Model reduction for active control design using multiple-point Arnoldi methods

Abstract

A multiple-point Arnoldi method is derived for model reduction of computational fluid dynamic systems. By choosing the number of frequency interpolation points and the number of Arnoldi vectors at each frequency point, the user can select the accuracy and range of validity of the resulting reduced-order model while balancing computational expense. The multiple-point Arnoldi approach is combined with a singular value decomposition approach similar to that used in the proper orthogonal decomposition method. This additional processing of the basis allows a further reduction in the number of states to be obtained, while retaining a significant computational cost advantage over the proper orthogonal decomposition. Results are presented for a supersonic diffuser subject to mass flow bleed at the wall and perturbations in the incoming flow. The resulting reduced-order models capture the required dynamics accurately while providing a significant reduction in the number of states. The reduced-order models are used to generate transfer function data, which are then used to design a simple feedforward controller. The controller is shown to work effectively at maintaining the average diffuser throat Mach number.