DOI QR코드

DOI QR Code

A Continuous Robust Control Strategy for the Active Aeroelastic Vibration Suppression of Supersonic Lifting Surfaces

  • Zhang, K. (Department of EECS at the University of Central Florida) ;
  • Wang, Z. (Department of EECS at the University of Central Florida) ;
  • Behal, A. (Department of EECS and NanoScience Technology Center at the University of Central Florida) ;
  • Marzocca, P. (Mechanical and Aeronautical Engineering at Clarkson University)
  • Received : 2012.03.19
  • Accepted : 2012.04.16
  • Published : 2012.06.30

Abstract

The model-free control of aeroelastic vibrations of a non-linear 2-D wing-flap system operating in supersonic flight speed regimes is discussed in this paper. A novel continuous robust controller design yields asymptotically stable vibration suppression in both the pitching and plunging degrees of freedom using the flap deflection as a control input. The controller also ensures that all system states remain bounded at all times during closed-loop operation. A Lyapunov method is used to obtain the global asymptotic stability result. The unsteady aerodynamic load is considered by resourcing to the non-linear Piston Theory Aerodynamics (PTA) modified to account for the effect of the flap deflection. Simulation results demonstrate the performance of the robust control strategy in suppressing dynamic aeroelastic instabilities, such as non-linear flutter and limit cycle oscillations.

Keywords

References

  1. Librescu, L., Marzocca, P., and Silva, W.A., "Supersonic/ Hypersonic Flutter and Post-flutter of Geometrically Imperfect Circular Cylindrical Panels", Journal of Spacecraft and Rockets, Vol. 39, No. 5, 2002, pp. 802-812. https://doi.org/10.2514/2.3882
  2. Mukhopadhyay, V., "Benchmark Active Control Technology", Journal of Guidance, Control, and Dynamics, Part I 23 (2000) 913-960.
  3. Mukhopadhyay, V., "Benchmark Active Control Technology", Journal of Guidance, Control, and Dynamics, Part II 23 (2000) 1093-1139. https://doi.org/10.2514/2.4659
  4. Mukhopadhyay, V., "Benchmark Active Control Technology", Journal of Guidance, Control, and Dynamics, Part III 24 (2001) 146-192. https://doi.org/10.2514/2.4693
  5. Marzocca, P., Librescu L.,Silva W.A., "Flutter, Postflutter and Control of a Supersonic 2-D Lifting Surface", Journal of Guidance, Control, and Dynamics, vol. 25, no. 5, pp. 962-970, September - October 2002. https://doi.org/10.2514/2.4970
  6. Breitbach, E.J., Effects of Structural Non-linearities on Aircraft Vibration and Flutter, AGARD TR-665, North Atlantic Treaty Organization, Neuilly sur Seine, France, 1978.
  7. Librescu, L., "Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures", Aeroelastic Stability of Anisotropic Multilayered Thin Panels, 1st ed., Book series, edited by Leipholz, H., Noordhoff International Publishing, Leyden, The Netherlands, 1975, Chapter 1, pp. 53-63, 106-158, Appendix A, pp. 543-550.
  8. Dowell, E.H., and Ilgamov, M., Studies in non-linear Aeroelasticity, 1st ed., Springer-Verlag, New York, 1988, Chapter 2, pp. 29-63, Chapter 6, pp. 206-277.
  9. Librescu, L., "Aeroelastic Stability of Orthotropic Heterogeneous Thin Panels in the Vicinity of the Flutter Critical Boundary, Part One: Simply supported panels", Journal de Mecanique, Part I, vol. 4, no. 1, pp. 51-76, 1965.
  10. Librescu, L., Aeroelastic Stability of Orthotropic Heterogeneous Thin Panels in the Vicinity of the Flutter Critical Boundary, Part Two Journal de Mecanique, Part II, vol. 6, no. 1, pp. 133-152, 1967.
  11. Pak, C., Friedmann, P.P, and Livne, E., "Digital Adaptive Flutter Suppression and Simulation Using Approximate Transonic Aerodynamics", Journal of Vibration and Control, vol. 1, no. 4, Nov. 1995, pp. 363-388. https://doi.org/10.1177/107754639500100401
  12. Ko., J., Strganac, T.W., and Kurdila, A.J., "Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Non-linearity", Non-linear Dynamics, vol. 18 pp. 289-301, 1999. https://doi.org/10.1023/A:1008323629064
  13. Xing, W. and Singh, S.N., "Adaptive Output Feedback Control of a Non-linear Aeroelastic Structure", J. Guidance, Control and Dynamics, vol. 23, no. 6, pp. 1109-1116, 2000. https://doi.org/10.2514/2.4662
  14. Zhang, R. and Singh, S.N., "Adaptive Output Feedback Control of an Aeroelastic System with Unstructured Uncertainties", J. Guidance, Control, and Dynamics, vol. no. 3, pp. 502-509, 2001.
  15. Singh, S.N. and Wang, L., "Output Feedback form and Adaptive Stabilization of a Non-linear Aeroelastic System", J. Guidance, Control and Dynamics, vol. 25, no. 4, pp. 725-732, 2002. https://doi.org/10.2514/2.4939
  16. Behal, A., Marzocca, P., Rao V.M., Gnann, A., "Nonlinear adaptive Model Free Control of an Aeroelastic 2-D Lifting Surface", Journal of Guidance, Control and Dynamics, 29(2), pp. 382-390, March-April 2006. https://doi.org/10.2514/1.14011
  17. Behal, A., Rao, V. M., Marzocca, P., and Kamaludeen, M., "Adaptive Control for a Nonlinear Wing Section with Multiple Flaps", Journal of Guidance, Control, and Dynamics, vol. 29, no. 3, pp. 744-749, May-June 2006. https://doi.org/10.2514/1.18182
  18. Reddy, K.K., Chen, J., Behal, A., and Marzocca, P., "Multi-Input/Multi-Output Adaptive Output Feedback Control Design for Aeroelastic Vibration Suppression", Journal of Guidance, Control, and Dynamics, vol. 30, no. 4, pp. 1040-1048, July-August 2007. https://doi.org/10.2514/1.27684
  19. Wang, Z., Behal, A., and Marzocca, P., "Adaptive and Robust Aeroelastic Control of Nonlinear Lifting Surfaces with Single/Multiple Control Surfaces: A Review", International Journal of Aeronautical and Space Science, vol. 11, no. 4, pp. 285-302, December 2010. https://doi.org/10.5139/IJASS.2010.11.4.285
  20. Wang, Z., Behal, A., and Marzocca, P., "Robust Adaptive Output Feedback Control Design for a MIMO Aeroelastic System", International Journal of Aeronautical and Space Science, vol. 12, no. 2, pp. 157-167, June 2011.
  21. Zeng, J., Wang, J., de Callafon, R., and Brenner, M., "Suppression of the Aeroelastic/Aeroservoelastic Interaction Using Adaptive Feedback Control Instead of Notching Filters", AIAA Atmospheric Flight Mechanics Conference, Portland, OR, 2011.
  22. Wang, Z., Behal, A., and Marzocca, P., "Continuous Robust Control for Two-Dimensional Airfoils with Leadingand Trailing-Edge Flaps", Journal of Guidance, Control, and Dynamics, vol. 35, no. 2, pp. 510-519, March-April 2012. https://doi.org/10.2514/1.54347
  23. Zhang, F. and Söffker, D., "Quadratic Stabilization of a Nonlinear Aeroelastic System Using a Novel Neural-Networkbased controller", Science China Technological Sciences, vol. 54, no. 5, pp. 1126-1133, May 2011. https://doi.org/10.1007/s11431-011-4346-8
  24. Wang, Z., Behal, A., Marzocca, P., "Model-Free Control Design for MIMO Aeroelastic System Subject to External Disturbance", J. of Guidance Control and Dynamics, vol. 34, pp. 446-458, 2011. https://doi.org/10.2514/1.51403
  25. Rao, V. M., Behal, A., Marzocca, P., Rubillo, C.M., "Adaptive aeroelastic Vibration Suppression of a Supersonic Airfoil with Flap", J. Aerospace Science and Technology, vol. 10, Issue 4, pp. 309--315, May 2006. https://doi.org/10.1016/j.ast.2006.03.006
  26. Zhang, X., Behal, A., Dawson, D.M., and Xian, B., "Output Feedback Control for a Class of Uncertain MIMO Nonlinear Systems With Non-Symmetric Input Gain Matrix", in Proc. of IEEE Conference on Decision and Control, Seville, Spain, pp. 7762-7767, 2005.
  27. Chen, J., Behal, A., and Dawson, D.M, "Robust Feedback Control for a Class of Uncertain MIMO Nonlinear Systems", IEEE Transactions on Automatic Control, vol. 53, no. 2, pp. 591-596, Mar. 2008. https://doi.org/10.1109/TAC.2008.916658
  28. Xian, B., Dawson, D. M., "de Queiroz, M. S., and Chen, J., A Continuous Asymptotic Tracking Control Strategy for Uncertain Nonlinear Systems", IEEE Transactions on Automatic Control, vol. 49, no. 7, Jul. 2004, pp. 1206-1211. https://doi.org/10.1109/TAC.2004.831148
  29. Ashley, H. and Zartarian, G., "Piston Theory - A New Aerodynamic Tool for the Aeroelastician", Journal of the Aerospace Sciences, vol. 23, no. 10, 1956, pp. 1109-1118.
  30. Lighthill, M.J., "Oscillating Airfoils at High Mach Numbers", Journal of Aeronautical Science, vol. 20, no. 6, 1953, pp. 402-406. https://doi.org/10.2514/8.2657
  31. Liu, D.D., Yao, Z.X., Sarhaddi, D., and Chavez, F.R., "From Piston Theory to a Unified Hypersonic-Supersonic Lifting Surface Method", Journal of Aircraft, vol. 34, no. 3, pp. 304-312, 1997. https://doi.org/10.2514/2.2199
  32. Rodden, W.P., Farkas, E.F., Malcom, H.A., and Kliszewski, A.M., Aerodynamic Influence Coefficients from Piston Theory: Analytical Development and Computational Procedure, Aerospace Corporation, TDR-169 (3230-11) TN-2, 1962.
  33. Librescu, L., Chiocchia, G., Marzocca, P., "Implications of Cubic Physical/Aerodynamic Nonlinearities on the Character of the Flutter Instability Boundary", International Journal of Nonlinear Mechanics, 38, pp. 173-199, March 2003. https://doi.org/10.1016/S0020-7462(01)00054-3
  34. Thuruthimattam, B.J., Friedmann, P.P., McNamara, J.J., and Powell, K.G., "Aeroelasticity of a Generic Hypersonic Vehicle", 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper no. 2002-1209, April 2002.
  35. Hornik, K., Stinchombe, M. and White, H., "Multilayer Feedforward Networks are Universal Approximators", J. Neural Networks, vol. 2, pp. 359-366, March 1989. https://doi.org/10.1016/0893-6080(89)90020-8
  36. Krstic, M., Kanellakopoulos, I., and Kokotovic, P., Nonlinear and Adaptive Control Design, John Wiley & Sons, New York, 1995.

Cited by

  1. Sliding mode-based continuous guidance law with terminal angle constraint vol.120, pp.1229, 2016, https://doi.org/10.1017/aer.2016.50
  2. ℒ1 adaptive control of an aeroelastic system with unsteady aerodynamics and gust load vol.24, pp.2, 2018, https://doi.org/10.1177/1077546316640407
  3. Robust output feedback control for aeroelastic vibration suppression of a 2-DOF airfoil under quasi-steady flow 2017, https://doi.org/10.1177/1077546317731209
  4. Continuous robust control for aeroelastic vibration control of a 2-D airfoil under unsteady flow vol.22, pp.12, 2016, https://doi.org/10.1177/1077546314554821
  5. Robust Higher-Order Sliding-Mode Finite-Time Control of Aeroelastic Systems vol.37, pp.5, 2014, https://doi.org/10.2514/1.G000456
  6. Adaptive Control of Multi-Input Aeroelastic System with Constrained Inputs vol.38, pp.12, 2015, https://doi.org/10.2514/1.G001022
  7. Robust Switching Control and Subspace Identification for Flutter of Flexible Wing vol.2018, pp.1875-9203, 2018, https://doi.org/10.1155/2018/9734684