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Limit-cycle taming by nonlinear controlwith applications to flutter

Published online by Cambridge University Press:  04 July 2016

F. Mastroddi  and
L. Morino
F. Mastroddi
Affiliation:
University of Rome La Sapienza, Rome, Italy
L. Morino
Affiliation:
University of Rome III, Rome, Italy
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Abstract

This paper addresses the problem of limit-cycle taming,which is defined in this paper as the use ofnonlinear control laws to ensure that thelimit-cycle behaviour of the system beyond thestability boundary is of a benign rather than adestructive nature. Specifically, we consider aone-parameter (denoted by λ) autonomous dynamicsystem having algebraic nonlinearities. We assumethat the system has a stable solution, x = 0, for λ< λ0, and experiences a Hopfbifurcation at λ = λ0. Using a singularperturbation analysis about the stability boundary,it is shown that, using a simple nonlinear controllaw, limit-cycle taming is always possible in theneighbourhood of a Hopf bifurcation. The controlsystem proposed for limit-cycle taming is fullynonlinear, and therefore does not affect the linearbehaviour of the system (in particular its stabilitycharacteristics). Hence, limit-cycle taming may beused in conjunction with a standard linear activecontrol (e.g. use of linear active control toincrease the stability boundary). Applications ofthe theory to the problem of flutter arepresented.

Information

Type
Research Article
Information
The Aeronautical Journal , Volume 100 , Issue 999 , November 1996 , pp. 389 - 396
Copyright
Copyright © Royal Aeronautical Society 1996 

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Footnotes

†

Assistant Professor, Dipartimento Aerospaziale,via Eudossiana 16, 00184 Roma

‡

Professor, Dipartimento di Meccanica eAutomatica, via C. Segre 60, 00146 Roma

References

1. Guckenheimer, J. and Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Field, Springer Verlag, New York, 1983.Google Scholar
2. Morino, L. A Perturbation method for treating nonlinear panel flutter problems, AIM J, 1969, 7, pp 405–411.Google Scholar
3. Smith, L. L. and Morino, L. Stability analysis of nonlinear differential autonomous system with applications to flutter, AIM J, 1976, 14, pp 333–341.Google Scholar
4. Sandri, G. The foundations of nonequilibrium statistical mechanics, I, Ann of Physc, October 1963, 24, pp 332–379.Google Scholar
5. Frieman, E.A. J Maths Phys, 1963, 4, pp 410.Google Scholar
6. Nayfeh, J. A. A perturbation method for treating nonlinear oscillation problems, J Maths Phys, 1965, 64, pp 368–374.Google Scholar
7. Nayfeh, A.H. and Mook, D.Y. Nonlinear Oscillations, Wiley, New York, 1979.Google Scholar
8. Nayfeh, A.H. and Balachandran, B. Applied Nonlinear Dynamics, John Wiley & Sons New York, 1995.Google Scholar
9. Morino, L. Flutter taming - a new tool for aeroelastic designer, AFOSR-83-0163, CCAD-TR-84-01, Department of Aerospace and Mechanical Engineering, Boston University, Boston, 1984.Google Scholar
10. Abed, E.H. and Fu, J.-H. Local feedback stabilization and bifurcation control. I. Hopf bifurcation, Syst Cntl Lett, 1986, 7, pp 11–17.Google Scholar
11. Abed, E.H. and Fu, J.-H. Local feedback stabilization and bifurcation control. II. Stationary bifurcation, Syst Cntl Lett, 1987, 8, pp 467–473.Google Scholar
12. Mastroddi, F. Aeroservoelasticita: problematiche nonlineari, Tesidi Dottorato di Ricerca, Aerospace Department, Universita degli Studi di Roma La Sapienza, Rome, Italy, 1994.Google Scholar
13. Friedland, B. Control Systems Design - An Introduction to Space State Methods, Me Graw-Hill, New York, NY, 1986.Google Scholar
14. Cole, J. and Kevorkian, J. Uniformly valid asymptotic approximation for certain nonlinear differential equation, Nonlinear Differential Equation in Nonlinear Mechanics, Academic Press, New York, 1963, 9, pp 113–120.Google Scholar
15. Morino, M., Mastroddi, F. and Cutroni, M. Lie transformation method for dynamical system having chaotic behaviour, Nonlinear Dyn, June 1995, 7, (4), pp 403–428.Google Scholar
16. Morino, L. and Kuo, C.C. Detailed Extension of Perturbation Method for Panel Flutter, ASRL TR-164-2, Aeroelastic and Structures Research Lab, Department of Aeronautics and Astronautics, Massachussetts Institute of Technology, Cambridge, Massachussetts, March 1971.Google Scholar
17. Morino, L., Mastroddi, F., De troia, R. and Pecora, M. On finite-state aerodynamic modeling with applications to aeroservoelasticity, Proceedings of international Forum on Aeroelasticity and Structural Dynamics, Strasbourg, Francia, 24-26 May 1993, pp 97–116.Google Scholar
18. Morino, M., Mastroddi, F., De troia, R., Ghiringhelli, G.L. and Mantegazza, P. Matrix fraction approach for finite-state aerodynamic modeling, AIAA J, April 1995, 33, (4) pp 703–711.Google Scholar
19. Morino, L., Mastroddi, F. and De troia, R. Instability taming by nonlinear control with application to flutter, proceedings of the XII conferenza AIDAA, Como, Italy, July 1993, pp 1035–1046.Google Scholar