Model-order reduction of lumped parameter systems via fractional calculus

TL;DR

This paper explores using fractional calculus to create compact, accurate reduced-order models of non-homogeneous systems, offering a promising alternative to traditional integer order methods with potential for exact dynamic response matching.

Contribution

It introduces a novel fractional calculus-based approach for model order reduction, enabling high accuracy and order reduction without sacrificing analytical solutions.

Findings

Fractional models can exactly match original system responses under certain conditions.

Reduced models have frequency-dependent, complex order derivatives.

Fractional approach improves efficiency and accuracy in system simulation.

Abstract

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.