A Closed-Loop Nonlinear Control and Sliding Mode Estimation Strategy for Fluid Flow Regulation

Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite-time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed-loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier-Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced-order model contains a  measurement equation that is in a nonstandard mathematical form.This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite-time estimation of the unmeasurable states of the reduced-order model using direct sensor measurements of the flow field velocity.The estimated states are utilized as feedback measurements in a closed-loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov-based stability analysis is presented to prove that the closed-loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed-loop AFC system, comparing 2 different designs for the SMO.