A methodology for areal modeling of structural dynamics based on a Takagi–Sugeno fuzzy system

Abstract

For simulation analysis and controller design mathematical models are necessary. This also applies to characterize the structural dynamics of mechanical systems, but current modeling approaches are limited to describe a restricted amount of predefined geometric points. A procedure to model the mechanical behavior of an arbitrary point along a line or within a surface area is missing. We propose a novel method to tackle this issue, by adapting Takagi–Sugeno Fuzzy Systems and combining them with the general linear description of mechanical systems. The presented method consists of two paths, each designed to meet a specific purpose, subject to numerical complexity and representation aberration. In the end, both cases lead to nonlinear differential equations, which provide a continuous estimation of the properties of an area. The accuracy and performance of our approach is verified by different experimental and simulation setups. One specific example is a galvanometer laser scanner, for which the new method is inevitable for a precise system modeling.