Frequency weighted H2 optimization of multi-mode input shaper
An optimization-based design of a robust multi-mode input shaper is presented with an embedded weighting of the frequency response. By prefixing the delay length in the shaper, the optimization design task is formulated as a standard quadratic programming problem. The shaper robustness in terms of z...
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| Published in | Automatica (Oxford) Vol. 121 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.11.2020
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| Abstract | An optimization-based design of a robust multi-mode input shaper is presented with an embedded weighting of the frequency response. By prefixing the delay length in the shaper, the optimization design task is formulated as a standard quadratic programming problem. The shaper robustness in terms of zeroed or upper-bounded residual vibration function for the modes to be precompensated is imposed via the equality and inequality constraints. As the main result, an additional degree of freedom in the shaper design is introduced via parametrization of the quadratic form cost matrix and utilized to modulate the amplitude frequency response over a given frequency range. In particular, this allows to embed the high-frequency roll-off to the shaper and improve its insensitivity to modelling errors by adjusting its stop-band response. The proposed shaper design is demonstrated and experimentally validated on a problem of positioning a flexible manipulator arm with multiple oscillatory modes. |
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| AbstractList | An optimization-based design of a robust multi-mode input shaper is presented with an embedded weighting of the frequency response. By prefixing the delay length in the shaper, the optimization design task is formulated as a standard quadratic programming problem. The shaper robustness in terms of zeroed or upper-bounded residual vibration function for the modes to be precompensated is imposed via the equality and inequality constraints. As the main result, an additional degree of freedom in the shaper design is introduced via parametrization of the quadratic form cost matrix and utilized to modulate the amplitude frequency response over a given frequency range. In particular, this allows to embed the high-frequency roll-off to the shaper and improve its insensitivity to modelling errors by adjusting its stop-band response. The proposed shaper design is demonstrated and experimentally validated on a problem of positioning a flexible manipulator arm with multiple oscillatory modes. |
| ArticleNumber | 109202 |
| Author | Goubej, Martin Schlegel, Miloš Vyhlídal, Tomáš |
| Author_xml | – sequence: 1 givenname: Martin surname: Goubej fullname: Goubej, Martin email: mgoubej@ntis.zcu.cz organization: NTIS Research Centre, Faculty of Applied Sciences, University of West Bohemia, Technická 14, 306 14 Pilsen, Czechia – sequence: 2 givenname: Tomáš surname: Vyhlídal fullname: Vyhlídal, Tomáš email: tomas.vyhlidal@fs.cvut.cz organization: Department of Instrumentation and Control Engineering, and Center of Advanced Aerospace Technology, Faculty of Mechanical Engineering, Czech Technical University in Prague, Technická 4, 166 07, Prague 6, Czechia – sequence: 3 givenname: Miloš surname: Schlegel fullname: Schlegel, Miloš email: schlegel@kky.zcu.cz organization: NTIS Research Centre, Faculty of Applied Sciences, University of West Bohemia, Technická 14, 306 14 Pilsen, Czechia |
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| DOI | 10.1016/j.automatica.2020.109202 |
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| Keywords | Input shaping Time delay Multiple modes H2 optimal design |
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| References | Smith (b26) 1957; 45 Van den Broeck, Diehl, Swevers (b28) 2010; 18 Baumgart, Pao (b1) 2007; 43 Tuttle, Seering (b27) 1994 Meckl, Arestides (b14) 1998 Van den Broeck, L., Pipeleers, G., De Caigny, J., Demeulenaere, B., Swevers, J., & De Schutter, J. (2008). A linear programming approach to design robust input shaping. In Singer, Seering (b19) 1990; 112 Hyde, Seering (b11) 1991 Schlegel, Goubej (b18) 2010 Pilbauer, Michiels, Vyhlídal (b16) 2017; 354 Robertson, Singhose (b17) 2001 (pp. 80–85). Vyhlídal, Kučera, Hromčík (b31) 2013; 49 Goubej, Schlegel (b9) 2014 Kungurtsev, Pilbauer, Vyhlídal, Hromčík, Michiels (b12) 2017; 50 Singh, Vadali (b20) 1995; 62 Singhose, Porter, Tuttle, Singer (b24) 1997; 119 Cole, Wongratanaphisan (b4) 2011; 133 Singhose, Crain, Seering (b22) 1997; 144 Singhose, Seering, Singer (b25) 1994; 116 Cole (b2) 2011; 47 Goubej (b7) 2014 Pilbauer, Michiels, Vyhlidal (b15) 2016; 49 Singhose, Eloundou, Lawrence (b23) 2010; 33 Goubej (b8) 2016 Lim, Stevens, How (b13) 1999; 121 Cole, Wongratanaphisan (b5) 2013; 18 Elliott (b6) 1987 Hromcik, Vyhlidal (b10) 2017; 62 Vyhlídal, Hromčík (b30) 2015; 59 Cole (b3) 2012; 48 Singhose (b21) 2009; 10 |
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| SubjectTerms | [formula omitted] optimal design Input shaping Multiple modes Time delay |
| Title | Frequency weighted H2 optimization of multi-mode input shaper |
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