Linear quadratic regulator-based model reference adaptive control for suppression of freeplay-induced limit cycle oscillations in a nonlinear aeroelastic airfoil

Nonlinear aeroelasticity with pitch freeplay can generate finite-amplitude limit cycle oscillation below or near the linear flutter boundary. This study examines flutter suppression in a two-degree-of-freedom pitch-plunge airfoil benchmark with quasi-steady aerodynamic coupling, freeplay nonlinearity, and trailing-edge flap actuation. A conservative linear quadratic regulator is designed as the stabilizing baseline and augmented with a model reference adaptive control layer whose regressor explicitly includes the piecewise freeplay restoring function. This structure allows the adaptive input to compensate the nonlinear torsional contribution rather than treating it only as an unmodeled disturbance. Closed-loop simulations are conducted for inflow velocities from 11.2 to 12.0 m/s, covering limit-cycle and post-flutter cases, with controller activation tested both initially and after an uncontrolled oscillation has developed. At 11.6 m/s with delayed activation, the combined controller reduces the residual pitch amplitude from approximately 1.05×10−3 rad for the linear quadratic regulator baseline to 3.49×10−5 rad, corresponding to a 96.7% reduction relative to the selected non-aggressive baseline, while maintaining bounded flap motion below the imposed saturation limit. Additional numerical checks under measurement noise, bounded external disturbances, and deterministic parameter perturbations support a practical boundedness interpretation within the tested quasi-steady benchmark envelope.