A data-driven nonlinear state-space model of the unsteady lift force on a pitching wing

Accurate unsteady aerodynamic models are essential to estimate the forces on rapidly pitching wings and to develop model-based controllers. As system identification is arguably the most successful framework for model predictive control in general, in this paper we investigate whether system identification can be used to build data-driven models of pitching wings. The forces acting on the pitching wing can be considered a nonlinear dynamic function of the pitching angle and therefore require a nonlinear dynamic model. In this work, a nonlinear data-driven model is developed for a pitching wing. The proposed model structure is a polynomial nonlinear state-space model (PNLSS), which is an extension of the classical linear state-space model with nonlinear functions. The PNLSS model is trained on experimental data of a pitching wing. The experiments are performed using a dedicated wind tunnel setup. The pitch angle is considered as the input to the model, while the lift coefficient is considered as the output. Three models are trained on swept-sine signals at three offset angles with a fixed pitch amplitude and a range of reduced frequencies. The three training datasets are selected to cover the linear and nonlinear operating regimes of the pitching wing. The PNLSS models are validated on single-sine experimental data at the respective pitch offset angles. The PNLSS models are able to capture the nonlinear aerodynamic forces more accurately than a linear and semi-empirical models, especially at higher offset angles.