On delay partial differential and delay differential thermal models for variable pipe flow

Abstract

A new formulation of physical thermal models for variable plug flow through a pipe is proposed. The derived model is based on a commonly used onedimensional distributed parameter model, which explicitly takes into account the heat capacity of the jacket of the pipe. The main result of the present contribution is the constitution of the equivalence of this model with a serial connection of a pure delay or transport system and another partial-differential equation (PDE), subsequently called delay-partial-differential equation (DPDE)-model. The means for obtaining the proposed model comprise operational calculus in the Laplace domain as well as classical theory of characteristics. The finitedimensional approximation of the DPDE-model leads to a delay-differential equation (DDE)-system, which can be seen as a generalization of commonly used DDE-models consisting of a first-order low-pass filter subject to an input delay. The proposed model is compared to several alternative models in simulations and experimental studies.

Further experimental results on modelling and algebraic control of a delayed looped heating-cooling process under uncertainties

“…It is worth noting that a novel modelling approach combining PDEs and DDEs into the so-called delay partial differential equations (DPDEs) was proposed for constant [ 30 ] and time-varying [ 5 , 31 ] flows recently. It comes from a one-dimensional PDE model that includes the transport process and the wall dynamics revealing delays.…”

Analysis of the Sign of the Solution for Certain Second-Order Periodic Boundary Value Problems with Piecewise Constant Arguments

“…Delay differential equations find interesting applications in fields like biology, fisiology, physics, etc. Some interesting and recent applications of this type of equations appear, for instance, when proposing a mathematical model for electrohydraulic servomechanisms [1], absorption complexities in pharmacokinetics [2], the approximation of Fitzhugh-Nagumo and Hodgkin-Huxley models for action potential generation in excitable cells [3], tick population with diapause [4], or thermal models for variable pipe flow [5].…”