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Modular Redesign of Mechatronic Systems: Formulation of Module Specifications Guaranteeing System Dynamics Specifications

Lars A. L. Janssen, Rob H. B. Fey, Bart Besselink, Nathan van de Wouw

TL;DR

The paper tackles the challenge of guaranteeing system-level dynamic specifications for complex, modular mechatronic systems when components are designed by separate teams. It develops a modular redesign framework that models modules with FRFs $G^{(j)}(i\\omega)$, interconnects them via a fixed structure $\\mathcal{K}$, and defines system-level FRF bounds through $\\mathcal{E}_A(\\omega)$ using $V_A(\\omega)$ and $W_A(\\omega)$ such that $\\|V_A(\\omega)(G_A(i\\omega)-\\hat{G}_A(i\\omega))W_A(\\omega)\\|<1$. A central theorem links module-level specifications $\\mathcal{E}^{(j)}(\\omega)$ to the assembly specification $\\mathcal{E}_A(\\omega)$ via a nominal system $N(i\\omega)$ and a positive-definite condition on a Schur-complement-like matrix, enabling an alternating-LMI algorithm to automatically synthesize module FRF specifications. The workflow supports fully parallel redesign: engineers modify their module to satisfy $\\hat{G}^{(j)}(i\\omega)\\in\\mathcal{E}^{(j)}(\\omega)$, and, if all modules comply, the assembled system satisfies $\\hat{G}_A(i\\omega)\\in\\mathcal{E}_A(\\omega)$. Demonstrations on a two-DOF mass-spring-damper, a pillar-plate benchmark, and an industrial wire bonder show the method’s scalability, the trade-off between conservatism and redesign freedom, and the computational advantages of modular verification over full-system reanalysis. The approach offers a practical path toward faster, cost-effective modular redesign for complex mechatronic systems with rigorous FRF-based guarantees.

Abstract

Complex mechatronic systems are typically composed of interconnected modules, often developed by independent teams. This development process challenges the verification of system specifications before all modules are integrated. To address this challenge, a modular redesign framework is proposed in this paper. Herein, first, allowed changes in the dynamics (represented by frequency response functions (FRFs)) of the redesigned system are defined with respect to the original system model, which already satisfies system specifications. Second, these allowed changes in the overall system dynamics (or system redesign specifications) are automatically translated to dynamics (FRF) specifications on module level that, when satisfied, guarantee overall system dynamics (FRF) specifications. This modularity in specification management supports local analysis and verification of module design changes, enabling design teams to work in parallel without the need to iteratively rebuild the system model to check fulfilment of system FRF specifications. A modular redesign process results that shortens time-to-market and decreases redesign costs. The framework's effectiveness is demonstrated through three examples of increasing complexity, highlighting its potential to enable modular mechatronic system (re)design.

Modular Redesign of Mechatronic Systems: Formulation of Module Specifications Guaranteeing System Dynamics Specifications

TL;DR

The paper tackles the challenge of guaranteeing system-level dynamic specifications for complex, modular mechatronic systems when components are designed by separate teams. It develops a modular redesign framework that models modules with FRFs , interconnects them via a fixed structure , and defines system-level FRF bounds through using and such that . A central theorem links module-level specifications to the assembly specification via a nominal system and a positive-definite condition on a Schur-complement-like matrix, enabling an alternating-LMI algorithm to automatically synthesize module FRF specifications. The workflow supports fully parallel redesign: engineers modify their module to satisfy , and, if all modules comply, the assembled system satisfies . Demonstrations on a two-DOF mass-spring-damper, a pillar-plate benchmark, and an industrial wire bonder show the method’s scalability, the trade-off between conservatism and redesign freedom, and the computational advantages of modular verification over full-system reanalysis. The approach offers a practical path toward faster, cost-effective modular redesign for complex mechatronic systems with rigorous FRF-based guarantees.

Abstract

Complex mechatronic systems are typically composed of interconnected modules, often developed by independent teams. This development process challenges the verification of system specifications before all modules are integrated. To address this challenge, a modular redesign framework is proposed in this paper. Herein, first, allowed changes in the dynamics (represented by frequency response functions (FRFs)) of the redesigned system are defined with respect to the original system model, which already satisfies system specifications. Second, these allowed changes in the overall system dynamics (or system redesign specifications) are automatically translated to dynamics (FRF) specifications on module level that, when satisfied, guarantee overall system dynamics (FRF) specifications. This modularity in specification management supports local analysis and verification of module design changes, enabling design teams to work in parallel without the need to iteratively rebuild the system model to check fulfilment of system FRF specifications. A modular redesign process results that shortens time-to-market and decreases redesign costs. The framework's effectiveness is demonstrated through three examples of increasing complexity, highlighting its potential to enable modular mechatronic system (re)design.
Paper Structure (11 sections, 1 theorem, 25 equations, 17 figures, 2 tables, 1 algorithm)

This paper contains 11 sections, 1 theorem, 25 equations, 17 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. General framework for modular modelling
  3. User-defined system FRF specifications
  4. Computation of module specifications with assembly specification guarantees
  5. Use case systems
  6. Two DOF mass-spring-damper model
  7. Plate Pillar model
  8. Wire bonder model
  9. Conclusions
  10. Acknowledgments
  11. System specification examples

Key Result

Theorem 1

Consider the nominal system in (eq:N) and the specification-related scaling matrices in (eq:W). If there exists such that holds$A^H$ denotes the conjugate transpose of $A$., where, given that $I_n$ denotes an identity matrix of dimension $\mathbb{R}^{n\times n}$, then, satisfaction of the module specifications for all $\omega \in \Omega$, i.e., for all $j=1,2,\dots,k$, implies satisfaction of

Figures (17)

  • Figure 1: Integrated design procedure.
  • Figure 2: Modular design procedure.
  • Figure 3: A schematic example of the modular modelling framework with a fixed interconnected structure $\mathcal{K}$ where a) given the original system model and b) the redesigned system model.
  • Figure 4: Two equivalent visualizations of an original system FRF $G_A(i\omega)$, specifications $\mathcal{E}_A(\omega)$, and a redesigned system FRF $\hat{G}_A \in \mathcal{E}_A$. In addition, three specific frequency points are highlighted to show that $\mathcal{E}_A(\omega)$ not only restricts the magnitude, but also the phase of $\hat{G}_A(i\omega)$.
  • Figure 5: Visualization of the proposed work-flow to enable modular redesign with guarantees on the system specifications.
  • ...and 12 more figures

Theorems & Definitions (10)

  • Remark 1
  • Definition 1
  • Remark 2
  • Definition 2
  • Theorem 1
  • proof
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6