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Sliding mode robust control of supersonic three degrees-of-freedom airfoils

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  • Control Applications
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Abstract

The robust aeroelastic control of a three-degrees-of-freedom (3DOF) linear and non-linear wing-flap system under sliding mode control (SMC) and operation in supersonic flight speeds is presented. Open- and closed-loop aeroelastic responses to blast and sonic-boom excitation in the wing-flap system with uncertainty, as well as flutter analysis, are investigated along with the implementation of a Sliding Mode Observer (SMO). The effectiveness of control in reducing the amplitude of oscillation and preventing flutter instability is demonstrated.

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Abbreviations

a :

Non-dimensional elastic axis position measured from the mid-chord, positive aft

B :

Ratio of the nonlinear to the linear pitching stiffness

M, H, K :

Mass, damping, and stiffness matrices

b :

Half-chord length

e :

Non-dimensional leading-edge flap position measured from the mid-chord, positive aft

F a , F c :

Aerodynamic and control load vectors

h, α, β :

Plunging, pitching, and flap displacements

I α , I β :

Mass moment of inertia per unit span of the wing-flap system about the elastic axis (EA) and of the flap about the flap axis (FA) of rotation, respectively

k h , k α , k β :

Stiffness parameters in plunging, torsional stiffness of the wing and flap about the EA

L, M ea , H β :

Total lift per span, aerodynamic moment, and hinge moment

l α , m ea , h β :

Non-dimensional aerodynamic lift, moment, and torque

m :

Airfoil mass per unit span

M F , M f :

Flutter speed and flight speed

ρ ∞ :

undisturbed density

U∞, V:

free stream speed and its nondimensional counterpart

r α , r β :

Non-dimensional radii of gyration of the wingflap system about EA

S α , x α :

Static unbalance about EA and its nondimensional counterpart

S β , x β :

Static unbalance about FA and its nondimensional counterpart

t, τ :

Time variable and its nondimensional counterpart

κ :

Polytropic gas coefficient

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Authors and Affiliations

  1. Department of Mechanical Engineering, Korea University, 136-701, Seoul, Korea

    Bok-Hee Lee, Jeong-hwan Choo & Sungsoo Na

  2. Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, 13699-5725, USA

    Piergiovanni Marzocca

  3. Department of Engineering and Mechanics, Virginia Polytechnic and State University, Blacksburg, VA, 24061, USA

    Liviu Librescu

Authors
  1. Bok-Hee Lee
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  2. Jeong-hwan Choo
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  3. Sungsoo Na
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  4. Piergiovanni Marzocca
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  5. Liviu Librescu
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Corresponding author

Correspondence to Sungsoo Na.

Additional information

Recommended by Editorial Board member Hyo-Choong Bang under the direction of Editor Jae Weon Choi. The authors would like to acknowledge the late Professor Liviu Librescu of Virginia Tech, who help, guide and support through the years have made this research possible. He will be remembered and deeply missed. S. Na also acknowledges the financial support from KOSEF (No. 2009-0063170).

Bok-Hee Lee received his B.S. degree in Mechanical Engineering from Korea University in 2006, and he is now a graduate student of Korea University. His research interests include vibration control of aerospace wing and composite turbine blade.

Jeong-hwan Choo received his B.S. degree in Mechanical Engineering from Dongguk University in 2008, and he is now a graduate student of Korea University. His research interests include active vibration control and aeroelasticity.

Sung-soo Na graduated from Korea University with his B.S. and M.S. degree both in Mechanical Engineering. He earned his Ph.D degree in 1997 at the Dept. of Engineering Science and Mechanics at VPI in USA. He has been a Professor at the Dept. of Mechanical Enigneering in Korea University in Seoul, Korea since 2001. His research interest lies in Vibration Control, Protein Dynamics, Protein Mechanics and BioNano Mechanics

Pier Marzocca received his Ph.D. degree in Aeronautical and Aerospace Engineering in 2001 from Politecnico di Torino in Italy. He is currently an Associate Professor in the Department of Mechanical and Aeronautical Engineering, Clarkson University, USA. He is senior member of AIAA, ASME, SAE, Chair of the SAE Unmanned Aircraft System Committee and serves as an Associate Editor of Journal of Thermal Stresses and Journal of Aerospace Engineering. His current research interests include unsteady aerodynamics, flow and aeroelastic control, aircraft and wind turbine technologies.

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Lee, BH., Choo, Jh., Na, S. et al. Sliding mode robust control of supersonic three degrees-of-freedom airfoils. Int. J. Control Autom. Syst. 8, 279–288 (2010). https://doi.org/10.1007/s12555-010-0214-8

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  • DOI: https://doi.org/10.1007/s12555-010-0214-8

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