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Function Approximation Technique (FAT)-Based Adaptive Feedback Linearization Control for Nonlinear Aeroelastic Wing Models Considering Different Actuation Scenarios

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Abstract

This paper introduces a comprehensive study on vibration damping of a lumped aeroelastic wing model with translational linear and torsional nonlinear spring elements considering different actuation scenarios. The wing models have two degrees of freedom (DoFs) representing translational and torsional oscillations. On the other hand, the flap angles represent the control inputs that attempt to regulate the wing vibrations. Depending on the number of flaps designed, three actuation scenarios are investigated including fully actuated, overactuated, and underactuated wing models. For a fully actuated wing system (Scenario 1), conventional adaptive control strategies can be used for damping wing oscillations; however, adaptive approximation control is adopted in this work due to its capabilities for controlling (regulating) the dynamic system in the presence of the unknown system parameters. On the other hand, in the overactuated wing model (Scenario 2), the wing system has more control inputs than the DoFs and hence infinite solutions for the control input response are obtained. The Pseudoinverse matrix is a powerful tool to resolve this problem. In Scenario 3, the control inputs are less than the DoFs and hence a partial feedback linearization control strategy with an adaptive approximation compensator is used for regulation purposes; however, the internal dynamics of the underactuated wing system should be stable. Simulation experiments are performed to prove the effectiveness of control methods of the investigated scenarios.

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REFERENCES

  1. G. Dimitriadis, Introduction to Nonlinear Aeroelasticity (Wiley, Chichester, 2017).

    Book  Google Scholar 

  2. H. Horikawa and E. H. Dowell, “An elementary explanation of the flutter mechanism with active feedback controls,” J. Aircraft 16 (4), 225–232 (1979). https://doi.org/10.2514/3.58509

    Article  Google Scholar 

  3. J. Heeg, “Analytical and experimental investigation of flutter suppression by piezoelectric actuation,” NASA Technical Paper 3241 (1993).

  4. C. Y. Lin, “Strain actuated aeroelastic control,” MSc Thesis (Dept. of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge, MA, 1993).

  5. K. Lazarus, “Multivariable high-authority control of plate-like active lifting surfaces,” PhD Dissertation (Dept. of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge, MA, 1992).

  6. J. Lelkes and T. Kalmár-Nagy, “Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber,” Nonlinear Dyn. 103, 2997–3018 (2021). https://doi.org/10.1007/s11071-020-05725-0

    Article  Google Scholar 

  7. E. Dowell, J. Edwards, and T. Strganac, “Nonlinear aeroelasticity,” J. Aircraft 40 (5), 857–874 (2003). https://doi.org/10.2514/2.6876

    Article  Google Scholar 

  8. B. H. K. Lee, S. J. Price, and Y. S. Wong, “Nonlinear aeroelastic analysis of airfoils: Bifurcation and chaos,“ Prog. Aerosp. Sci. 35 (3), 205–334 (1999). https://doi.org/10.1016/S0376-0421(98)00015-3

    Article  Google Scholar 

  9. S. J. Price, H. Alighanbari, and B. H. K. Lee, “The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities,” J. Fluids Struct. 9 (2), 175–193 (1995). https://doi.org/10.1006/jfls.1995.1009

    Article  Google Scholar 

  10. L. C. Zhao and Z. C. Yang, “Chaotic motions of an airfoil with non-linear stiffness in incompressible flow,” J. Sound Vib. 138 (2), 245–254 (1990). https://doi.org/10.1016/0022-460X(90)90541-7

    Article  MATH  Google Scholar 

  11. C. C. Marsden, “An experimental and analytical investigation of the nonlinear behaviour and modal analysis of a structurally nonlinear, two-dimensional airfoil in subsonic flow,” PhD Thesis (McGill University, Montréal, 2005).

  12. H. Golparvar, S. Irani, and M. Mousavi Sani, “Experimental investigation of linear and nonlinear aeroelastic behaviour of a cropped delta wing with store in low subsonic flow,” J. Braz. Soc. Mech. Sci. Eng. 38 (4): 1113–1130 (2016). https://doi.org/10.1007/s40430-015-0436-z

    Article  Google Scholar 

  13. J. Xiang, Y. Yan, and D. Li, “Recent advance in nonlinear aeroelastic analysis and control of the aircraft,” Chin. J. Aeronaut. 27 (1), 12–22 (2014). https://doi.org/10.1016/j.cja.2013.12.009

    Article  Google Scholar 

  14. F. Afonso, J. Vale, É. Oliveira, F. Lau, and A. Suleman, “Non-linear aeroelastic response of high aspect-ratio wings in the frequency domain,” Aeronaut. J. 121 (1240), 858–876 (2017). https://doi.org/10.1017/aer.2017.29

    Article  Google Scholar 

  15. E. Livne, “Aircraft active flutter suppression: State of the art and technology maturation needs,” J. Aircraft 55 (1), 410-450 (2018). https://doi.org/10.2514/1.C034442

    Article  Google Scholar 

  16. M. Berci, “On aerodynamic models for flutter analysis: A systematic overview and comparative assessment,” A-ppl. Mech. 2 (3), 516–541 (2021). https://doi.org/10.3390/applmech2030029

    Article  Google Scholar 

  17. O. Doaré, “Dissipation induced instabilities of structures coupled to a flow,” in Dynamic Stability and Bifurcation in Nonconservative Mechanics, Ed. by D. Bigoni and O. Kirillov, CISM International Centre for Mechanical Sciences, Vol. 586 (Springer, Cham, 2019), pp. 63–102. https://doi.org/10.1007/978-3-319-93722-9_2

  18. A. R. Ansari and A. R. B. Novinzadeh, “Designing a control system for an airplane wing flutter employing gas actuators,” Int. J. Aerosp. Eng. 2017, 4209619, 1–9 (2017). https://doi.org/10.1155/2017/4209619

    Article  Google Scholar 

  19. A. Malher, C. Touzé, O. Doaré, G. Habib, and G. Kerschen, “Flutter control of a two-degrees-of-freedom airfoil using a nonlinear tuned vibration absorber,” J. Comput. Nonlinear Dyn. 12 (5), 051016 (2017). https://doi.org/10.1115/1.4036420

    Article  Google Scholar 

  20. A.-C. Huang, C.-Y. Kai, and Y.-F. Chen, Adaptive Control of Underactuated Mechanical Systems (World Scientific, Singapore, 2015).

    Book  Google Scholar 

  21. J. Ko, A.J. Kurdila, and T. W. Strganac, “Nonlinear control of a prototypical wing section with torsional nonlinearity,” J. Guid., Control, Dyn. 20 (6), 1181–1189 (1997). https://doi.org/10.2514/2.4174

    Article  MATH  Google Scholar 

  22. T. O’Neil and T. W. Strganac, “Nonlinear aeroelastic response—Analyses and experiments,” in 36th Structures, Structural Dynamics and Materials Conference, New Orleans, LA, 1995, p. AIAA 95-1404. https://doi.org/10.2514/6.1995-1404

  23. J. Ko, T. W. Strganac, and A. J. Kurdila, “Stability and control of a structurally nonlinear aeroelastic system,” J. Guid., Control, Dyn. 21 (5), 715–725 (1998). https://doi.org/10.2514/2.4317

    Article  Google Scholar 

  24. J. Ko, T. W. Strganac, and A. J. Kurdila, “Adaptive feedback linearization for the control of a typical wing section with structural nonlinearity,” Nonlinear Dyn. 18, 289–301 (1999). https://doi.org/10.1023/A:1008323629064

    Article  MATH  Google Scholar 

  25. S. Jiffri, S. Fichera, J. E. Mottershead, and A. Da Ronch, “Experimental nonlinear control for flutter suppression in a nonlinear aeroelastic system,” J. Guid., Control, Dyn. 40 (8), 1925–1938 (2017). https://doi.org/10.2514/1.G002519

    Article  Google Scholar 

  26. G. Innocenti and P. Paoletti, “Stabilization of a nonlinear wing section: A case study for control with inexact nonlinearity cancellations,” in 2015 European Control Conference (ECC), Linz, Austria, 2015, pp. 2108–2113. https://doi.org/10.1109/ECC.2015.7330851

  27. N. D’Amico, L. J. Adamson, S. Fichera, P. Paoletti, G. Innocenti, and J. E. Mottershead, “Nonlinear aeroservoelastic control in the presence of uncertainty,” in AIAA Scitech 2020 Forum, Orlando, FL, 2020, p. AIAA 2020-1676. https://doi.org/10.2514/6.2020-1676

  28. P. Preumont, Vibration Control of Active Structures: An Introduction (Springer, Cham, 2018). https://doi.org/10.1007/978-3-319-72296-2

  29. H. F. N. Al-Shuka and E. N. Abas, “Regressor-free adaptive vibration control of constrained smart beams with axial stretching,” SN Appl. Sci. 2 (12), 2146 (2020). https://doi.org/10.1007/s42452-020-03859-9

    Article  Google Scholar 

  30. H. F. N. Al-Shuka, “FAT-based adaptive backstepping control of an electromechanical system with an unknown input coefficient,” FME Trans. 49 (1), 113–120 (2021). https://doi.org/10.5937/fme2101113A

    Article  Google Scholar 

  31. H. F. N. Al-Shuka, “Proxy-based sliding mode vibration control with an adaptive approximation compensator for Euler–Bernoulli smart beams,” J. Eur. Syst. Autom. 53 (6), 825–834 (2021). https://doi.org/10.18280/jesa.530608

    Article  Google Scholar 

  32. H. F. N. Al-Shuka, B. Corves, and W.-H. Zhu, “Function approximation technique-based adaptive virtual decomposition control for a serial-chain manipulator,” Robotica 32 (3), 375–399 (2014). https://doi.org/10.1017/S0263574713000775

    Article  Google Scholar 

  33. H. F. N. Al-Shuka and R. Song, “Hybrid regressor and approximation-based adaptive control of robotic manipulators with contact-free motion,” in Proc. 2018 2nd IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), Xi’an, China, 2018, pp. 325–329. https://doi.org/10.1109/IMCEC.2018.8469628

  34. H. F. N. Al-Shuka and R. Song, “Decentralized adaptive partitioned approximation control of high degrees-of-freedom robotic manipulators considering three actuator control modes,” Int. J. Dyn. Control 7 (2), 744–757 (2019). https://doi.org/10.1007/s40435-018-0482-3

    Article  MathSciNet  Google Scholar 

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The authors did not receive support from any organization for the submitted work.

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Authors and Affiliations

  1. Department of Aeronautical Engineering, University of Baghdad, Baghdad, Iraq

    Hayder F. N. Al-Shuka

  2. Department of Mechanism Theory, Machine Dynamics and Robotics (IGMR), RWTH Aachen University, Aachen, Germany

    B. Corves

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  1. Hayder F. N. Al-Shuka
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Correspondence to Hayder F. N. Al-Shuka.

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Al-Shuka, H.F., Corves, B. Function Approximation Technique (FAT)-Based Adaptive Feedback Linearization Control for Nonlinear Aeroelastic Wing Models Considering Different Actuation Scenarios. Math Models Comput Simul 15, 152–166 (2023). https://doi.org/10.1134/S2070048223010106

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