Grey box modelling for control: Qualitative models as a unifying framework

Abstract

AbstractGrey box modelling traditionally reflects that both a priori and experimental knowledge are being incorporated into the model‐building process, where both of them may exhibit uncertain character. A brief investigation into various grey box modelling approaches reveals that they differ mainly with respect to the required model accuracy. Moreover, the goal of the model application has to be considered in the model building, since this goal defines the desired accuracy of the model, which is represented as model uncertainty.This paper advocates the view that grey box modelling is model building which incorporates uncertainty description. Qualitative differential and algebraic equations are proposed in this paper as a unifying framework for development of dynamic models with uncertainty. the steps in the model development cycle are defined for this unifying framework, wherein the computational complexity issues are addressed at each step. It is also shown how qualitative differential and algebraic equations can be specialized to important well‐known grey box model forms such as robust models with parametric uncertainty, constraint qualitative differential equations and digraph models. the presented concepts and grey box model forms are illustrated on a simple example: a heat exchanger with bypass.