Bifurcation analysis and control in a second-order DC–AC inverter with quasi-PIR controller

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-02-24 DOI:10.1016/j.cnsns.2025.108702

Ronghua Wu , Xiaohong Zhang , Wei Jiang , Shaojiang Zhong

{"title":"Bifurcation analysis and control in a second-order DC–AC inverter with quasi-PIR controller","authors":"Ronghua Wu , Xiaohong Zhang , Wei Jiang , Shaojiang Zhong","doi":"10.1016/j.cnsns.2025.108702","DOIUrl":null,"url":null,"abstract":"<div><div>The evolution of complex dynamics in the second-order inverter with quasi-proportional integral resonance (PIR) controller is analyzed detailly in this paper, it is revealed that this inverter’s state changes not only from period-1 to chaos via period-doubling bifurcation, but also from stability to low-frequency oscillation via Hopf bifurcation, which will decrease the working life of the inverter. On the basis of this discovery, a logarithmic proportional time-delay feedback control strategy is proposed. The controlled object’s output current first subtracts to its own delay a period of time to form a difference term, which is subsequently fed into a proportional link to make difference with the constant <span><math><mi>e</mi></math></span>. The absolute value result is then fed into the natural logarithm and proportional links to obtain the control term, which is lastly applied to the controlled object in a feedback manner. Furthermore, the range of the feedback proportional coefficient is obtained via analyzing the controlled object’s stability. The comparative analysis shows that this strategy enhances the stability domain for each parameter by more than 8% in the quasi-PIR controlled second-order inverter, and stabilizes the low frequency oscillation caused by Hopf bifurcation.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108702"},"PeriodicalIF":3.4000,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570425001133","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

The evolution of complex dynamics in the second-order inverter with quasi-proportional integral resonance (PIR) controller is analyzed detailly in this paper, it is revealed that this inverter’s state changes not only from period-1 to chaos via period-doubling bifurcation, but also from stability to low-frequency oscillation via Hopf bifurcation, which will decrease the working life of the inverter. On the basis of this discovery, a logarithmic proportional time-delay feedback control strategy is proposed. The controlled object’s output current first subtracts to its own delay a period of time to form a difference term, which is subsequently fed into a proportional link to make difference with the constant

e

. The absolute value result is then fed into the natural logarithm and proportional links to obtain the control term, which is lastly applied to the controlled object in a feedback manner. Furthermore, the range of the feedback proportional coefficient is obtained via analyzing the controlled object’s stability. The comparative analysis shows that this strategy enhances the stability domain for each parameter by more than 8% in the quasi-PIR controlled second-order inverter, and stabilizes the low frequency oscillation caused by Hopf bifurcation.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.