驱动忆阻性负载逆变系统中Hopf分岔控制的研究  

Study on Control of Hopf Bifurcation in Inverter with Memristive Load

作　　者：曹红博 王发强 CAO Hongbo;WANG Faqiang(School of Electrical Engineering,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学电气工程学院,西安710049

出　　处：《西安交通大学学报》2023年第7期38-49,共12页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51377124)。

摘　　要：针对驱动忆阻性负载逆变系统易发生Hopf分岔、导致系统出现振荡频率大于工频频率但远小于开关频率的不稳定现象,提出交流输出电压微分反馈控制方法,实现了对系统中Hopf分岔行为的有效控制。驱动忆阻性负载逆变系统因Hopf分岔引起的振荡现象属于慢尺度不稳定行为,因此建立了交流输出电压微分反馈控制下系统的平均模型,基于谐波平衡法求得系统变量的周期解,以Floquet理论揭示了系统中出现慢尺度不稳定行为的机理,给出了确保系统稳定运行的控制参数取值范围。此外,通过计算Floquet乘数对积分参数的敏感值,分析了交流输出电压微分反馈控制下系统在积分参数受到扰动时的抗干扰能力。研究结果表明:交流输出电压微分反馈控制方法可有效控制驱动忆阻性负载逆变系统中的Hopf分岔行为,能大幅度增加确保系统稳定的控制参数取值范围,并可增强系统的抗干扰能力。最后,通过PSpice仿真结果和电路实验结果的一致性,验证了理论分析的正确性和所提出的控制方法的有效性。Inverter with memristive load is prone to Hopf bifurcation;therefore it is subject to instability,which means the oscillation frequency is greater than the line frequency but much smaller than the switching frequency in the system.To address this problem,in this paper,an AC output voltage differential feedback control is proposed to effectively control the Hopf bifurcation in system.The oscillations caused by Hopf bifurcation in the inverter with memristive load are slow-scale instability behavior.Considering this,an average model of the system under AC output voltage differential feedback control is built.The harmonic balance method is used to obtain the periodic solutions of the system variables.Then the mechanism of the slow-scale instability is illustrated according to Floquet theory,and the control parameter range to ensure stable system operation is provided accordingly.In addition,by calculating the sensitive value of the Floquet multiplier with respect to the integral parameter,the anti-interference ability of the system under AC output voltage differential feedback control when the integral parameter is disturbed is analyzed.The results of theoretical research indicate that the AC output voltage differential feedback control is effective to control the Hopf bifurcation in system,and will greatly widen the control parameter range that ensures stable system operation while enhancing the anti-interference ability of the system.At the end,the correctness of the theoretical analyses and the effectiveness of the proposed control method are verified by the consistency between PSpice simulation and physical experiment.

关 键 词：忆阻性负载 逆变系统 谐波平衡法 FLOQUET理论 分岔控制 

分 类 号：O322[理学—一般力学与力学基础] TM132[理学—力学]