Frequency Response Function identification for multivariable motion control: Optimal experiment design with element-wise constraints

Nic Dirkx (Corresponding author), Jeroen van de Wijdeven, Tom Oomen

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Frequency Response Functions (FRFs) are essential in mechatronic systems and its application ranges from system design and validation to controller design and diagnostics. The aim of this paper is to optimally design experiments for FRF identification of multivariable motion systems subject to element-wise power constraints. A multivariable excitation design framework is established that explicitly addresses the frequency-wise directionality of the system to be identified. The design problem involves solving a rank-constrained optimization problem, which is non-convex and NP-hard in most cases. Two algorithms to solving this problem approximately are presented that rely on a convex (semi-definite) relaxation of the original problem. Additionally, exact solutions for several special cases are presented. The two algorithms are shown to overcome the limitations of traditional excitation design. This is confirmed by experimental results from a 7 × 8 wafer stage setup, which show a significant improvement of the FRF quality using the proposed techniques over traditional design approaches.

Original languageEnglish
Article number102440
Number of pages12
JournalMechatronics
Volume71
DOIs
Publication statusPublished - Nov 2020

Keywords

  • Frequency response function
  • Multisines
  • Multivariable systems
  • Optimal experiment design
  • Rank-constrained optimization
  • System identification

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