Ordinary differential equations (ODEs) as uncertainty approximator: Application for suppressing wing rock fluctuations in delta wings

Abstract

This paper introduces a robust control approach that uses linear ODE solutions to approximate the uncertainties in the wing rock dynamics of slender delta wings. The dynamic response of wing rock motion at various angles of attack (AOA) is characterized by significant uncertainties and is particularly sensitive to external disturbances. The methodology uses ordinary differential equations to model the system’s uncertainty, including unmodeled dynamics and external influences. A key advantage of the proposed method is that it does not require an exact model of the plant or specific data about the uncertainties. The stability of the closed-loop system is ensured through a Lyapunov-based evaluation, which guarantees that all error trajectories remain bounded. Simulation results demonstrate that the control scheme effectively stabilizes the rolling motion even in the presence of uncertainties. Finally, the effectiveness of the proposed methodology is validated through comparisons with the extended state observer (ESO), fuzzy logic system, and radial basis function neural network (RBFNN).