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 state-space 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.