Nonlinear Optimal Control of the Aircraft's Wing-Rock Effect Under a 5th-Order Model

A new nonlinear optimal control method is proposed for solving the problem of control and stabilization of the roll motion of aircrafts under the wind-rock effect, with the use of a 5th-order dynamic model. It is proven that the 5-th order dynamic model of the wing-rock effect is a differentially flat system which can be transformed into the input-output linearized form. Next it is shown that the wing-rock model admits nonlinear optimal control. To apply nonlinear optimal control the dynamics of the wing-rock effect undergoes approximate linearization around a temporary operating point that is updated at each iteration of the control algorithm. The linearization takes place through first-order Taylor series expansion and through the computation of the Jacobian matrices of the system's state-space description. For the approximately linearized model of the wing-rock dynamics an H-infinity feedback controller is designed. Actually, the H-infinity controller gives a solution to the optimal control problem for the wing-rock effect under model uncertainty and parametric variations. For the computation of the feedback gains of the H-infinity controller an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control algorithm are demonstrated through Lyapunov analysis. First, it is shown that the control scheme achieves the H-infinity tracking performance which signifies elevated robustness for the control loop of the wing-rock dynamics against model uncertainties and external perturbations. Next, it is also proven that the control loop of the 5th-order wing-rock model is globally asymptotically stable. The proposed control method achieves fast and accurate tracking of setpoints under moderate variations of the control inputs.