From differential equations to PDC controller design via numerical transformation

This paper proposes a transformation method capable of transforming analytically given differential equations of dynamic models into Takagi-Sugeno fuzzy inference model (TS fuzzy model), whereupon various parallel distributed compensation (PDC) controller design techniques can readily be executed. Joining the transformation method and the PDC techniques leads to a controller design framework. The transformation method is specialized to minimize the number of fuzzy rules in the resulting TS fuzzy model according to a given acceptable transformation error, the PDC design thus results in a computational complexity minimized controller which is highly desired in many cases of real applications. The paper presents examples to show the effectiveness of the proposed transformation.

[1]  Yuan-Cheng Fung,et al.  An introduction to the theory of aeroelasticity , 1955 .

[2]  A. Kurdila,et al.  Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Nonlinearity , 1997, 4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III.

[3]  Andrew J. Kurdila,et al.  Nonlinear Control of a Prototypical Wing Section with Torsional Nonlinearity , 1997 .

[4]  Vincent J. Harrand,et al.  Computational and Experimental Investigation of Limit Cycle Oscillations of Nonlinear Aeroelastic Systems , 2002 .

[5]  A. Kurdila,et al.  Stability and Control of a Structurally Nonlinear Aeroelastic System , 1998 .

[6]  Ron J. Patton,et al.  Polytopic and TS models are nowhere dense in the approximation model space , 2002, IEEE International Conference on Systems, Man and Cybernetics.

[7]  J. Vandewalle,et al.  An introduction to independent component analysis , 2000 .

[8]  Yeung Yam,et al.  SVD-based complexity reduction to TS fuzzy models , 2002, IEEE Trans. Ind. Electron..

[9]  Yeung Yam,et al.  SVD-based reduction to MISO TS models , 2003, IEEE Trans. Ind. Electron..

[10]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[11]  Earl H. Dowell,et al.  Flutter and Stall Response of a Helicopter Blade with Structural Nonlinearity , 1992 .

[12]  Zhichun Yang,et al.  Chaotic motions of an airfoil with non-linear stiffness in incompressible flow , 1990 .

[13]  Kazuo Tanaka,et al.  Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities , 1996, IEEE Trans. Fuzzy Syst..

[14]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[15]  Thomas W. Strganac,et al.  Applied Active Control for a Nonlinear Aeroelastic Structure , 1998 .

[16]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Andrew J. Kurdila,et al.  Nonlinear Control Theory for a Class of Structural Nonlinearities In a Prototypical Wing Section , 1997 .

[18]  Yeung Yam,et al.  Reduction of fuzzy rule base via singular value decomposition , 1999, IEEE Trans. Fuzzy Syst..

[19]  Kazuo Tanaka,et al.  Corrections To "robust Stabilization Of A Class Of Uncertain Nonlinear Systems Via Fuzzy Control: Quadratic Stabilizability, H Control Theory, And Linear Matrix Inequalities" [Correspondence] , 1997, IEEE Trans. Fuzzy Syst..

[20]  Zhichun Yang,et al.  Analysis of limit cycle flutter of an airfoil in incompressible flow , 1988 .