Reduced-order Modeling of Modular, Position-dependent Systems with Translating Interfaces

TL;DR

The paper tackles the challenge of modeling position-dependent dynamics in modular mechatronic systems with translating interfaces. It introduces a position-dependent interconnection structure built from a fixed grid of virtual interconnection points and interpolation to connect identical subsystem models, yielding a single ROM barG_c(s) that remains valid across the entire operating range. The approach integrates with a modular MOR framework to guarantee FRF accuracy bounds, while subsystems' FRFs are computed once, enabling efficient evaluation across operating points. A wire bonder case study demonstrates accurate dynamics over the operating range and shows that modular reduction can achieve significant computational savings without sacrificing fidelity, supporting robust design and diagnostics for translating-interface systems.

Abstract

Many complex mechatronic systems consist of multiple interconnected dynamical subsystems, which are designed, developed, analyzed, and manufactured by multiple independent teams. To support such a design approach, a modular model framework is needed to reduce computational complexity and, at the same time, enable multiple teams to develop and analyze the subsystems in parallel. In such a modular framework, the subsystem models are typically interconnected by means of a static interconnection structure. However, many complex dynamical systems exhibit position-dependent behavior (e.g., induced by translating interfaces) which cannot be not captured by such static interconnection models. In this paper, a modular model framework is proposed, which allows to construct an interconnected system model, which captures the position-dependent behavior of systems with translating interfaces, such as linear guide rails, through a position-dependent interconnection structure. Additionally, this framework allows to apply model reduction on subsystem level, enabling a more effective reduction approach, tailored to the specific requirements of each subsystem. Furthermore, we show the effectiveness of this framework on an industrial wire bonder. Here, we show that including a position-dependent model of the interconnection structure 1) enables to accurately model the dynamics of a system over the operating range of the system and, 2) modular model reduction methods can be used to obtain a computationally efficient interconnected system model with guaranteed accuracy specifications.

Figures (25)

• Figure 1: Example of an interconnected system where the input-to-output dynamic behavior from input $u$ to output $y$ is position-dependent, i.e., it depends on $x$.
• Figure 2: Comparison of modeling workflows for position-dependent system models with, in the left column, the standard static interconnection structure. In the right column, the proposed position-dependent interconnection structure is given, which significantly reduces required effort for changing the operating points.
• Figure 3: Block diagram representation of the interconnected system $G_c(s)$ with subsystem models $G_1\dots,G_k$, and the interconnection matrix $\mathcal{K}$.
• Figure 4: Illustration of an interconnection structure between two arbitrary subsystems $j$ and $\ell$ with a translating interface with (a) (physical) interconnection points for a specific operation point, and (b) position-dependent approach with a fixed grid of virtual interconnection points. Filled markers indicate virtual interconnections points that are active at a specific operating point, and used to interpolate the characteristics of each interconnection. Empty markers indicate currently inactive interconnection points.
• Figure 5: Block-diagram representation of the interconnected system (a) $G_c$, i.e., with static interconnection matrix $\mathcal{K}$, and (b) $\bar{G}_c$, i.e., with position-dependent interconnection matrix $\bar{\mathcal{K}}$.

Theorems & Definitions (1)

• Remark 1