Details
| Original language | English |
|---|---|
| Pages (from-to) | 245-257 |
| Number of pages | 13 |
| Journal | Applied Mathematics and Computation |
| Volume | 78 |
| Issue number | 2-3 |
| Publication status | Published - 11 Jun 1996 |
| Externally published | Yes |
Abstract
Almost all undesirable vibrations in technical systems are caused by unknown or uncertain excitations. In cases where these vibrations need to be actively attenuated it is very often not possible to equip the system for that purpose with enough actuators. Also, in general, necessary control actions via these actuators cannot be employed over a desired range because of their boundedness. We propose a control scheme that allows for these control deficiencies no matter how small the bounds of the controllers are and how many actuators are implemented. The scheme is based on Lyapunov stability theory; it relates to robustness vis-à-vis unknown but bounded excitations. In addition to the controller design via Lyapunov theory, a stability analysis is carried out to compute the ball of ultimate boundedness for a certain class of Lyapunov functions. To demonstrate the effectiveness of the control we consider a mechanical system with 2 degrees of freedom where the masses are elastically coupled. The unknown excitation acts on one of these masses. Two controllers are compared particularly with respect to attenuation of vibrations.
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Applied Mathematics and Computation, Vol. 78, No. 2-3, 11.06.1996, p. 245-257.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Robust constrained control for vibration suppression of mismatched systems
AU - Reithmeier, E.
AU - Leitmann, G.
PY - 1996/6/11
Y1 - 1996/6/11
N2 - Almost all undesirable vibrations in technical systems are caused by unknown or uncertain excitations. In cases where these vibrations need to be actively attenuated it is very often not possible to equip the system for that purpose with enough actuators. Also, in general, necessary control actions via these actuators cannot be employed over a desired range because of their boundedness. We propose a control scheme that allows for these control deficiencies no matter how small the bounds of the controllers are and how many actuators are implemented. The scheme is based on Lyapunov stability theory; it relates to robustness vis-à-vis unknown but bounded excitations. In addition to the controller design via Lyapunov theory, a stability analysis is carried out to compute the ball of ultimate boundedness for a certain class of Lyapunov functions. To demonstrate the effectiveness of the control we consider a mechanical system with 2 degrees of freedom where the masses are elastically coupled. The unknown excitation acts on one of these masses. Two controllers are compared particularly with respect to attenuation of vibrations.
AB - Almost all undesirable vibrations in technical systems are caused by unknown or uncertain excitations. In cases where these vibrations need to be actively attenuated it is very often not possible to equip the system for that purpose with enough actuators. Also, in general, necessary control actions via these actuators cannot be employed over a desired range because of their boundedness. We propose a control scheme that allows for these control deficiencies no matter how small the bounds of the controllers are and how many actuators are implemented. The scheme is based on Lyapunov stability theory; it relates to robustness vis-à-vis unknown but bounded excitations. In addition to the controller design via Lyapunov theory, a stability analysis is carried out to compute the ball of ultimate boundedness for a certain class of Lyapunov functions. To demonstrate the effectiveness of the control we consider a mechanical system with 2 degrees of freedom where the masses are elastically coupled. The unknown excitation acts on one of these masses. Two controllers are compared particularly with respect to attenuation of vibrations.
UR - http://www.scopus.com/inward/record.url?scp=23644457965&partnerID=8YFLogxK
U2 - 10.1016/0096-3003(96)00012-4
DO - 10.1016/0096-3003(96)00012-4
M3 - Article
AN - SCOPUS:23644457965
VL - 78
SP - 245
EP - 257
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 2-3
ER -