The modeling of multibody systems with fractional-order elements

Proceedings of the 14th International Carpathian Control Conference (ICCC) Pub Date : 2013-05-26 DOI:10.1109/CARPATHIANCC.2013.6560539

J. Kowal, W. Lepiarz

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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.

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含分数阶元素的多体系统建模

分数阶模型，即由任意实阶微分方程描述的模型，在高级控制理论中越来越受欢迎。在本研究中，展示了分数阶元素在多体动力学系统中的实现。在多体系统建模工具与控制系统建模工具的协同分析中，采用了分数阶单元模型。联合分析采用多体动力学软件求解所有常阶、整阶微分方程，控制系统建模软件求解分数阶微分方程。该仿真结果可用于在MSC Adams软件环境中构建的虚拟样机，以模拟多体分数阶系统的行为。文中给出了1自由度和6自由度两种模型的实例。本研究旨在为分数阶元仿生多体系统的建模提供软件工具和方法。控制和多体系统建模软件工具之间的联合仿真使仿生设备的精确和经济有效的开发成为可能。此外，仿生元件的分数阶模型比整数阶模型更能描述某些现象。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings of the 14th International Carpathian Control Conference (ICCC)

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