Open-loop linear modeling method for unstable flow utilizing built-in data-driven feedback controllers

The linear models of complex unstable flow systems serve as essential foundations for conducting model-based flow characteristic analysis and control design. The primary obstacle faced by linear modeling these systems lies in balancing the inherent flow disturbances with the necessary excitation signals. This article develops a linear modeling approach based on the idea of closed-loop identification. To extend the applicability of traditional linear modeling techniques, this method employs time-variant or strongly nonlinear data-driven controllers, such as model-free adaptive controllers and deep reinforcement learning controllers, to automatically adjust the amplitude of the predesigned training signal in real time during the training process. Consequently, the strict requirements for obtaining the unstable steady base flow of unstable systems and for designing training signals are weakened. These data-driven controllers have been validated to fulfill the identifiability conditions of closed-loop systems derived from the uniqueness and convergence consistency of identification parameters. Then, the feasibility of the proposed linear modeling method is validated through two typical examples: low Reynolds number laminar flow around a cylinder and transonic buffet flow around a NACA0012 airfoil. The results confirm that this method successfully identifies the intrinsic linear characteristics of different flow systems, thus facilitating the advancement and application of model-based control design and simplification methods.