含PID控制器的迟滞非线性控制系统的主共振及奇异性

Principal resonance and singularity of a hysteretic nonlinear control system with a PID controller

针对含PID控制器的迟滞非线性闭环控制系统,用Backlash神经网络模型逼近系统迟滞非线性部分,建立动力学模型。研究了系统在简谐激励下的主共振,利用平均法得到了系统的分岔方程,并用奇异性理论进行了分析,得到了转迁集和分岔图。另外还研究了系统参数对开折参数和分岔参数的影响,从而为系统参数的选择提供理论指导。

A hysteretic closed-loop nonlinear control system with a PID controller was studied.A model based on Backlash neutral network was adopted to approach the hysteretic nonlinear part of the system,the dynamic model of the system was established.The principal resonance of the system under a simple harmonic excitation was studied.The bifurcation equation of the system was obtained with the averaging method,and then the system＇s singularity was analyzed completely,the transition sets and bifurcation plots were gained.The effects of the system＇s parameters on its unfolding and bifurcation parameters were discussed. The results provided a theoretical guidance for selecting the system＇s parameters.