Comparativo de desempenho dos controladores LQR e SDRE aplicados à dinâmica não linear de uma aeronave de caça em voo longitudinal

Abstract

Modern high performance aircraft operate critical flight regimes where some system nonlinearities directly influence their dynamic response. This work considers the study of a fighter aircraft operating at high angles of attack of the wing. The mathematical model was developed through a system of nonlinear differential equations that represent the dynamics of an aircraft in longitudinal flight, considering the effect of wind speed variation due to atmospheric turbulence on the aircraft dynamic response. The 0-1 test is performed to determine if the system is chaotic or periodic, related to the speed and angle of attack of the aircraft. As an object of study, all the considerations and analyses regarding the F-8 aircraft "Crusader" were took into account. Control designs are proposed linear and nonlinear, considering the tail deflection angle as a control action parameter. Controllers are designed from linear methodologies with the Quadratic Linear Regulator (LQR) control and nonlinear with the State Dependent Riccati Equation (SDRE) control. Controllers are subjected to the same operating conditions in order to stabilize wing angle oscillations, considering critical regions of aircraft behavior, for comparison of the control. Numerical simulations demonstrated the efficiency of the proposed control strategies, relating the comparative dynamics analyzes with and without the actions of the controllers, in order to compare the ability to respond quickly and reliably to recover the aircraft from a stall situation. Where the SDRE controller was more efficient compared to the LQR controller when subjected to more severe stall regions.