Modular Model Reduction of Interconnected Systems: A Robust Performance Analysis Perspective

TL;DR

This paper develops a mathematical framework linking the accuracy of reduced-order subsystem models to the stability and accuracy of the interconnected system, enabling better modular model reduction for complex engineering systems.

Contribution

It introduces a relation that predicts how subsystem reduction accuracy affects the overall interconnected system's stability and accuracy.

Findings

The framework predicts interconnected system stability based on subsystem reductions.

It allows translating system accuracy requirements into subsystem reduction specifications.

Demonstrated on a structural dynamics example.

Abstract

Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular model reduction, in which the subsystem models are reduced individually, is a practical and an efficient method to obtain accurate reduced-order models of such complex systems. However, when subsystems are reduced individually, without taking their interconnections into account, the effect on stability and accuracy of the resulting reduced-order interconnected system is difficult to predict. In this work, a mathematical relation between the accuracy of reduced-order linear-time invariant subsystem models and (stability and accuracy of) resulting reduced-order interconnected linear time-invariant model is introduced. This result can subsequently be used in two ways. Firstly, it can be used to translate accuracy characteristics of the reduced-order subsystem models directly to accuracy properties of the interconnected reduced-order model. Secondly, it can also be used to translate specifications on the interconnected system model accuracy to accuracy requirements on subsystem models that can be used for fit-for-purpose reduction of the subsystem models. These applications of the proposed analysis framework for modular model reduction are demonstrated on an illustrative structural dynamics example.