A Sliding Mode Observer-based Limit Cycle Oscillation Suppression using a Robust Active Flow Control Technique

This paper presents a sliding mode observer (SMO)-based robust control method, which achieves simultaneous estimation, fluid flow velocity regulation and limit cycle oscillation (LCO) suppression in a flexible airfoil. The proposed control design is based on a dynamic model that incorporates the fluid structure interactions (FSI) in the airfoil. The FSI describe how the flow field velocity at the surface of a flexible structure gives rise to fluid forces acting on the structure. In the proposed control method, the LCO are controlled via control of the flow field velocity near the surface of the airfoil using surface-embedded synthetic jet actuators. The flow field velocity is expressed using a proper orthogonal decomposition based reduced-order flow model that formally incorporates the actuation effects of synthetic jet actuator. Specifically, this flow field velocity profile is driven to a desired time-varying profile, which results in a LCO-stabilizing fluid forcing function acting on the airfoil. A sliding mode observer is designed to estimate the unmeasurable states in the reduced-order model of the actuated flow field dynamics. The SMO is rigorously proven to achieve local finite-time estimation of the unmeasurable state in the presence of the parametric uncertainty in the SJA. A Lyapunov-based stability analysis is used to prove that the active flow control system asymptotically converges to the LCO-stabilizing forcing function that suppresses the LCO. Numerical simulation results demonstrate that the augmented observer provides a reduction in the control effort required to stabilize the LCO.