Control-oriented model reduction for a class of hyperbolic systems with application to managed pressure drilling

Abstract

This paper presents a model reduction approach for systems of hyperbolic partial differential equations (PDEs) with nonlinear boundary conditions. These systems can be decomposed into a feedback interconnection of a linear hyperbolic subsystem and a static nonlinear mapping. This structure motivates us to reduce the overall model complexity by only reducing the linear subsystem (the PDE part). We show that the linear PDE subsystem can effectively be approximated by a cascaded structure of systems of continuous time difference equations (CTDEs) and ordinary differential equations (ODEs), where the CTDE captures the infinite-dimensional nature of the PDE model. These systems are constructed by adapting an interpolation method based on frequency-domain data. Models in the form of hyperbolic PDEs with nonlinear boundary conditions are for example encountered in managed pressure drilling (MPD). The proposed technique is verified by application to such an MPD model.