State-Space Modeling and Analysis of Morphing Trailing Edge Flaps for Active Flutter Suppression

In this paper, a state-space model approach for a two-dimensional airfoil fitted with a morphing trailing-edge is presented. The variable chordwise implementation is represented as a fourth order equation to describe the variable camber line of the trailing edge. This design allows for discontinuity in slope but not displacement at the control surface “hinge”. Aerodynamic forces with respect to angle of attack and control surface deflection are calculated from thin airfoil theory to be utilized for linear implementation in the state-space model. Structural parameters and equations of motion for the state space model are derived from Nonlinear Aeroelastic Test Apparatus (NATA) benchmark wing section. Using this linear time-invariant system, a full-state Linear Quadratic Regulator can be determined for the airfoil to assist in suppressing flutter. Closed-loop eigen analysis demonstrates a range of 3.1 to 3.3x stability increase for the airfoil. This approach allows for the design of a controller to regulate heave-pitch response and critical flutter speed.