NONLINEAR ESTIMATION AND CONTROL OF UNCERTAIN DYNAMIC SYSTEMS WITH APPLICATIONS IN FLUID FLOW CONTROL
Reliable control of fluid flow dynamic systems is critical in a wide range of engineering applications, including combustion, turbo machinery, automotive systems, and aeronautics. The potential benefits include aerodynamic drag reduction, aeroacoustics noise reduction, and lift enhancement in aircraft. While passive and open loop active flow control (AFC) methods are adequate for many applications, there remain several open problems in the design of reliable closed-loop active flow control systems. Closed-loop AFC techniques utilize real-time sensor measurement information to automatically adjust the control signal in response to realistic, time-varying dynamic conditions. Significant theoretical challenges exist, however, in closed-loop active flow control design. Specifically, the equations governing the dynamics of fluid flow systems are in the form of nonlinear partial differential equations, which are not amenable to control design. Additional control design challenges arise as a result of unmodeled flow field perturbations due to real-time control actuation. In this dissertation, robust and adaptive nonlinear control methods are presented, which are rigorously proven to achieve reliable tracking of fluid flow velocity fields. To achieve the result, the governing flow field dynamic equations are re-cast as a finite set of nonlinear ordinary differential equations using the well-accepted proper orthogonal decomposition (POD) technique. The POD-based reduced-order model incorporates the complete actuated flow field dynamics, including input-multiplicative time-varying parametric uncertainty due to actuator perturbations. The main contributions presented in this dissertation include rigorous control developments and stability analyses of new robust and adaptive nonlinear control design methods, which are specifically designed to address the aforementioned open challenges in closed-loop AFC.