{"title":"A periodically-switched ODE model for N-bunch beamloading in a storage ring","authors":"C. Schwartz, A. Nassiri","doi":"10.1109/PAC.1999.795452","DOIUrl":null,"url":null,"abstract":"A new baseband formulation of the coupled cavity/longitudinal-bunch ODEs is derived. Assuming linearity, a model of the form x/spl dot/(t)=A(t)x(t)+B(t)u(t) arises, where A(t) and B(t) are piecewise constant, and periodic with the revolution period T/sub 0/. Such models, known in the control community as (periodic) switched systems, have known (in)stability criteria and control theoretic properties, which can be useful in the analysis and control of multiple bunch beamloading.","PeriodicalId":20453,"journal":{"name":"Proceedings of the 1999 Particle Accelerator Conference (Cat. No.99CH36366)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1999-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 1999 Particle Accelerator Conference (Cat. No.99CH36366)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/PAC.1999.795452","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A new baseband formulation of the coupled cavity/longitudinal-bunch ODEs is derived. Assuming linearity, a model of the form x/spl dot/(t)=A(t)x(t)+B(t)u(t) arises, where A(t) and B(t) are piecewise constant, and periodic with the revolution period T/sub 0/. Such models, known in the control community as (periodic) switched systems, have known (in)stability criteria and control theoretic properties, which can be useful in the analysis and control of multiple bunch beamloading.
推导了耦合腔/纵束ode的一种新的基带公式。假设线性，一个形式为x/spl点/(t)= a (t)x(t)+B(t)u(t)的模型出现，其中a (t)和B(t)是分段常数，并且周期为t/下标0/。这种模型在控制界被称为(周期)切换系统，具有已知的(in)稳定性准则和控制理论性质，可用于多束波束加载的分析和控制。
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