Dahms Thomas, Hövel Philipp, Schöll Eckehard
Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Nov;76(5 Pt 2):056201. doi: 10.1103/PhysRevE.76.056201. Epub 2007 Nov 1.
Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar [Phys. Rev. E 50, 3245 (1994)] to an unstable focus. This system represents a generic model of an unstable steady state which can be found, for instance, in Hopf bifurcation. In addition to the original controller design, we investigate effects of control loop latency and a bandpass filter on the domain of control. Furthermore, we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase. We present an analysis of the domain of control and support our results by numerical calculations.
时间延迟反馈方法可用于控制不稳定的周期轨道以及不稳定的稳态。我们展示了由索科拉尔 [《物理评论E》50, 3245 (1994)] 引入的扩展时间延迟自同步在一个不稳定焦点上的应用。该系统代表了一个不稳定稳态的通用模型，例如在霍普夫分岔中可以找到。除了原始的控制器设计，我们还研究了控制回路延迟和带通滤波器对控制域的影响。此外，我们考虑通过一个由可变相位参数化的旋转耦合矩阵将控制力耦合到系统。我们给出了对控制域的分析，并通过数值计算支持我们的结果。
