Methodology to Develop Nonlinear State-Space Models for Active Control of Transonic Aeroelastic Phenomenon

This paper aims to develop a reduced-order modelling methodology for nonlinear, unsteady, aerodynamic loads for active control transonic aeroelastic instabilities. To this end, a NACA0012 airfoil equipped with a flap is chosen as the test configuration. The aim here is to understand the interaction between the transonic shock dynamics and flap actuation at various amplitudes and frequencies. The high-fidelity simulations are carried out for two angles of attack, i.e. 𝛼 = 0.0◦, 4.0◦. It is found that transonic buffet characteristics significantly change with airfoil geometry. Additionally, the flap is seen to be ineffective in the separated flow regions, thereby making the Cl-β slopes highly nonlinear. However, increasing the frequencies of flap oscillations, increases flap effectiveness, increases control over buffet motion and moves towards linear lift responses. Furthermore, we also evaluate the performance of several Bayesian Filters that are crucial in the state-estimation process of the active control of nonlinear systems. It is observed that nonlinear filters such as Unscented Karman Filter perform better than the traditional linear Kalman Filter as system response to flap actuation becomes nonlinear in the presence of separated boundary layer.