Frequency Response Function identification for multivariable motion control: Optimal experiment design with element-wise constraints
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 eleme...
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| Published in | Mechatronics (Oxford) Vol. 71; p. 102440 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.11.2020
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| ISSN | 0957-4158 1873-4006 1873-4006 |
| DOI | 10.1016/j.mechatronics.2020.102440 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 102440 |
| Author | Oomen, Tom Dirkx, Nic van de Wijdeven, Jeroen |
| Author_xml | – sequence: 1 givenname: Nic surname: Dirkx fullname: Dirkx, Nic email: nic.dirkx@asml.com organization: ASML Research Mechatronics & Control, Veldhoven, The Netherlands – sequence: 2 givenname: Jeroen surname: van de Wijdeven fullname: van de Wijdeven, Jeroen organization: ASML Research Mechatronics & Control, Veldhoven, The Netherlands – sequence: 3 givenname: Tom surname: Oomen fullname: Oomen, Tom organization: Eindhoven University of Technology, Department of Mechanical Engineering, Eindhoven, The Netherlands |
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| Cites_doi | 10.1016/j.automatica.2004.11.021 10.1109/TAC.2014.2351656 10.23919/EUSIPCO.2017.8081370 10.1007/s101070050006 10.1109/TIM.2006.887036 10.1109/CDC.2009.5400682 10.1016/S1474-6670(17)58365-2 10.1287/moor.1070.0268 10.1080/10556789808805690 10.1016/S0967-0661(01)00166-6 10.1016/S1474-6670(17)39898-1 10.1016/j.automatica.2008.05.022 10.1016/j.automatica.2007.09.011 10.1016/j.ifacol.2019.11.744 10.1109/CDC.1974.270473 10.1016/j.automatica.2006.05.016 10.1016/j.automatica.2017.04.039 10.1109/ACC.2014.6858927 10.1109/TAC.1974.1100701 10.4310/CIS.2011.v11.n3.a1 10.1007/BF02288367 10.3182/20140824-6-ZA-1003.02690 10.1145/227683.227684 |
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| Keywords | Multivariable systems System identification Rank-constrained optimization Optimal experiment design Frequency response function Multisines |
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| Title | Frequency Response Function identification for multivariable motion control: Optimal experiment design with element-wise constraints |
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