Paper:
Language: English:

Determination of Different Polytopic Models of the Prototypical Aeroelastic Wing Section by TP Model Transformation

Péter Baranyi^, Zoltán Petres^,**, Péter L. Várkonyi^,
Péter Korondi^, and Yeung Yam^**

^Computer and Automation Research Institute of the Hungarian Academy of Sciences, H-1111 Budapest, Kende utca 13-17, Hungary
^Institute of Industrial Science, The University of Tokyo
^Budapest University of Technology and Economics, H-1117 Budapest, Goldmann György tér 3, Hungary
^****Automation and Computer-Aided Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China

Received: September 22, 2005

Accepted: December 28, 2005

Keywords: non-linear control design, TP model transformation, convex decomposition

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.4 pp. 486-493, 2006

Abstract

The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) models into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) models. The main advantage of the TP model transformation is that the Linear Matrix Inequality (LMI) based control design frameworks can immediately be applied to the resulting polytopic models to yield controllers with tractable and guaranteed performance. The effectiveness of the LMI design depends on the type of the convex combination in the polytopic model. Therefore, the main objective of this paper is to study how the TP model transformation is capable of determining different types of convex hulls of the LTI models. The study is conducted trough the example of the prototypical aeroelastic wing section.

Reference

[1] P. Baranyi, “Output-feedback design of 2-D Aeroelastic System,” Journal of Guidance, Control, and Dynamics (in Press).

[2] P. Baranyi, “Tensor Product Model Based Control of 2-D Aeroelastic System,” Journal of Guidance, Control, and Dynamics (in Press).

[3] P. Baranyi, “TP model transformation as a way to LMI based controller design,” IEEE Transaction on Industrial Electronics, 51(2), April, 2004.

[4] P. Baranyi, D. Tikk, Y. Yam, and R. J. Patton, “From Differential Equations to PDC Controller Design via Numerical Transformation,” Computers in Industry, Elsevier Science, 51, pp. 281-297, 2003.

[5] P. Baranyi, and A. R. Varkonyi-Koczy, “TP Transformation Based Dynamic System Modeling for Nonlinear Control,” IEEE Transaction on Instrumentation and Measurement, 54(6), pp. 2191-2203, December, 2005.

[6] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix Inequalities in System and Control Theory,” Philadelphia PA:SIAM, ISBN 0-89871-334-X, 1994.

[7] E. H. Dowell, H. C. J. Curtiss, R. H. Scanlan, and F. Sisto, “A Modern Course in Aeroelasticity,” Stifthoff and Noordhoff, Alpen aan den Rijn, The Netherlands, Editor: E. H. Dowell, 1978.

[8] Y. C. Fung, “An Introduction to the Theory of Aeroelasticity,” John Wiley and Sons, New York, 1955.

[9] P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, “LMI Control Toolbox,” The MathWorks, Inc., 1995.

[10] J. Ko, A. J. Kurdila, and T. W. Strganac, “Nonlinear Control of a Prototypical Wing Section with Torsional Nonlinearity,” Journal of Guidance, Control, and Dynamics, 20(6), pp. 1181-1189, November-December, 1997.

[11] J. Ko, and T. W. Strganac, “Stability and Control of a Structurally Nonlinear Aeroelastic System,” Journal of Guidance, Control, and Dynamics, 21(5), pp. 718-725, 1998.

[12] T. O’Neil, and T. W. Strganac, “An Experimental Investigation of Nonlinear Aeroelastic Response,” AIAA paper 95-1404, proc. 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, New Orleans, Lousiana, pp. 2043-2051, 1995.

[13] C. W. Scherer, and S. Weiland, “Linear Matrix Iequalities in Control,” DISC course lecture notes, DOWNLOAD:
http://www.cs.ele.tue.nl/SWeiland/lmid.pdf ,
2000.

[14] D. Tikk, P. Baranyi, R. Patton, and J. Tar, “Approximation Capability of TP model forms,” Australian Journal of Intelligent Information Processing Systems, 8(3), pp. 155-163, 2004.

[15] W. Xing, and S. N. Singh, “Adaptive output feedback control of a nonlinear aeroelastic structure,” Journal of Guidance, Control, and Dynamics, 23(6), pp. 1109-1116, 2000.

[16] L. C. Zhao, and Z. C. Yang, “Chaotic Motions of an Airfoil with Nonlinear Stiffness in Incompressible Flow,” Journal of Sound and Vibration, 138(2), pp. 245-254, 1990.