In the paper, two adaptive fuzzy control schemes including indirect and direct frameworks are developed for suppressing the wing-rock motion that is a highly nonlinear aerodynamic phenomenon in which limit cycle roll oscillations are experienced by aircraft at high angles of attack. In the two control topologies, a dynamic fuzzy system called Extended Sequential Adaptive Fuzzy Inference System (ESAFIS) is constructed to represent the dynamics of the wing-rock system. ESAFIS is an online learning fuzzy system in which the rules are added or deleted based on the input data. In the indirect control scheme, the ESAFIS is used to estimate the nonlinear dynamic function and then a stable indirect fuzzy controller is designed based on the estimator. In the direct control scheme, the ESAFIS controller is directly designed to imitate an ideal stable control law without determining the model of the dynamic function. Different from the original ESAFIS, the adaptive tuning algorithms for the consequent parameters are established in the sense of Lyapunov theorem to ensure the stability of the overall control system. A sliding mode controller is also designed to compensate for the modelling errors of ESAFIS by augmenting the indirect/direct fuzzy controller. Finally, comparisons with a neuron control scheme using the RBF network and a fuzzy control scheme with Takagi–Sugeno (TS) system are presented to depict the effectiveness of the proposed control strategies. Simulation results show that the proposed fuzzy controllers achieve better tracking performance with dynamically allocating the rules online. 
Adaptive fuzzy control of aircraft wing-rock motion