Optimal Flutter Suppression of Nonlinear Typical Wing Section Using Time-Domain Finite Elements Method

AbstractIn this paper, the optimal time-domain finite element method is applied to the flutter suppression of a nonlinear two-dimensional typical wing section. The aeroelastic governing equations are based on the inclusion of stiffness nonlinearity in pitching motion and on the quasi-steady aerodynamics. The flutter suppression problem is formulated as a general optimization problem with equality constraints that are functions of state variables. Using the variational approach, the optimality conditions are derived and the resulting equations are discretized in time-domain. Then, by setting out the discrete equations, a set of nonlinear algebraic equations is generated, and through the Newton–Raphson method, the optimum answer is attained. The numerical results are presented in which the performance of the nonlinear optimal control system designed by the time-domain finite element technique for nonlinear aeroelastic wing sections is illustrated.

[1]  Dewey H. Hodges,et al.  Finite element method for the solution of state-constrained optimal control problems , 1995 .

[2]  Youdan Kim,et al.  Time-Domain Finite Element Method for Inverse Problem of Aircraft Maneuvers , 1997 .

[3]  Woosoon Yim,et al.  State feedback control of an aeroelastic system with structural nonlinearity , 2003 .

[4]  Robert H. Scanlan,et al.  A Modern Course in Aeroelasticity , 1981, Solid Mechanics and Its Applications.

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

[6]  Chen Song,et al.  Application of output feedback sliding mode control to active flutter suppression of two-dimensional airfoil , 2010 .

[7]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

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

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

[10]  Liviu Librescu,et al.  Aeroelasticity of 2-D lifting surfaces with time-delayed feedback control , 2005 .

[11]  Liviu Librescu,et al.  Advances in the linear/nonlinear control of aeroelastic structural systems , 2005 .

[12]  Shijun Guo,et al.  Adaptive control of a nonlinear aeroelastic system , 2011 .

[13]  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.

[14]  Daniel G. Cole,et al.  Active Control and Closed-Loop Identification of Flutter Instability in Typical Section Airfoil , 2007 .

[15]  Dewey H. Hodges,et al.  Weak Hamiltonian finite element method for optimal control problems , 1991 .

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

[17]  H. Alighanbari,et al.  Nonlinear control design of an airfoil with active flutter suppression in the presence of disturbance , 2007 .

[18]  Na Zhao,et al.  Active control of supersonic/hypersonic aeroelastic flutter for a two-dimensional airfoil with flap , 2011 .

[19]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[20]  S. Fazelzadeh,et al.  Minimum-time Earth-Moon and Moon-Earth orbital maneuvers using time-domain finite element method , 2010 .

[21]  Y. Kim,et al.  Modelling of vibrating systems using time-domain finite element method , 2002 .