基于非线性动力学特性的控制设计策略

A strategy on control design base on nonlinear dynamics characteristic

通过对动力学中的非线性现象及其控制方法的探讨,研究了动力学中的非线性分岔特性,以经典的倒立振子/台车系统为例,考虑系统非线性特性,当控制变量的偏差大于某一值时,线性反馈控制难以使系统回复到原平衡位置.针对变结构控制的特点,基于动力系统中的非线性分岔特性和中心流形理论,提出了一种基于非线性的全局稳定的变结构控制策略,并可构造出相应的变结构控制器.以极限环及不稳定焦点为例进行了数值仿真,结果表明该控制设计策略具有良好的全局稳定性.

The nonlinear phenomena of dynamics and its control method were discussed. A bifurcation characteristic of nonlinear dynamics was investigated. Taking classical trolley system with bandstand as an example, considering nonlinear characteristic of the system, the linear feedback control was difficult to ensure the system revert to original balance position if the warp of control variables were larger than a fixed value. In allusion to sliding mode variable structure control system, based on bifurcation characteristic of nonlinear dynamics and centre manifodes theory, a strategy on variable structure control design of nonlinear complete stabilization was put forward, and corresponding controller can be constructed. Taking limit ring and instability focus for example, the control system was simulated. The research results revealed that the strategy on control design had favorable complete stabilization.