Abstract
Non-smooth nonlinearities such as freeplay, bilinear/piece-wise linear stiffness are among the various types of nonlinearity that have been encountered in aeroelastic systems. Freeplay, for example, may begin to appear as a result of ageing of components such as bolted joints and control surfaces, and has been known to be the cause of flutter-induced limit cycle oscillation (LCO). Therefore, it is evident that effectively controlling these nonlinearities is essential in avoiding the onset of LCO, or indeed any other type of nonlinear response. The present paper addresses the control of systems with non-smooth structural nonlinearities, through application of the feedback linearisation method. In systems with smooth nonlinearities, the required nonlinear feedback is also smooth, and therefore does not give rise to complexities associated with the feedback linearisation method. On the other hand, when controlling systems with non-smooth nonlinearities, the necessary control inputs are also non-smooth, and the applicability of feedback linearisation to such systems is of interest. This task is undertaken in the present work, through the use of numerical simulations on a 3 degree of freedom aeroservoelastic model. An example of a case where the parameterisation of the nonlinearity is uncertain is also addressed.
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References
Librescu L, Marzoeca P (2005) Advances in the linear/nonlinear control of aeroelastic structural systems. Acta Mech 178(3–4):147–186
Platanitis G, Strganac TW (2004) Control of a nonlinear wing section using leading- and trailing-edge surfaces. J Guid Control Dyn 27(1):52–58
Strganac T, Ko J, Thompson D (2000) Identification and control of limit cycle oscillations in aeroelastic systems. J Guid Control Dyn 23(6):1127–1133
Ko J, Strganac TW, Kurdila AJ (1999) Adaptive feedback linearization for the control of a typical wing section with structural nonlinearity. Nonlinear Dyn 18(3):289–301
Jiffri S, Paoletti P, Cooper JE, Mottershead JE (2014) Feedback linearisation for nonlinear vibration problems. Shock Vibr 2014:16. doi:10.1155/2014/106531. Article ID 106531
Jiffri S, Mottershead JE, Cooper JE (2013) Adaptive feedback linearisation and control of a flexible aircraft wing. In: Topics in modal analysis, vol 7, Proceedings of the 31st IMAC, a conference on structural dynamics 2013. Springer, Orange County CA, USA
Jiffri S, Mottershead JE, Cooper JE (2013) Active control of a nonlinear flexible aircraft wing, in international conference on structural engineering dynamics, Sesimbra, Portugal
Jiffri S, Mottershead JE, Cooper JE (2013) Nonlinear control of a flexible aeroelastic system, in international forum on aeroelasticity & structural dynamics. Bristol Marriott Royal Hotel, Bristol, UK
Recker DA, Kokotovic PV, Rhode D, Winkelman J (1991) Adaptive nonlinear control of systems containing a deadzone. In: Proceedings of the 30th IEEE conference on decision and control, vols 1–3. IEEE, New York, pp 2111–2115
Tao G, Kokotovic PV (1997) Adaptive control of systems with unknown non-smooth non-linearities. Int J Adapt Control Signal Process 11(1):81–100
Ma XL, Tao G (2000) Adaptive actuator compensation control with feedback linearization. IEEE Trans Autom Control 45(9):1705–1710
Zheng YF, Wen CY, Li ZG (2013) Robust adaptive asymptotic tracking control of uncertain nonlinear systems subject to nonsmooth actuator nonlinearities. Int J Adapt Control Signal Process 27(1–2):108–121
Tao G, Burkholder JO, Guo JX (2013) Adaptive output feedback actuator nonlinearity compensation for multivariable systems. In: 2013 American control conference. IEEE, New York, pp 3356–3361
Edwards JW, Ashley H, Breakwell JV (1979) Unsteady aerodynamic modeling for arbitrary motions. AIAA J 17(4):365–374
Conner MD, Tang DM, Dowell EH, Virgin LN (1997) Nonlinear behavior of a typical airfoil section with control surface freeplay: a numerical and experimental study. J Fluids Struct 11(1):89–109
Li D, Guo S, Xiang J (2010) Aeroelastic dynamic response and control of an airfoil section with control surface nonlinearities. J Sound Vib 329(22):4756–4771
Papatheou E, Tantaroudas ND, Da Ronch A, Badcock K, Mottershead JE, Cooper JE (2013) Active control for flutter suppression: an experimental investigation, in international forum on aeroelasticity and structural dynamics (IFASD), 24–26 June 2013, Bristol, UK
Theodorsen T (1935) General theory of aerodynamic instability and the mechanism of flutter. NACA Report no. 496, pp 413–433
Wright JR, Cooper JE (2007) Introduction to aircraft aeroelasticity and loads. Wiley, Chichester
Isidori A (1995) Nonlinear control systems. Springer, Berlin
Khalil HK (2002) Nonlinear systems, 3rd ed. Prentice Hall, Upper Saddle River
Acknowledgments
This research has been funded by EPSRC grant EP/J004987/1 under the project entitled “Nonlinear Active Vibration Suppression in Aeroelasticity”.
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Jiffri, S., Mottershead, J.E. (2015). Nonlinear Control of an Aeroelastic System with a Non-smooth Structural Nonlinearity. In: Sinha, J. (eds) Vibration Engineering and Technology of Machinery. Mechanisms and Machine Science, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-09918-7_28
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DOI: https://doi.org/10.1007/978-3-319-09918-7_28
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