Synchronization stability of a distributed hysteresis controlled system

Liang Chen, Dehong Lian, Tingshan Wang
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引用次数: 3

Abstract

The self-oscillatory system with hysteresis has been widely studied. However, most research deal with one hysteresis element in the system, seldom discuss the multi-hysteresis controllers, not to mention interactions between them. In the paper, we take a simple model with two coupled hysteresis controlled integrators as an example to study a synchronous phenomenon, that is similar to that happened in the large-scale distributed hysteresis controlled system, e.g. the supermarket refrigeration system. In the paper, synchronization is interpreted as a limit cycle in a state space created by switching among piecewise-affine dynamical system. Stability of the resultant limit cycle is examined by a Poincar'e map. We show that the synchronization takes place if the corresponding Poincar'e map is stable.
分布式迟滞控制系统的同步稳定性
具有滞回的自振荡系统得到了广泛的研究。然而,大多数研究只涉及系统中的一个迟滞元素,很少讨论多迟滞控制器,更不用说它们之间的相互作用。本文以具有两个耦合滞回控制积分器的简单模型为例,研究了与大型分布式滞回控制系统(如超市制冷系统)类似的同步现象。本文将同步解释为由分段仿射动力系统之间的切换所产生的状态空间中的极限环。用庞加莱图检验了所得极限环的稳定性。我们证明了如果对应的庞加莱映射是稳定的,同步就会发生。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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