%0 Generic %1 Poster_DDAYS05_PH %A Hövel, P. %A Schöll, E. %A Amann, A. %A Just, W. %D 2005 %K imported %T Time-delayed feedback control of chaotic systems with latency and low-pass filtering %X Chaotic systems can be controlled by time-delayed feedback methods. We perform a linear stability analysis of the system and present analytical results using the Lambert function. We investigate situations when latency times associated with the generation and injection of the control force cannot be ignored. We derive a theoretical explanation for experimentally observed, nontrivial features of the domain of control, e.g., gaps, maximum latency times. The explanation is done in the background of Floquet theory and we take both the unstable eigenmode and a single stable eigenmode into account. The presence of high frequency oscillations in the eedback signal can reduce the effectiveness of the control scheme. We show that this limitation can be eliminated by low-pass filtering the feedback signal before the generation of the control force. Thus, a filtered time-delayed feedback method leads to a separation of the timescales present in the system. The effects of a low-pass filter included in the control loop are discussed in the frequency regime using transfer functions.

@misc{Poster_DDAYS05_PH, abstract = {Chaotic systems can be controlled by time-delayed feedback methods. We perform a linear stability analysis of the system and present analytical results using the Lambert function. We investigate situations when latency times associated with the generation and injection of the control force cannot be ignored. We derive a theoretical explanation for experimentally observed, nontrivial features of the domain of control, e.g., gaps, maximum latency times. The explanation is done in the background of Floquet theory and we take both the unstable eigenmode and a single stable eigenmode into account. The presence of high frequency oscillations in the eedback signal can reduce the effectiveness of the control scheme. We show that this limitation can be eliminated by low-pass filtering the feedback signal before the generation of the control force. Thus, a filtered time-delayed feedback method leads to a separation of the timescales present in the system. The effects of a low-pass filter included in the control loop are discussed in the frequency regime using transfer functions. }, added-at = {2009-03-03T17:19:04.000+0100}, author = {H{\"o}vel, P. and Sch{\"o}ll, E. and Amann, A. and Just, W.}, biburl = {https://www.bibsonomy.org/bibtex/22d2b2c52fa07845a3dcb1f3e996d1209/bronckobuster}, howpublished = {Poster at the Dynamics Days Europe 2005}, interhash = {f3b25bc1e4f09fc088ae283b4acae46e}, intrahash = {2d2b2c52fa07845a3dcb1f3e996d1209}, keywords = {imported}, timestamp = {2009-03-03T17:19:56.000+0100}, title = {Time-delayed feedback control of chaotic systems with latency and low-pass filtering}, year = 2005 }