Active flow control under actuator uncertainty using a sliding mode estimation strategy

This paper presents a synthetic jet actuator (SJA)-based closed-loop active flow control and estimation method, which compensates for the parametric uncertainty inherent in SJAs. A proper orthogonal decomposition (POD)-based model reduction technique is first utilized to recast the Navier-Stokes partial differential equation as a set of ordinary differential equations in terms of the unknown Galerkin coefficients. The POD-based reduced-order model is then expressed in a control-oriented form, which incorporates the parametric uncertainty inherent in the SJA actuator model. A novel sliding mode estimator is designed to estimate the unknown Galerkin coefficients in the uncertain SJA-based reduced-order model. To the best of the authors' knowledge, this is the first time that a sliding mode estimation strategy is rigorously proven to achieve finite-time state estimation for a flow system in the presence of input-multiplicative parametric uncertainty. A rigorous proof of finite time state estimation is provided, and the estimates are used in a nonlinear control law, which achieves asymptotic regulation of a fluid flow field to a desired time-varying velocity profile. A Lyapunov-based stability analysis is utilized to prove asymptotic regulation of the flow field velocity, and numerical simulation results are provided to demonstrate the performance of the proposed closed-loop active flow control system.