Modelling Flow Control Problems Under Diverse Operating Conditions by Identification and Blending of Multiple Systems

Abstract

In this paper, a dynamical modelling procedure for fluid flow control problems is proposed. The resulting model is simple in that it consists of a number of linear time-invariant systems, but powerful in that it is capable of representing diverse operating conditions within a given flow envelope. The procedure makes use of snapshots of the flow process, which are obtained from experiments or computational fluid dynamics simulations. A proper orthogonal decomposition expansion of the flow is computed from snapshots, and the time coefficients of the expansion are coupled with the input values to form the estimation data. A linear statespace system representing the time coefficients is obtained using subspace system-identification methods. The procedure is repeated for a number of operating points, called breakpoints, which are characterized by one or more flow parameters of interest. The dynamical models obtained at the breakpoints are fused using the output-blending technique. The modelling procedure is illustrated with a flow control case study, where the flow dynamics are governed by the Navier-Stokes equations, the flow parameter of interest is the kinematic viscosity, and the control goal is to regulate the velocity of a given point inside the flow domain.