Robust Nonlinear Estimation And Control Of Fluid Flow Velocity Fields

A proper orthogonal decomposition (POD)-based model reduction technique is utilized to develop a closed-loop nonlinear flow control system. By using POD, the Navier-Stokes partial differential equations are recast as a set of nonlinear ordinary differential equations in terms of the unknown Galerkin coefficients. A sliding mode estimator is then employed to estimate, in finite time, the unknown coefficients in the reduced order model for the actuated flow system. The estimated coefficients are utilized as feedback measurements in a robust nonlinear control law. A rigorous analysis is utilized to analyze the convergence of the sliding mode estimator, and a Lyapunov-based stability analysis is used to prove asymptotic regulation of the flow field velocity to a desired velocity profile. The control objective of tracking a desired velocity profile presented here is a proof of concept only; the proposed methodology could be applied to various flow control objectives. Numerical simulation results are provided to demonstrate the capability of the estimator/control system to regulate the velocity of the flow field to a desired state.