Stability optimization of time-delay systems with zero-location constraints applied to non-collocated vibration suppression
We present an active control method for achieving non-collocated vibration absorption, implemented on a lumped mass system. The task of suppressing vibrations at a number of frequencies, at a target mass is recast into a problem of assigning zeros of the transfer function from the external excitatio...
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| Published in | Mechanical systems and signal processing Vol. 208; p. 110886 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
15.02.2024
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| Subjects | |
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| Abstract | We present an active control method for achieving non-collocated vibration absorption, implemented on a lumped mass system. The task of suppressing vibrations at a number of frequencies, at a target mass is recast into a problem of assigning zeros of the transfer function from the external excitation force to the position of the target mass. The controller design involves computing the controller parameters by utilizing the available output feedback to directly assign a set of zeros on the imaginary axis while simultaneously preserving the overall stability with a sufficient margin. The design also takes into account delays in the feedback path. The presence of delays leads to an infinite dimensional system for which, there exists in general, infinitely many characteristic roots. The requirement of achieving sufficient damping in the resulting closed-loop system together with suppressing vibrations of the desired frequency leads to a constrained optimization problem of minimizing the spectral abscissa function subject to zero-location constraints. These constraints exhibit polynomial dependence on the controller parameters. We present two approaches for controller parameterization for the single and multiple input case. Both approaches are based on constraint elimination and exploit the property that the constraints are affine in a selection of the gain parameters. Finally, the methodology is verified by simulating on a spring–mass–damper system following which, it is then validated experimentally on a laboratory setup. |
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| AbstractList | We present an active control method for achieving non-collocated vibration absorption, implemented on a lumped mass system. The task of suppressing vibrations at a number of frequencies, at a target mass is recast into a problem of assigning zeros of the transfer function from the external excitation force to the position of the target mass. The controller design involves computing the controller parameters by utilizing the available output feedback to directly assign a set of zeros on the imaginary axis while simultaneously preserving the overall stability with a sufficient margin. The design also takes into account delays in the feedback path. The presence of delays leads to an infinite dimensional system for which, there exists in general, infinitely many characteristic roots. The requirement of achieving sufficient damping in the resulting closed-loop system together with suppressing vibrations of the desired frequency leads to a constrained optimization problem of minimizing the spectral abscissa function subject to zero-location constraints. These constraints exhibit polynomial dependence on the controller parameters. We present two approaches for controller parameterization for the single and multiple input case. Both approaches are based on constraint elimination and exploit the property that the constraints are affine in a selection of the gain parameters. Finally, the methodology is verified by simulating on a spring–mass–damper system following which, it is then validated experimentally on a laboratory setup. |
| ArticleNumber | 110886 |
| Author | Bušek, Jaroslav Vyhlídal, Tomáš Michiels, Wim Kuře, Matěj Saldanha, Adrian |
| Author_xml | – sequence: 1 givenname: Adrian orcidid: 0000-0002-9978-6343 surname: Saldanha fullname: Saldanha, Adrian organization: Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001, Leuven, Belgium – sequence: 2 givenname: Wim orcidid: 0000-0002-0877-0080 surname: Michiels fullname: Michiels, Wim email: wim.michiels@kuleuven.be organization: Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001, Leuven, Belgium – sequence: 3 givenname: Matěj orcidid: 0000-0002-5001-9119 surname: Kuře fullname: Kuře, Matěj organization: Department of Instrumentation and Control Engineering, Faculty of Mechanical Engineering, and Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Technická 4, 16000, Prague 6, Czechia – sequence: 4 givenname: Jaroslav orcidid: 0000-0002-4220-7291 surname: Bušek fullname: Bušek, Jaroslav organization: Department of Instrumentation and Control Engineering, Faculty of Mechanical Engineering, and Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Technická 4, 16000, Prague 6, Czechia – sequence: 5 givenname: Tomáš orcidid: 0000-0002-1544-8575 surname: Vyhlídal fullname: Vyhlídal, Tomáš email: tomas.vyhlidal@fs.cvut.cz organization: Department of Instrumentation and Control Engineering, Faculty of Mechanical Engineering, and Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Technická 4, 16000, Prague 6, Czechia |
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| Keywords | Time-delay systems Vibration suppression Spectral optimization Zeros placement |
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| Snippet | We present an active control method for achieving non-collocated vibration absorption, implemented on a lumped mass system. The task of suppressing vibrations... |
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| SubjectTerms | Spectral optimization Time-delay systems Vibration suppression Zeros placement |
| Title | Stability optimization of time-delay systems with zero-location constraints applied to non-collocated vibration suppression |
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