Resolvent-Based ROM and Feedback Control for NACA0012 Airfoil Flow

Abstract

This study investigates resolvent-based model reduction and robust feedback control for separated flow over a NACA0012 airfoil at low Reynolds number. The incompressible Navier–Stokes equations are linearized about a steady base flow, and the resulting resolvent operator is sampled in the frequency domain. A low-order input–output model is then identified via vector fitting, yielding a reduced-order model that accurately reproduces the frequency response and impulse dynamics of the full system. Based on this model, an H-infinity loop-shaping controller is designed and tuned through appropriate weighting functions. The closed-loop simulations demonstrate global suppression of separation and a significant reduction of perturbation energy. Further, a sensor-placement study is conducted through a spatial traversal optimization. The results reveal a strong correlation between the optimal stability margin and the pole–zero separation, highlighting how non-minimum-phase behavior fundamentally limits achievable robustness and providing a physically interpretable guideline for sensor placement in airfoil flow control.