 (to appear).
Ko, J., Kurdila, A. J., and Strganac, T. W., ‘Stability and control of a structurally nonlinear aeroelastic system’, Journal of Guidance, Control, and Dynamics 21, 1998, 718–725.
Fung, Y. C., An Introduction to the Theory of Aeroelasticity, Wiley, New York, 1955.
Dowell, E. H. (ed.), A Modern Course in Aeroelasticity, Kluwer, Dordrecht, 1995.
Isidori, A., Nonlinear Control Systems, Springer-Verlag, New York, 1989.
Slotine, J. E. and Li, W., Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ, 1991.
Sastry, S. S. and Isidori, A., ‘Adaptive control of linearizable systems’, IEEE Transactions on Automatic Control 34, 1989, 1123–1131.
La Salle, J. and Lefschetz, S., Stability by Liapunov's Direct Method, Academic Press, New York, 1961.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ko, J., Strganac, T.W. & Kurdila, A.J. Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Nonlinearity. Nonlinear Dynamics 18, 289–301 (1999). https://doi.org/10.1023/A:1008323629064
Issue Date:
DOI: https://doi.org/10.1023/A:1008323629064