Reduced-Order Models for Feedback Control of Transient Energy Growth

Feedback flow control is developed to suppress the transient energy growth of flow disturbances in a linearized channel flow. Specifically, we seek a controller that minimizes the maximum transient energy growth, which can be formulated as a linear matrix inequality problem. Solving linear matrix inequality problems can be computationally prohibitive for high-dimensional systems encountered in flow control applications. Thus, we develop reduced-order fluids models using balance truncation and proper orthogonal decomposition techniques. These models are designed to optimally approximate system energy while preserving the input-output dynamics that are essential for controller synthesis. Controllers developed based on these reduced-order models are found to reduce transient energy growth and to outperform linear quadratic controllers in the context of a linearized channel flow.