State-Space modeling and active aeroelastic control of a typical airfoil section with three degrees of freedom. - Felipe Augusto Sviaghin Ferri (2008)
This dissertation presents a detailed analysis of a typical section model with three degrees of freedom. This is a classic model used for the study of basic aerodynamic and aeroelastic phenomena. The equations of motion are derived and discussed. The equations for the aerodynamic loads induced by arbitrary motion of the typical section and by arbitrary shaped wind gusts are derived. These equations are converted into a state-space formulation by replacing the nonlinear Wagner and Küssner functions by rational function approximations, that are Laplace transformable. The equations of motion, the aerodynamic loads and the gust loads equations and the Dryden model for stochastic wind gusts, all of these in the state-space form, are joined in a unified state-space model. This model is then used to perform simulations to evaluate the dynamic response and stability of the typical section. A control structure is presented, along with procedures for calculating the gains for this control structure by minimizing three different performance indices: linear quadratic, time weighted linear quadratic and H-infinity-norm. An angle of attack tracker is designed using these performance indices and its response to control input and gust disturbances is presented and discussed.