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.

中文翻译：

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多变量运动控制的频率响应函数识别：具有元素约束的优化实验设计

摘要 频率响应函数 (FRF) 在机电系统中是必不可少的，其应用范围从系统设计和验证到控制器设计和诊断。本文的目的是优化设计实验，用于受元素功率约束的多变量运动系统的 FRF 识别。建立了一个多变量激励设计框架，明确地解决了要识别的系统的频率方向性。设计问题涉及解决秩约束优化问题，该问题在大多数情况下是非凸和 NP 难的。提出了两种近似解决这个问题的算法，它们依赖于原始问题的凸（半定）松弛。此外，还提供了几种特殊情况的精确解决方案。这两种算法被证明克服了传统励磁设计的局限性。7 × 8 晶圆台设置的实验结果证实了这一点，这表明使用所提出的技术比传统设计方法显着提高了 FRF 质量。