Luc-André Grégoire, Mohammad Sleiman, Handy Fortin-Blanchette, K. Al-haddad
{"title":"Numerical stability of multi-rate system using Lyapunov's theorem: Applied to real-time simulation","authors":"Luc-André Grégoire, Mohammad Sleiman, Handy Fortin-Blanchette, K. Al-haddad","doi":"10.1109/ICIT.2015.7125472","DOIUrl":null,"url":null,"abstract":"This paper proposes a method to analyse stability of multi-rate system. Multi-rate systems are used to simulate different part of the circuit with different sampling rate. This allows to reduce computational burden of stiff system; by choosing the most appropriate time-step according to the time constant of the phenomena studied. Traditionally, stability of discrete system is done by studying the eigenvalues of the system which can only uses a single sampling time and therefore cannot be applied to multi-rate systems. Many examples, where simulation is done with multiple rate, can be found in literature with no proof of stability other than simulation results. In this paper, multi-rate system are first represented as non-linear system using a single time-step and their stability is then demonstrated using Lyapunov's theorem. The proposed method is supported by a numerical example.","PeriodicalId":156295,"journal":{"name":"2015 IEEE International Conference on Industrial Technology (ICIT)","volume":"77 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 IEEE International Conference on Industrial Technology (ICIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICIT.2015.7125472","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
This paper proposes a method to analyse stability of multi-rate system. Multi-rate systems are used to simulate different part of the circuit with different sampling rate. This allows to reduce computational burden of stiff system; by choosing the most appropriate time-step according to the time constant of the phenomena studied. Traditionally, stability of discrete system is done by studying the eigenvalues of the system which can only uses a single sampling time and therefore cannot be applied to multi-rate systems. Many examples, where simulation is done with multiple rate, can be found in literature with no proof of stability other than simulation results. In this paper, multi-rate system are first represented as non-linear system using a single time-step and their stability is then demonstrated using Lyapunov's theorem. The proposed method is supported by a numerical example.