Nonlinear Control of Fluid Flows

Abstract : The central objective of this research program was the development of methods for nonlinear distributed feedback control of various classes of fluid dynamic systems based on appropriate forms of the Navier-Stokes equations. We systematically synthesized practically-implement able (i.e., low-order) nonlinear feedback control algorithms that enforce the requested stability and performance specifications in the distributed parameter (infinite-dimensional) closed-loop system. We successfully implemented nonlinear low-order feedback control on several fluid dynamic system's including the Burgers' equation, the Korteweg-de-Vries Burgers equation. the Kuramoto-Sivashinsky equation and the two-dimensional channel flow. In the context of these studies, we systematically dealt with: (a) the accurate numerical simulation of the distributed models describing the fluid dynamic systems, (b) the derivation of low-order approximations of these distributed models, and (c) the synthesis of the controller (control algorithm and parameters) and the controller implementation (measurement sensor and control actuator type). Furthermore, we worked on the development of feedback control algorithms for fluid dynamic systems that can deal with the key practical issues of model uncertainty, time-delays in the measurement sensors and control actuators and constraints in the capacity of the control actuators. In addition, the issue of selection of optimal locations of the control actuators and measurement sensors was studied, and insights and fundamental understanding on the nature of the feedback control problem for fluid dynamic systems were provided. In addition to our research on nonlinear feedback control of the aforementioned fluid dynamic systems, we pursued research on active feedback control of two-dimensional flow over a plat plate for frictional drag reduction using blowing and shear stress measurements.