Model order reduction for linear time delay systems:A delay-dependent approach based on energy functionals

This paper proposes a model order reduction technique for asymptotically stable linear time delay systems with point-wise delays. The presented delay-dependent approach, which can be regarded as an extension of existing balancing model order reduction techniques for linear delay-free systems, is based on energy functionals that characterize observability and controllability properties of the time delay system. The reduced model obtained by this approach is an asymptotically stable time delay system of the same type as the original model, meaning that the approach is both stability- and structure-preserving. It also provides an a priori bound on the reduction error, serving as a measure of the reduction accuracy. The effectiveness of the proposed method is illustrated by numerical simulations.</p

Control-Oriented Modeling for Managed Pressure Drilling Automation Using Model Order Reduction

Automation of Managed Pressure Drilling (MPD) enables fast and accurate pressure control in drilling operations. The performance that can be achieved by automated MPD is determined by, firstly, the controller design and, secondly, the hydraulics model that is used as a basis for controller design. On the one hand, such hydraulics model should be able to accurately capture essential flow dynamics, e.g., wave propagation effects, for which typically complex models are needed. On the other hand, a suitable model should be simple enough to allow for extensive simulation studies supporting well scenario analysis and high-performance controller design. In this paper, we develop a model order reduction approach for the derivation of such a control-oriented model for {single-phase flow} MPD {operations}. In particular, a nonlinear model order reduction procedure is presented that preserves key system properties such as stability and provides guaranteed (accuracy) bounds on the reduction error. To demonstrate the quality of the derived control-oriented model, {comparisons with field data and} both open-loop and closed-loop simulation-based case studies are presented

On Extended Model Order Reduction for Linear Time Delay Systems

This chapter presents a so-called extended model-reduction technique for linear delay differential equations. The presented technique preserves the infinite-dimensional nature of the system and facilitates the preservation of properties such as system parameterizations (uncertainties). It is proved in this chapter that the extended model-reduction technique also preserves stability properties and provides a guaranteed a-priori bound on the reduction error. The reduction technique relies on the solution of matrix inequalities that characterize controllability and observability properties for time delay systems. This work presents conditions on the feasibility of these inequalities, and studies the applicability of the extended model reduction to a spatio-temporal model of neuronal activity, known as delay neural fields. Lastly, it discusses the relevance of this technique in the scope of model reduction of uncertain time delay systems, which is supported by a numerical example

An approximate well-balanced upgrade of Godunov-type schemes for the isothermal Euler equations and the drift flux model with laminar friction and gravitation

In this article, approximate well-balanced (WB) finite-volume schemes are developed for the isothermal Euler equations and the drift flux model (DFM), widely used for the simulation of single- and two-phase flows. The proposed schemes, which are extensions of classical schemes, effectively enforce the WB property to obtain a higher accuracy compared with classical schemes for both the isothermal Euler equations and the DFM in case of nonzero flow in the presences of both laminar friction and gravitation. The approximate WB property also holds for the case of zero flow for the isothermal Euler equations. This is achieved by defining a relevant average of the source terms which exploits the steady-state solution of the system of equations. The new extended schemes reduce to the original classical scheme in the absence of source terms in the system of equations. The superiority of the proposed WB schemes to classical schemes, in terms of accuracy and computational effort, is illustrated by means of numerical test cases with smooth steady-state solutions. Furthermore, the new schemes are shown numerically to be approximately first-order accurate

On Extended Model Order Reduction for Linear Time Delay Systems

This chapter presents a so-called extended model-reduction technique for linear delay differential equations. The presented technique preserves the infinite-dimensional nature of the system and facilitates the preservation of properties such as system parameterizations (uncertainties). It is proved in this chapter that the extended model-reduction technique also preserves stability properties and provides a guaranteed a-priori bound on the reduction error. The reduction technique relies on the solution of matrix inequalities that characterize controllability and observability properties for time delay systems. This work presents conditions on the feasibility of these inequalities, and studies the applicability of the extended model reduction to a spatio-temporal model of neuronal activity, known as delay neural fields. Lastly, it discusses the relevance of this technique in the scope of model reduction of uncertain time delay systems, which is supported by a numerical example