Preliminary Study on Stability of a Hovering Bi-flap Flapping Wing Platform using Cycle-Averaged Linear Models

Woei Leong Chan, Muhammad Azli Bin Jaffar, Quoc Viet Nguyen

Abstract


A preliminary study on the stability of a bi-flap flapping wing hovering platform is presented in this paper. The work includes the derivation of cycle-average linear longitudinal and lateral models, the experiment to determine the stability derivatives, and analysis on the identified system matrices. Also discussed in the paper is the validity of using a cycle-averaged model to represent the dynamics of the flapping wing platform, and the validity of using small perturbation theory to linearize the nonlinear model. Results show that the platform is unstable longitudinally and laterally about the hovering equilibrium. Longitudinally, the natural modes are short period unstable oscillatory mode, fast subsidence mode, and slow divergent mode. Laterally, the natural modes are neutral mode, fast subsidence mode, and long period unstable oscillatory mode.

Keywords


cycle-averaged model; bi-flap; flapping wing; stability

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References


D. B. Doman, M. W. Oppenheimer, and D. O. Sigthorsson, “Dynamics and control of a minimally actuated biomimetic vehicle: part I – aerodynamic model,” presented at 2009 AIAA Guidance, Navigation, and Control Conference, Chicago, IL.

X. Deng, L. Schenato, W. C. Wu, and S. Sastry, “Flapping flight for biomimetic robotic insects part I: system modelling,” IEEE Transaction on Robotics, volume 22, number 4, 2006, pp. 776-788.

Z. A. Khan, S. K. Agrawal, “Control of longitudinal flight dynamics of a flapping-wing micro air vehicle using time-averaged model and differential flatness based controller,” in Proc. American Control Conference, New York, 2007, pp. 5284–5289.

M. Sun, J. Wang, and Y. Xiong, “Dynamic flight stability of hovering insects,” Acta Mechanica Sinica, volume 23, number 3, 2007, pp. 231- 246.

G. K. Taylor and A. L. R. Thomas, “Animal flight dynamics II. Longitudinal stability in flapping flight,” Journal of Theoretical Biology, volume 214, 2002, pp. 351-370.

M. Sun and Y. Xiong, “Dynamic flight stability of a hovering bumblebee,” The Journal of Experimental Biology, volume 208, 2005, pp. 447-459.

N. Xu and M. Sun, “Lateral dynamic flight stability of a model bumblebee in hovering and forward flight,” Journal of Theoretical Biology, volume 319, 2013, pp. 102-115.

N. Gao, H. Aono, H. Liu, “A numerical analysis of dynamic flight stability of hawkmoth hovering,” Journal of Biomechanical Science and Engineering, volume 4, number 1, pp. 105–116, 2009.

N. Gao, H. Aono, H. Liu, “Perturbation analysis of 6DoF flight dynamics and passive dynamic stability of hovering fruit fly Drosophila melanogaster,” Journal of Theoretical Biology, volume 270, number 1, pp. 98–111, February 2011.

I. Faruque, J. S. Humbert, “Dipteran insect flight dynamics. Part 1: longitudinal–directional motion about hover,” Journal of Theoretical Biology, volume 264, number 2, 2010, pp. 538-552.

I. Faruque, J. S. Humbert, “Dipteran insect flight dynamics. Part 2: lateral–directional motion about hover,” Journal of Theoretical Biology, volume 265, number 3, 2010, pp. 306-313.

Y. Zhang, M. Sun, “Dynamic flight stability of a hovering model insect: lateral motion,” Acta Mechanica Sinica, volume 26, number 2, 2010, pp. 175–90.

M. Groen, B. Bruggeman, B. Remes, R. Ruijsink, B. van Oudheusden, and H. Bijl, “Improving flight performance of the flapping wing MAV DelFly II,” presented at 2010 International Micro Air Vehicle conference and competitions (IMAV), Braunschweig, Germany.

R. C. Nelson, Flight stability and automatic control 2nd Edition. Singapore: McGraw-Hill, 1998, ch. 4.


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