基于延时反馈的电力非线性系统Hopf分岔反控制  

Anti-Control of Hopf Bifurcation of a Power Nonlinear System Based on Time-Delayed Feedback

作　　者：张中华[1] 袁惠群[2] 付景超[1] 

机构地区：[1]东北电力大学理学院,吉林吉林132012 [2]东北大学机械工程与自动化学院,辽宁沈阳110819

出　　处：《数学的实践与认识》2015年第21期156-164,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11201057);吉林省科技发展计划项目(20130101065JC);博士科研启动基金项目(BSJXM-201427)

摘　　要：针对无刷直流电机等效非线性动力系统,设计基于Washout滤波器辅助和延迟反馈相结合的控制器对系统进行Hopf分岔反控制.根据Hopf分岔理论讨论系统在稳定的平衡点处发生Hopf分岔时,延迟参数应满足的条件.讨论结果表明,当延迟参数满足一定条件时,可使系统在所期望的平衡点处发生Hopf分岔,从而实现系统的Hopf分岔反控制.此外,方法也可用于混沌控制.数值仿真证明了控制器的有效性.For the equivalent nonlinear dynamic system of brushless DC motor, the con- troller based on Washout-filter-aided and time-delayed feedback is designed to control the Hopf bifurcation behaviors of system. Hopf bifurcation theory is used to discuss the parame- ter conditions under which controlled system undergoes Hopf bifurcation at stable equilibrium point. The researches shows that the Hopf bifurcation occurs at a desired location when delay parameter satisfies certain conditions, thus the anti- control of Hopf bifurcation is achieved. Besides, the method can be used to control chaos. Some numerical simulations are given to illustrate the effectiveness of the results found.

关 键 词：非线性动力系统 HOPF分岔 分岔反控制 Washout滤波器 延迟反馈 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]