Reduced-order Dynamic Modeling and Robust Nonlinear Control of Fluid Flow Velocity Fields

A robust nonlinear control method is developed for fluid flow velocity tracking, which formally addresses the inherent challenges in practical implementation of closed-loop active flow control systems. A key challenge being addressed here is flow control design to compensate for model parameter variations that can arise from actuator perturbations. The control design is based on a detailed reduced-order model of the actuated flow dynamics, which is rigorously derived to incorporate the inherent time-varying uncertainty in the both the model parameters and the actuator dynamics. To the best of the authors’ knowledge, this is the first robust nonlinear closed-loop active flow control result to prove exponential tracking control of a reduced-order actuated flow dynamic model, which formally incorporates input-multiplicative time-varying parametric uncertainty and nonlinear coupling between the state and control signal. A rigorous Lyapunov-based stability analysis is utilized to prove semiglobal exponential tracking of a desired flow field velocity profile over a given spatial domain. A detailed comparative numerical study is provided, which demonstrates the performance improvement that is achieved using the proposed robust nonlinear flow control method to compensate for model uncertainty and uncertain actuator dynamics.