Limit cycle oscillation in aeroelastic systems and its adaptive fractional-order fuzzy control
- 224 Downloads
Alaeroelastic system is a complex system which can produce limit cycles oscillation. In this paper, an adaptive fractional-order fuzzy controller is presented to suppress flutter in an alaeroelastic system. The studied system is a kind of nonlinear system with two freedoms (the plunge displacement and the pitch angle). A terminal sliding mode control is proposed, the fuzzy system parameters are updated by fractional-order differential equations and the stability of the closed-loop system is discussed by means of Lyapunov stability theory. Finally, numerical simulations are demonstrated to verify the effectiveness of proposed method.
KeywordsAlaeroelastic system Limit cycle oscillation Terminal sliding mode control Adaptive fractional-order fuzzy control
This work is supported by the National Natural Science Foundation of China (Grant No. 61403157), the Natural Science Foundation for the Higher Education Institutions of Anhui Province of China (Grant No. KJ2016A665), the Foundation for Distinguished Young Talents in Higher Education of Anhui of China (Grant No. GXFXZD2016204), and the Natural Science Foundation of Huainan Normal University (Grant No. 2014XK19ZD, 2016xj52 ).
- 4.Hua CC, Liu D, Guan XP (2014) Necessary and sufficient stability criteria for a class of fractional-order delayed systems. IEEE Trans Circ Syst II Exp Briefs 61(1):59–63Google Scholar
- 15.Lu J, Wang Z, Cao J, et al (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurcat Chaos. doi: 10.1142/S0218127412501763
- 22.vanderPol B, vanderMark J (1927) Frequency demultiplication. Nature 120: 363–364Google Scholar
- 24.Lee YS, FVakakis A, Bergman LA, McFarland DM (2006) Suppression of limit cycle oscillations in the Van der Pol oscillator by means of passive nonlinear energy sinks(NESs). Struct Control Health Monit 13:41–75Google Scholar
- 36.Balasubramaniam P, Syed Ali M (2011) Stochastic stability of uncertain fuzzy recurrent neural networks with Markovian jumping parameters. Int J Comput Math 88(5):892–904Google Scholar
- 39.Balasubramaniam P, Syed Ali M (2010) Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 161:608–618Google Scholar
- 40.Pan Y, Sun T, Yu H (2016) Composite adaptive dynamic surface control using online recorded data. Int J Robust Nonlinear Control. doi: 10.1002/rnc.3541
- 41.Zhang XL, Zhang FY (2012) Synchronizing uncertain chaotic systems by using adaptive fuzzy chattering free sliding mode control. J Comput Inf Syst 8:10509–10515Google Scholar
- 43.Balasubramaniam P, Syed Ali M (2011) Stability analysis of Takagi-Sugeno stochastic fuzzy Hopfield neural networks with discrete and distributed time varying delays. Neurocomputing 74(10):1520–1526Google Scholar