Skip to main content
Log in

Advances in the linear/nonlinear control of aeroelastic structural systems

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

Active aeroelastic control is a recently emerging technology aimed at providing solutions to a large class of problems involving the aeronautical/aerospace flight vehicle structures that are prone to instability and catastrophic failures, and to oscillations that can yield structural failure by fatigue. In order to prevent such damaging phenomena to occur, the linear/nonlinear aeroelastic control technology should be applied. Its goals are among others: (i) to alleviate and even suppress the vibrations appearing in the subcritical flight speed range, (ii) to enlarge the flight envelope by increasing the flutter speed, and (iii) to enhance the post-flutter behavior by converting the unstable limit cycle oscillation to a stable one. A short review of the available control techniques and capabilities is presented first. Attention is focused on the open/closed-loop of 2D and 3D lifting surfaces as well as on panels exposed to supersonic flowfields. A number of concepts involving various control methodologies, such as proportional, velocity, linear quadratic regulator, modified bang-bang, sliding mode observer, time-delay control, fuzzy, etc., as well as results obtained with such controls are presented. Emphasis is placed on theoretical and numerical results obtained with the various control strategies that are considered in a comparative way. Finally, conclusions and directions for further work are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. Mukhopadhyay (1995) ArticleTitleFlutter suppression control law design and testing for the active flexible wing J Aircraft (Special Adaptive Flexible Wing Issue) 32 45–51

    Google Scholar 

  2. V. Mukhopadhyay (2003) ArticleTitleHistorical perspective on analysis and control of aeroelastic responses J. Guidance Control Dyn. 26 673–684

    Google Scholar 

  3. Librescu, L, Na, S. S., Marzocca, P., Chung, C.-H., Jeong, I.-J.: Active aeroelastic control of 2- D wing-flap systems in a compressible/incompressible flow field and exposed to blast pulses IMECE 2003-43392. In: Proc. 2003 ASME Int. Mechanical Engineering Congress and Exposition, Washington, D.C, pp. 15–21, November 2003

  4. L. Librescu S. S. Na P. Marzocca C. Chung M. Kwak (2005) ArticleTitleActive aeroelastic control of 2D wing flap systems operating in an incompressible flowfield and impacted by a blast pulse J. Sound Vibr. 83 685–706 Occurrence Handle10.1016/j.jsv.2004.05.010

    Article  Google Scholar 

  5. R. C. Scott S. T. Hoadley C. D. Wieseman M. H. Durham (2001) ArticleTitleBenchmark active controls technology model aerodynamic data J. Guidance Control Dyn. 23 914–921

    Google Scholar 

  6. J. Block T. M. Strganac (1998) ArticleTitleApplied active control for a nonlinear aeroelastic structure J. Guidance Control Dyn. 21 838–845

    Google Scholar 

  7. J. Ko A. J. Kurdila T. W. Strganac (1997) ArticleTitleNonlinear control of a prototypical wing section with torsional nonlinearity J. Guidance Control Dyn. 20 1181–1189

    Google Scholar 

  8. Ko, J., Kurdila, A. J., Strganac, T. W.: Nonlinear adaptive control of an aeroelastic system via geometric methods. AIAA Paper 98-1795. In: Proc. 39th AIAA/ASME/ASCE/AHS/ACS Structures, Structural Dynamics and Materials Conf., Long Beach, CA, April 1998

  9. T. W. Strganac J. Ko D. E. Thompson A. J. Kurdila (2000) ArticleTitleIdentification and control of limit cycles oscillations in aeroelastic systems J. Guidance Control Dyn. 23 1127–1133

    Google Scholar 

  10. P. Marzocca L. Librescu W. A. Silva (2002) ArticleTitleFlutter, post-flutter and control of a supersonic 2-D lifting surface J. Guidance Control Dyn. 25 962–970

    Google Scholar 

  11. Y. Yuan P. Yu L. Librescu P. Marzocca (2004) ArticleTitleAeroelasticity of time-delayed feedback control of two-dimensional supersonic lifting surfaces J. Guidance Control Dyn. 27 795–803

    Google Scholar 

  12. P. Marzocca L. Librescu W. A. Silva (2004) ArticleTitleTime-delay effects on linear/nonlinear feedback control of simple aeroelastic systems J. Guidance Control Dyn. 28 53–62

    Google Scholar 

  13. Marzocca, P., Librescu, L., Silva, W. A.: Open/closed-loop nonlinear aeroelasticity for airfoils via Volterra series approach. AIAA Paper 2002-1484. In: Proc. 43rd AIAA/ASME/ASCE/AHS/ ASC Structures, Structural Dynamics and Materials Conf., Denver, CO, April 2002. Also appeared as J. Fluids Struct. 20, 197–215 (2005)

  14. Librescu, L., Marzocca, P., Silva, W. A.: Time-delay feedback aeroelastic control of 2-D lifting surfaces. IMECE 2002-32971. In: Proc. 5th Int. Symp. on Fluid-structure Interaction, Aeroelasticity, Flow-induced Vibration and Noise 2002 ASME Int. Mechanical Engineering Congress and Exposition, New Orleans, LA, November 2002 (also appeared as J. Fluids Struct 20, 197–215, 2005)

  15. Marzocca, P., Librescu, L., Silva, W. A.: Nonlinear time-delayed feedback control of aeroelastic systems: a functional approach. AIAA Paper 2003-1867. In: Proc 44th AIAA/ASME/ ASCE/ ASC Structures, Structural Dynamics and Materials Conf., Norfolk, VA, April 2003

  16. Yuan, Y., Yu, P., Librescu, L., Marzocca, P.: Analysis of a 2D supersonic lifting surface with time-delayed feedback control. AIAA Paper 2003-1733. In: Proc. 44th AIAA/ASME/ASCE/ ASC Structures, Structural Dynamics and Materials Conf., Norfolk, VA, April 2003

  17. M. Ramesh S. Narayanan (2001) ArticleTitleControlling chaotic motions in a two-dimensional airfoil using time-delayed feedback J. Sound Vibr. 239 1037–1049 Occurrence Handle10.1006/jsvi.2000.3181

    Article  Google Scholar 

  18. W. Xing S. N. Singh (2000) ArticleTitleAdaptive output feedback control of a nonlinear aeroelastic structure J. Guidance Control Dyn. 23 1109–1116

    Google Scholar 

  19. R. Zhang S. N. Singh (2001) ArticleTitleAdaptive output feedback control of an aeroelastic system with unstructured uncertainties J. Guidance Control Dyn. 24 502–509

    Google Scholar 

  20. H. Özbay G. R. Bachmann (1994) ArticleTitleController design for a two-dimensional thin airfoil flutter suppression J. Guidance Control Dyn. 17 722–728

    Google Scholar 

  21. Gern, F.H., Librescu, L. Synergistic interaction of aeroelastic tailoring and boundary moment control on aircraft wing flutter, NASA/CP 1999 209136/PT2, 719 733. In: Proc. CEAS/AIAA/ ICASE/NASA Int. Forum on Aeroelasticity and Structural Dynamics, June 1999

  22. L. Librescu L. Meirovitch O. Song (1996) ArticleTitleRefined structural modeling for enhancing vibrations and aeroelastic characteristics of composite aircraft wings La Recherche Aérospatiale 1 23–35

    Google Scholar 

  23. L. Librescu L. Meirovitch O. Song (1996) ArticleTitleIntegrated structural tailoring and control using adaptive materials for advanced aircraft wings J. Aircraft 33 203–213

    Google Scholar 

  24. Librescu, L, Na, S. S., Marzocca, P., Chung, C., Kwak, M. K.: Flutter instability and aeroelastic response of aircraft wing section with a flap in an incompressible flow. IMECE 2002-32983. In: Proc. 5th Int. Symp. on Fluid-structure Interaction, Aeroelasticity, Flow-induced Vibration and Noise, 2002 ASME Int. Mechanical Engineering Congress and Exposition, 17–22 November 2002, New Orleans, LA

  25. Librescu, L. Na, S. S., Marzocca, P., Chung, C., Kwak, M. K.: Active aeroelastic control of 2-D wing-flap systems in an incompressible flowfield. AIAA Paper 2003-1414. In: Proc. 44th AIAA/ ASE/ASCE/ASC Structures, Structural Dynamics and Materials Conf., Norfolk, VA., April 7–10, 2003

  26. Na, S.S., Librescu, L., Marzocca, P., Chung, C.: Aeroelastic response of flapped wing system using robust control methodology. AIAA Paper 2004-1673. In: Proc. 45th AIAA/ASME/ ASCE/ASC Structures, Structural Dynamics and Materials Conf., Palm Springs, CA, 19–22 April 2004

  27. Heeg, J., Scott, R. C., McGowan, A. M. R.: Aeroelastic research: using smart structures concepts, aeroelasticity and fluid structure interaction problems. In: Friedmann P.P., Chang J.C.I. (ed). AD-44. American Society of Mechanical Engineers, New York, pp. 161–173, 1994

  28. McGowan, A. M. R., Washburn, A. E., Horta, L. G., Bryant, R. G., Cox, D. E., Siochi, E. J., Padula, S. L., Holloway, N. M.: Recent results from NASA’s morphing project. In: Proc. 9th Int Symp. on Smart Structures and Materials, Society of Photo Optical Instrumentation Engineers, San Diego, CA, Paper 4698-11, March 2002

  29. Olds, S.D.: Modeling and LQR control of a two-dimensional airfoil. MS thesis, Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, April 1997

  30. York, D. L.: Analysis of flutter and flutter suppression via an energy method. MS Thesis, Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, May 1980

  31. D. J. Inman (2000) ArticleTitleActive modal control for smart structures Phil. Trans. Math. Phys. Engng. Sci. 359 205–219 Occurrence Handle10.1098/rsta.2000.0721

    Article  Google Scholar 

  32. M. Tadi (2003) ArticleTitleState dependent Riccati equation for control of aeroelastic flutter J. Guidance Control Dyn. 26 914–917

    Google Scholar 

  33. Djayapertapa, L., Allen, C.B.: Numerical simulation of active control of transonic flutter. In: Proc. 23rd ICAS Congress, Toronto, 411.1–411.10, 2002

  34. D. M. Guillot P. P. Friedmann (2000) ArticleTitleFundamental aeroservoelastic study combining unsteady computational fluid mechanics with adaptive control J. Guidance Control Dyn. 23 1117–1126

    Google Scholar 

  35. P. Friedmann D. Guillot E. Presente (1997) ArticleTitleAdaptive control of aeroelastic instabilities in transonic flow and its scaling J. Guidance Control Dyn. 20 1190–1199

    Google Scholar 

  36. S. Chiu S. Chand D. Moore A. Chaudhury (1991) ArticleTitleFuzzy logic for control of roll and moment for a flexible wing aircraft IEEE Control Sys. Mag. 11 42–48 Occurrence Handle10.1109/37.88591

    Article  Google Scholar 

  37. T. A. Weisshaar R. J. Ryan (1986) ArticleTitleControl of aeroelastic instabilities through stiffness cross coupling J. Aircraft 23 148–154

    Google Scholar 

  38. Anderson, K. R., White, K., Neal, J.: Survey of active aeroelastic control for flutter suppression Paper IMECE2004-60458 Proc. IMECE2004: 2004 ASME Int. Mechanical Engineering Congress and RD&D Expo, Anaheim, CA, November 13–19, 2004

  39. McGowan, A. M. R.: An examination of applying shunted piezoelectrics to reduce aeroelastic response. NASA LaRC, May 2003; available at http://techreports.larc.nasa.gov/ltrs/PDF/1999/ mtg/NASA-99-ceas-arm.pdf

  40. Librescu, L., Marzocca, P.: Flutter and post-flutter control of geometrically nonlinear panels operating in a supersonic / hypersonic flow field. IMECE2004-61373: Proc. IMECE2004, 2004 ASME Int. Mechanical Engineering Congress and Exposition, Session: AMD-10 B Multi-field Coupling in Dynamic Systems and Control, Anaheim, CA, November 13–19, 2004

  41. P. Marzocca L. Librescu G. Chiocchia (2001) ArticleTitleAeroelastic response of a 2D lifting surfaces to gust and arbitrary explosive loading signatures Int. J. Impact Engng. 25 41–65 Occurrence Handle10.1016/S0734-743X(00)00033-6

    Article  Google Scholar 

  42. R. H. Scanlan R. Rosenbaum (1951) Introduction to the study of aircraft vibration and flutter Macmillan New York

    Google Scholar 

  43. E. H. Dowell (1978) A modern course in aeroelasticity Sijthoff and Noordhoff The Netherlands

    Google Scholar 

  44. R. L. Bisplinghoff H. Ashley R. L. Halfman (1996) Aeroelasticity Dover New York

    Google Scholar 

  45. P. Marzocca L. Librescu W. A. Silva (2002) ArticleTitleAeroelastic response of nonlinear wing section by functional series technique AIAA J. 40 813–824

    Google Scholar 

  46. V. V. Bolotin (1963) Nonconservative problems of the theory of elastic stability Macmillan New York 274–312

    Google Scholar 

  47. Librescu, L.: Aeroelastic stability of orthotropic heterogeneous thin panels in the vicinity of the flutter critical boundary. J. Mécanique 4, 51–76 (1965) (Part I); 6, 133–152 (1967) (Part II)

    Google Scholar 

  48. L. Librescu (1975) Elastostatics and kinetics of anisotropic and heterogeneous shell-type structures, aeroelastic stability of anisotropic multilayered thin panels Noordhoff Leyden 106–158

    Google Scholar 

  49. E. H. Dowell (Eds) (1974) Aeroelasticity of plates and shells Kluwer Dordrecht

    Google Scholar 

  50. P. Friedmann M. Hanin (1968) ArticleTitleSupersonic nonlinear flutter of orthotropic or isotropic panels with arbitrary flow direction Israel J. Technol. 6 46–57

    Google Scholar 

  51. B. H. K. Lee S. J. Price Y. S. Wong (1999) ArticleTitleNonlinear aeroelastic analysis of airfoils: bifurcation and chaos Progr. Aerosp. Sci. 35 205–334 Occurrence Handle10.1016/S0376-0421(98)00015-3

    Article  Google Scholar 

  52. I. Lee S. H. Kim (1995) ArticleTitleAeroelastic analysis of a flexible control surface with structural nonlinearity J. Aircraft 32 868–874

    Google Scholar 

  53. C. Mei (1977) ArticleTitleA finite element approach of nonlinear panel flutter AIAA J. 15 1107–1110

    Google Scholar 

  54. L. Morino (1969) ArticleTitleA perturbation method for treating nonlinear panel flutter problems AIAA J. 7 405–411

    Google Scholar 

  55. F Mastroddi L. Morino (1996) ArticleTitleLimit-cycle taming by nonlinear control with application to flutter Aeronaut J. 100 389–396

    Google Scholar 

  56. Hopf, E.: Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems (Bifurcation of a periodic solution from a stationary solution of a system of differential equations.) Ber. Math. Phys. Klasse der sächsischen Akad. Wiss. (Leipzig) 94, 3–32 (1942).

  57. P. J. Holmes (1977) ArticleTitleBifurcations to divergence and flutter in flow-induced oscillations: a finitedimensional analysis J. Sound Vibr. 53 471–503 Occurrence Handle10.1016/0022-460X(77)90521-1

    Article  Google Scholar 

  58. J. Guckenheimer P. Holmes (1986) Nonlinear oscillations, dynamical systems, and bifurcations of vector field Springer New York

    Google Scholar 

  59. L. Librescu (1981) On the effect of physical nonlinearities in the aeroelastic stability problem of supersonic panels J. Hult J. Lemaitre (Eds) Physical nonlinearities in structural analysis Springer Berlin 156–159

    Google Scholar 

  60. L. Librescu G. Chiocchia P. Marzocca (2003) ArticleTitleImplications of cubic physical / aerodynamic nonlinearities on the character of the flutter instability boundary Int. J. Non-Linear Mech. 38 173–199 Occurrence Handle10.1016/S0020-7462(01)00054-3

    Article  Google Scholar 

  61. Breitbach, E. J.: Effects of structural nonlinearities on aircraft vibration and flutter. AGARD TR 665 (1977), and In: Proc. 34th Structures and Materials AGARD Panel Meeting, Voss, Norway, AGARD Report 554 (1977).

  62. L. Librescu P. Marzocca W. A. Silva (2002) ArticleTitleSupersonic/hypersonic flutter and postflutter of geometrically imperfect circular cylindrical panels J. Spacecraft Rockets 39 802–812

    Google Scholar 

  63. N. K. Chandiramani L. Librescu R. Plaut (1996) ArticleTitleFlutter of geometrically imperfect sheardeformable laminated flat panels using nonlinear aerodynamics J. Sound Vibr. 192 79–100 Occurrence Handle10.1006/jsvi.1996.0177

    Article  Google Scholar 

  64. O. O. Bendiksen (2004) ArticleTitleModern developments in computational aeroelasticity Proc. I MECH E Part G, J. Aerospace Engng. 218 157–177

    Google Scholar 

  65. P. P. Friedmann (1999) ArticleTitleRenaissance of aeroelasticity and its future J. Aircraft 36 105–121

    Google Scholar 

  66. E. Livne (2003) ArticleTitleFuture of airplane aeroelasticity J. Aircraft 40 1066–1092

    Google Scholar 

  67. E. Dowell J. Edwards T. Strganac (2003) ArticleTitleNonlinear aeroelasticity J. Aircraft 40 857–874

    Google Scholar 

  68. R. Lind M. Brenner (1999) Robust aeroservoelastic stability analysis Springer London

    Google Scholar 

  69. J. M. Barker G. J. Balas (2000) ArticleTitleComparing linear parameter-varying gain-scheduled control techniques for active flutter suppression J. Guidance Control Dyn. 23 948–955

    Google Scholar 

  70. R. C. Scott L. E. Pado (2000) ArticleTitleActive control of wind-tunnel model aeroelastic response using neural networks J. Guidance Control Dyn. 23 1100–1108

    Google Scholar 

  71. S. S. Na L. Librescu (2000) ArticleTitleOptimal vibration control of thin walled anisotropic cantilevers exposed to blast loading J. Guidance Control Dyn. 23 491–500

    Google Scholar 

  72. S. S. Na L. Librescu (2000) ArticleTitleOptimal dynamic response control of adaptive thin walled cantilevers carrying heavy stores and exposed to blast pulses J. Intell. Mater. Struct. 11 703–712 Occurrence Handle10.1177/104538900772663928

    Article  Google Scholar 

  73. S. S. Na L. Librescu (2002) ArticleTitleOptimal dynamic response control of elastically tailored nonuniform thin walled adaptive beams J. Aircraft 39 469–479

    Google Scholar 

  74. S. S. Na L. Librescu J. H. Shim (2004) ArticleTitleModified bang-bang vibration control applied to adaptive thin-walled beam cantilevers AIAA J. 42 1717–1721

    Google Scholar 

  75. J. C. Bruch SuffixJr. J. M. Sloss S. Adali I. S. Sadek (1999) ArticleTitleModified bang-bang piezoelectric control of vibrating beams J. Smart Mater. Struct. 8 647–653 Occurrence Handle10.1088/0964-1726/8/5/315

    Article  Google Scholar 

  76. Na, S., Park, C., Kim, M.-H., Librescu, L., Marzocca, P., Jeong, I.-J.: Aeroelastic response of flapped wing systems using multiobjective state feedback methodology. ICAST 2004, 15th Int Conf. on Adaptive Structures and Technologies, Bar Harbor, Maine, October 25–27, 2004.

  77. E. Albano W. P. Rodden (1969) ArticleTitleA doublet-lattice method for calculating lift distribution on oscillating surfaces in subsonic flows AIAA J. 7 279–285

    Google Scholar 

  78. Tobak, M.: On the use of the indicial function concept in the analysis of unsteady motion of wings and wing-tail combinations. NASA R-1188, 1954.

  79. Marzocca, P., Librescu, L., Kim, D.-H., Lee, I.: Linear/nonlinear unsteady aerodynamic modeling of 2-D lifting surfaces via a combined CDF/analytical approach. AIAA Paper 2003– 925, 44th AIAA/ASME/ASCE/ASC Structures, Structural Dynamics and Materials Conf., Norfolk, VA, April 7–10, 2003.

  80. Kim, D., Lee, I., Marzocca, P., Librescu, L.: Linear/nonlinear aeroelastic computation of 2-D lifting surfaces using a combined CFD/analytical approach. AIAA Paper 2004–1756, 45th AIAA/ASME/ ASCE/ASC Structures, Structural Dynamics and Materials Conf., Palm Springs, CA, 19–22 April 2004.

  81. Leishman, J. G.: Unsteady aerodynamics. In: Principles of helicopter aerodynamics, chap. 8, pp. 302–377. Cambridge: Cambridge University Press 2000.

  82. Marzocca, P., Librescu, L., Chiocchia, G.: Unsteady aerodynamics in various flight speed regimes for flutter/dynamic response analyses. AIAA Paper 2000–4299, Proc. 18th AIAA Applied Aerodynamic Conf., Denver, CO, August 14–17, 2000.

  83. P. Marzocca L. Librescu G. Chiocchia (2002) ArticleTitleAeroelastic response of a 2-D airfoil in compressible flight speed regimes exposed to blast loadings Aerosp. Sci. Technol. 6 259–272 Occurrence Handle10.1016/S1270-9638(02)01169-0

    Article  Google Scholar 

  84. Mazelsky, B., Drischler, J. A.: Numerical determination of indicial lift and moment functions for a two-dimensional sinking and pitching airfoil at Mach numbers 0.5 and 0.6. NACA-TN-2739, July 1952.

  85. Lomax, H.: Indicial aerodynamics, part II, chap. 6. AGARD Manual on Aeroelasticity, 1996.

  86. Marzocca, P., Librescu, L., Chiocchia, G.: Aeroelasticity of two-dimensional lifting surfaces via indicial function approach. Aeronaut. J. 147–153 (2002).

  87. Reisenthel, P. H.: Development of a nonlinear indicial model for maneuvering fighter aircraft AIAA Paper 96-0896, 34th Aerospace Sciences Meeting, Reno, NA, January 1996

  88. R. C. Nelson A. Pelletier (2003) ArticleTitleThe unsteady aerodynamics of slender wings and aircraft undergoing large amplitude maneuvers Progr. Aerosp. Sci. 39 185–248 Occurrence Handle10.1016/S0376-0421(02)00088-X

    Article  Google Scholar 

  89. J. Sitaraman J. D. Baeder (2004) ArticleTitleComputational-fluid-dynamics-based enhanced indicial aerodynamic models J. Aircraft 41 798–810

    Google Scholar 

  90. G. P. Guruswamy (1990) ArticleTitleUnsteady aerodynamic and aeroelastic calculations for wings using Euler equations AIAA J. 28 461–469

    Google Scholar 

  91. L. Librescu S. Na (2001) ArticleTitleActive vibration control of doubly tapered thin walled beams using piezoelectric actuation Thin Walled Struct. 39 65–82 Occurrence Handle10.1016/S0263-8231(00)00054-9

    Article  Google Scholar 

  92. Librescu, L., Na, S. S., Kim, S.: Comparative study on vibration control methodologies applied to adaptive anisotropic cantilevers. AIAA 2002-1539. In: Proc. 43rd AIAA/ASME/ASCE/ASC Structures, Structural Dynamics and Materials Conf., Denver, CO, 2002

  93. S. S. Na L. Librescu (1998) ArticleTitleOscillation control of cantilevers via smart materials technology and optimal feedback control: actuator location and power consumption issues J. Smart Mater Struct. 7 833–842 Occurrence Handle10.1088/0964-1726/7/6/011

    Article  Google Scholar 

  94. I. Chopra (2002) ArticleTitleReview of state of art of smart structures and integrated systems AIAA J. 40 2145–2187

    Google Scholar 

  95. E. F. Crawley (1994) ArticleTitleIntelligent structures for aerospace: a technology overview and assessment AIAA J. 31 1689–1699

    Google Scholar 

  96. E. F. Crawley T. DeLuis (1988) ArticleTitleUse of piezoelectric actuators as elements of intelligent structures AIAA J. 25 1373–1385

    Google Scholar 

  97. H. S. Tzou G. L. Anderson (Eds) (1992) Intelligent structural systems Kluwer Norwell, MA

    Google Scholar 

  98. H. S. Tzou (1993) Piezoelectric shells – distributed sensing and control of continuum Kluwer Dordrecht

    Google Scholar 

  99. A. Kugi K. Schlacher H. Irschik (1999) ArticleTitleInfinite dimensional control of nonlinear beam vibrations by piezoelectric actuator and sensor layers Nonlinear Dyn. 19 71–91 Occurrence Handle10.1023/A:1008393904114

    Article  Google Scholar 

  100. H. Irschik M. Krommer U. Pichler (2003) ArticleTitleDynamic shape control of beam type structures by piezoelectric actuation and sensing Int. J. Appl. Electromag. Mech. 17 251–258

    Google Scholar 

  101. J. C. Doyle G. Stein (1981) ArticleTitleMultivariable feedback design: concepts for a classical/modern synthesis IEEE Trans. Automatic Control 26 4–16 Occurrence Handle10.1109/TAC.1981.1102555

    Article  Google Scholar 

  102. M. G. Safonov A. J. Laub G. L. Hartmann (1981) ArticleTitleFeedback properties of multivariable systems: the role and use of the return difference matrix IEEE Trans. Automatic Control 26 47–65 Occurrence Handle10.1109/TAC.1981.1102566

    Article  Google Scholar 

  103. N. A. Lehtomaki N. S. Sandell SuffixJr. M. Athans (1981) ArticleTitleRobustness results in linear quadratic Gaussian based multivariable control designs IEEE Trans. Automatic Control 26 75–92 Occurrence Handle10.1109/TAC.1981.1102565

    Article  Google Scholar 

  104. M. J. Balas (1978) ArticleTitleFeedback control of flexible systems IEEE Trans. Automatic Control 23 673–679 Occurrence Handle10.1109/TAC.1978.1101798

    Article  Google Scholar 

  105. Edwards, C., Spurgeon, S.: Sliding mode control: theory and applications. Taylor & Francis 1998.

  106. M. H. Kim D. J. Inman (2001) ArticleTitleReduction of observation spillover in vibration suppression using a sliding mode observer J. Vibr. Contr. 7 1087–1105

    Google Scholar 

  107. Na, S. S., Librescu, L., Marzocca, P., Kim, M.-H., Jeong, I.-J., Chung, C.: Aeroelastic response of flapped wing systems using robust estimation control methodology. J. Guidance Control Dyn. (in press)

  108. H. Y. Hu E. H. Dowell L. N. Virgin (1998) ArticleTitleStability estimation of high dimensional vibrating systems under state delay feedback control J. Sound Vibr. 214 497–511 Occurrence Handle10.1006/jsvi.1998.1548 Occurrence HandleMR1634007

    Article  MathSciNet  Google Scholar 

  109. P. Yu (2003) Bifurcation dynamics in control systems R. Chen D. J. Hill X. Yu (Eds) Bifurcation control, theory and applications Springer Berlin 99–126

    Google Scholar 

  110. M. Basso A. Evangelisti R. Genesio A. Tesi (1998) ArticleTitleOn bifurcation control in time-delay feedback systems J. Bifurcation Chaos 8 713–721 Occurrence Handle10.1142/S0218127498000504

    Article  Google Scholar 

  111. J. Blair S. A. Campbell (1994) ArticleTitleStability and bifurcations of equilibria in a multiple-delayed differential equation SIAM J. Appl. Math. 54 1402–1424 Occurrence Handle10.1137/S0036139993248853

    Article  Google Scholar 

  112. G. Gilsinn (2002) ArticleTitleEstimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool chatter Nonlinear Dyn. 30 103–154 Occurrence Handle10.1023/A:1020455821894

    Article  Google Scholar 

  113. K. Gu S. Niculescu (2003) ArticleTitleSurvey on recent results in the stability and control of time-delay systems J. Dyn. Sys. Trans. ASME 125 158–165

    Google Scholar 

  114. S. Phoojaruenchanachai K. Furuta (1992) ArticleTitleMemoryless stabilization of uncertain linear systems including time-varying state delays IEEE Trans. Automatic Control 37 1022–1026 Occurrence Handle10.1109/9.148363

    Article  Google Scholar 

  115. Gu, Y., Geng, C., Qian, J., Wang, L.: Robust H-inf control for linear time-delay system subject to normbounded nonlinear uncertainty. Proc. 1998 American Control Conf., Philadelphia, PA, June 1998, pp. 2417–2420 (1998)

  116. J. C. Shen (1997) ArticleTitleDesigning stabilizing controllers and observers for uncertain linear systems with time-varying delay Automatica 33 331–333 Occurrence Handle10.1016/S0005-1098(96)00176-8

    Article  Google Scholar 

  117. J. H. Su (1994) ArticleTitleFurther result on the robust stability of linear systems with a single time-delay Sys. Control Lett. 23 375–379 Occurrence Handle10.1016/0167-6911(94)90071-X

    Article  Google Scholar 

  118. P. Yu Y. Yuan J. Xu (2002) ArticleTitleStudy of double Hopf bifurcation and chaos for an oscillator with timedelayed feedback Comm. Nonlinear Sci. Num. Simul. 7 69–91 Occurrence Handle10.1016/S1007-5704(02)00007-2

    Article  Google Scholar 

  119. S. J. Niculescu (2001) Delay effects on stability, a robust control approach. Lecture Notes in Control and Information Sciences 269 Springer London

    Google Scholar 

  120. E. Ott C. Grebogi J. A. Yorke (1990) ArticleTitleControlling chaos Phys. Rev. Lett. 64 1196–1199 Occurrence Handle10.1103/PhysRevLett.64.1196 Occurrence Handle10041332

    Article  PubMed  Google Scholar 

  121. K. Pyragas (1992) ArticleTitleContinuous control of chaos by self-controlling feedback Phys. Lett. A 170 421–428 Occurrence Handle10.1016/0375-9601(92)90745-8

    Article  Google Scholar 

  122. A. D. Myshkis (1951) ArticleTitleGeneral theory of differential equations with delay Am. Math. Soc. Transl. 55 1–62

    Google Scholar 

  123. L. S. Pontryagin (1955) ArticleTitleOn the zeros of some elementary transcendental functions Am. Math. Soc Transl. 2 95–110

    Google Scholar 

  124. Górecki, H., Popek, L.: Control of the systems with time-delay. IFAC 3rd Symp. on Control of Distributed Parameter Systems, Toulouse, France, 1982

  125. Kolmanovskii, V. B., Nosov, V. R.: Stability of functional differential equations. Mathematics in Science and Engineering, vol. 180. Academic Press, London 1986

  126. Stépán, G.: Retarded dynamical systems: stability and characteristic functions. Pitman Research Notes in Mathematics Series 210. Longman Scientific and Technical, co-published in the USA. Wiley, New York 1989.

  127. Marshall, J. E., Görecki Walton, K., Korytowski, A.: Time-delay systems, stability and performance criteria with applications. In Bell GM. (ed) Series in Mathematics and its Applications. Chichester: Ellis Horwood 1992

  128. N. Olgac B. T. Holm-Hansen (1994) ArticleTitleA novel active vibration absorption technique: delayed resonator J. Sound Vibr. 176 93–104 Occurrence Handle10.1006/jsvi.1994.1360

    Article  Google Scholar 

  129. W. Just T. Bernard M. Ostheimer E. Reibold H. Benner (1997) ArticleTitleOn the mechanism of time-delayed feedback control Phys. Rev. Lett. 78 203–206 Occurrence Handle10.1103/PhysRevLett.78.203

    Article  Google Scholar 

  130. H. Y. Hu Z. H. Wang (1998) ArticleTitleStability analysis of damped SDOF systems with two time-delays in state feedback J. Sound Vibr. 214 213–225 Occurrence Handle10.1006/jsvi.1997.1499 Occurrence HandleMR1632242

    Article  MathSciNet  Google Scholar 

  131. Liapunov, A. M.: General theory of the stability of motion. Moskva: Izd., (1950), (English translation: New York: Academic Press 1966)

  132. N. N. Bautin (1984) The behavior of dynamical systems near the boundaries of the domain of stability (in Russian) EditionNumber2 Nauka Moskva

    Google Scholar 

  133. Mei, C., Abdel-Motagaly, K., Chen, R.: Review of nonlinear panel flutter at supersonic and hypersonic speed. CEAS/AIAA/ICASE/NASA Langley Int. Forum on Aeroelasticity and Structural Dynamics, NASA CP-1999-209136/PT 1 (Whitlow, W. Jr., Todd E.N., eds.), pp 171–188 (1999).

  134. C. Mei K. Abdel-Motagaly R. Chen (1999) ArticleTitleReview of nonlinear panel flutter at supersonic and hypersonic speeds Appl. Mech. Rev. 52 321–332

    Google Scholar 

  135. Bismarck-Nasr, M.N.: Structural dynamics in aeronautical engineering. (Przemieniechi J.S., ed.), pp. 229–289. AIAA Education Series; Reston, VA: AIAA, 1999.

  136. G. Cheng C. Mei (2004) ArticleTitleFinite element modal formulation for hypersonic panel flutter analysis with thermal effects AIAA J. 42 687–695

    Google Scholar 

  137. Dowell, E. H., Ilgamov, M.: Studies in nonlinear aeroelasticity, pp. 29–63; 206–277. New York: Springer 1988

  138. D. H. Kim I. Lee (2000) ArticleTitleTransonic and low-supersonic aeroelastic analysis of two degree of freedom airfoil with freeplay nonlinearity J. Sound Vibr. 234 859–880 Occurrence Handle10.1006/jsvi.2000.2907

    Article  Google Scholar 

  139. V. Volterra (1959) Theory of functionals and of integral and integro-differential equations Dover New York

    Google Scholar 

  140. Rugh, W.J.: Nonlinear systems theory, the Volterra-Wiener approach. The Johns Hopkins University Press 1981.

  141. K. Worden G. R. Tomlinson (2001) Nonlinearity in structural dynamics detection, identification and modeling Institute of Physics Publishing Bristol

    Google Scholar 

  142. Dugundji, J. Experimental studies in aeroelasticity of unswept and forward swept graphite/ epoxy wings. In: Proc. Raymond L. Bisplinghoff Memorial Symp., pp. 149–160. Gainesville, FL: University of Florida Press 1986

  143. Weisshaar, T. A.: Aeroelastic tailoring of forward swept wings. J. Aircraft 18, 669–676 (1981); also: Aeroelastic tailoring for unconventional aircraft configurations. Proc. CEAS Int. Forum on Aeroelasticity and Structural Dynamics 1, 89–102 (2001), and Proc. Raymond L. Bisplinghoff Memorial Symp. (Hajela P, eds.), pp. 336–352. Gainesville, FL: University of Florida Press 1986

    Google Scholar 

  144. Weisshaar, T. A.: Aeroelastic tailoring – creative use of unusual materials. AIAA Paper 87 0976. In: Proc. 28th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conf., April 1987

  145. L. Librescu J. Simovich (1988) ArticleTitleGeneral formulation for the aeroelastic divergence of composite swept-forward wing structures J. Aircraft 25 364–371

    Google Scholar 

  146. L. Librescu A. A. Khdeir (1988) ArticleTitleAeroelastic divergence of swept-forward composite wings including warping restraint effect AIAA J. 26 1373–1377

    Google Scholar 

  147. L. Librescu S. Thangjitham (1991) ArticleTitleAnalytical studies on static aeroelastic behavior of forward swept composite wing structures J. Aircraft 28 151–157

    Google Scholar 

  148. L. Librescu P. Marzocca W. A. Silva (2004) ArticleTitleLinear/nonlinear supersonic panel flutter in a hightemperature field J. Aircraft 41 918–924

    Google Scholar 

  149. Librescu, L., Marzocca, P., Silva, W. A.: Linear/nonlinear aeroelastic behavior of thermally damaged flat panels in a supersonic flow field. In: 5th Int. Congress of Thermal Stresses and Related Topics, TS2003, Virginia Polytechnic Institute and State University, Blacksburg, VA, June 8–11, 2003.

  150. Librescu, L., Marzocca, P.: Flutter and postflutter active control of thermally degraded panels in a high supersonic flowfield. In: 6th Int. Congress of Thermal Stresses and Related Topics, TS2005, Vienna, Austria, May 26–29, 2005.

  151. D. D. Liu Z. X. Yao D. Sarhaddi F. R. Chavez (1997) ArticleTitleFrom piston theory to a unified hypersonic– supersonic lifting surface method J. Aircraft 34 304–312

    Google Scholar 

  152. Polli, G. M., Librescu, L., Mastroddi, F.: Aerothermoelastic response of composite aircraft swept wings impacted by a laser beam. In: 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., April 19–22, 2004. AIAA-2004-2046.

  153. E. H. Dowell D. M. Tang (2002) ArticleTitleNonlinear aeroelasticity and unsteady aerodynamics AIAA J. 40 1697–1707

    Google Scholar 

  154. H. Irschik K. Schlacher (Eds) (2004) Advanced dynamics and control of structures and machines CISM Courses and Lectures, vol. 444 International Center for Mechanical Sciences Springer Wien New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. Librescu.

Additional information

This paper represents an updated version of the General Lecture presented at the 3rd European Conference on Structural Control, July 12–15, 2004, Vienna, Austria.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Librescu, L., Marzocca, P. Advances in the linear/nonlinear control of aeroelastic structural systems. Acta Mechanica 178, 147–186 (2005). https://doi.org/10.1007/s00707-005-0222-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-005-0222-6

Keywords

Navigation