The modeling of multibody systems with fractional-order elements

Abstract

The fractional-order models, that is models described by differential equations of arbitrary real order, are gaining popularity in advanced control theory. In this study, an implementation of fractional-order elements in multibody dynamics systems is shown. A fractional-order model of elements is used in co-analysis between multibody system modeling tool and control system modeling tool. The co-analysis uses multibody dynamics software to solve all ordinary, integer-order differential equations and control system modeling software to solve fractional-order differential equations. Results of such simulation may be used in virtual prototype built in MSC Adams software environment to simulate behavior of multibody fractional-order system. Two example models are shown in this paper, one with 1 degree of freedom (DOF) and one with 6 DOF. The research was conducted in order to prepare software tools and methods, which can be used in modeling of bionic multibody systems with fractional-order elements. A co-simulation between control and multibody system modeling software tools enables accurate and cost-effective development of bionic devices. Furthermore, fractional-order models of bionic elements describe certain phenomena better than in integer-order models.