非线性双环反馈数据采样系统的动态行为

The Dynamic Behavior of a Nonlinear Double loop Feedback Sampled-data System

在控制系统中利用非线性双环反缋使非稳定系统成为稳定是一个重要的科研课题,本文就此作了研究.为便于分析及硬件实现,这里采用了近似于铁磁电感特性(不包括饱和部分)的分段线性双环反馈.在参数域内详细分析了平衡点的特性;重点研究了反聩参数对该系统动态行为的影响.通过计算机模拟,观察到该系统动态行为中明显的混沌现象以及混沌吸引子的自相似结构.最后,在理论上严格地证明了该系统中混沌现象的存在性.从而说明,为避免此类系统中混沌现象的出现,必须选择恰当的反馈参数.

In control system, to stabilize an unstable system by using a nonlinear double-loop feedback is an important method.This paper reports a result concerning this subject. A piecewise linear double-loop feedback similar to the characteristics of ferromagnetic inductor (excluding the saturation part) is used for analytical and parctical convenience. The characteristics of the equilibria in the parameter region are analized in detail, and the effects of the feedback parameter to the dynamics of the system are studied emphatically. The self-similarity structures of the choatic attractors are observed clearly. And the existence of choatic behavior of the system is proved by using Marotto theorem,thus showing the importance of choosing suitable feed-back parameters.