Closed-loop fluid flow control using a low dimensional model

Abstract

This paper is devoted to the problem of defining a control strategy to minimize the drag of a bluff body in a 2-D cross-flow. A reduced model is obtained using a robust statistical reduction approach and an optimal orbit in the phase space is determined using an open-loop control strategy. This open-loop control law is inexpensive to derive as it relies on a reduced order model. Since the deviations from the optimal orbit are meant to remain small, the non-linear flow model can be linearized around the orbit at each time. To compensate for the deviations, a closed-loop control is applied. The design of a robust controller is difficult due to the large number of state space variables, conflicting specifications and parameter uncertainties. Further, the model is a time-varying process, so that Linear Time Invariant design methods cannot be directly applied.