Global Asymptotic Stabilization of the Prototypical Aeroelastic Wing Section via Tp Model Transformation

A comprehensive analysis of aeroelastic systems has shown that these systems exhibit a broad class of pathological response regimes when certain types of non-linearities are included. In this paper, we propose a design method of a state-dependent non-linear controller for aeroelastic systems that includes polynomial structural non-linearities. The proposed method is based on recent numerical techniques such as the Tensor Product (TP) model transformation and the Linear Matrix Inequality (LMI) control design methods within the Parallel Distributed Compensation (PDC) frameworks. In order to link the TP model transformation and the LMI’s in the proposed design method, we extend the TP model transformation with a further transformation. As an example, a controller is derived that ensures the global asymptotic stability of the prototypical aeroelastic wing section via one control surface, in contrast with previous approaches which have achieved local stability or applied additional control actuator on the purpose of achieving global stability. Numerical simulations are used to provide empirical validation of the control results. The effectiveness of the controller design is compared with a former approach.