基于非线性反馈的轧机主传动机电耦联扭转系统的分岔控制  

Bifurcation Control for Electromechanical Coupling Vibration in Rolling Mill Drive System Based on Nonlinear Feedback

作　　者：刘彬[1] 刘爽[1] 张业宽[1] 闻岩[2] 

机构地区：[1]燕山大学信息科学与工程学院,秦皇岛066004 [2]燕山大学机械工程学院,秦皇岛066004

出　　处：《机械工程学报》2010年第8期160-166,共7页Journal of Mechanical Engineering

基　　金：国家'十一五'重大科技攻关(2007BAF02B10);河北省自然科学基金(F2008000882);河北省教育厅科学重点研究(ZH2007102)资助项目

摘　　要：针对轧机在轧制过程中轧辊与轧件间润滑条件变化引起系统失稳振荡,以及轧机主传动系统具有复杂机电耦联的特点,应用Lagrange-Maxwell原理建立一类含非线性摩阻的轧机主传动机电耦联扭转系统的非线性动力学方程,利用非线性动态分岔理论,分析该系统的稳定性,给出系统发生Hopf分岔的充要条件及周期运动稳定性的判别方法,分析超临界分岔和亚临界分岔对主传动系统扭转振荡的影响。为抑制传动系统因Hopf分岔引起的失稳振荡,选取驱动电动机定子电压为控制量,引入电动机速度反馈,构造非线性状态反馈控制器,并采用多尺度和谐波平衡法确定控制器参数,对系统的Hopf分岔点进行转移,并控制极限环的稳定性和幅值,该控制方法简单、易实现,数值模拟验证了所设计控制器的有效性。Considering unstable oscillation in the process of rolling mill caused by lubrication condition change between roller and rolled piece,and characteristics of complex electromechanical coupling in main drive system,the nonlinear dynamics equation of coupled electromechanical drive system of rolling mill is established with nonlinear friction drag based on Lagrange-Maxwell theory.According to dynamical bifurcation theory the stability of system is analyzed,and the necessary and sufficient condition of Hopf bifurcation and periodic motion＇s stability are given,besides that,the influence of supercritical and subcritical bifurcation on torsional vibration is analyzed.In order to suppress instability oscillation of drive system caused by Hopf bifurcation,a nonlinear feedback controller is proposed,choosing stator voltage of drive electric motor as control variable and motor velocity as state feedback,and controller parameters are determined by using multi-scale and harmonic balance method.After including the controller,the Hopf bifurcation points of system can be thansferred,and the stability and amplitude of limit cycle are controlled.This control method is simple and easy to put into practice.Numerical simulation verifies the effectiveness of the designed controller.

关 键 词：轧机主传动系统 机电耦联系统 非线性反馈控制 HOPF分岔 极限环 

分 类 号：TH113.1[机械工程—机械设计及理论]