{"title":"一种新的基于模型的分数阶微分器及其在分数阶PID控制器中的应用","authors":"Xing Wei, Dayan Liu, D. Boutat","doi":"10.1109/CDC.2015.7402796","DOIUrl":null,"url":null,"abstract":"This paper aims at designing a fractional order differentiator based on a integer order linear system with zero initial conditions, where the fractional derivatives of the output are estimated using the output observation corrupted by a non zero-mean noise. Firstly, an integral algebraic formula for the fractional derivatives of the output is exactly obtained in continuous noise free case, using an appropriated modulating function. Unlike the improper integrals in the definitions of the fractional derivatives, the obtained formula is given by a proper integral. Then, an additional condition is added to the used modulating function in order to deal with the non zero-mean noise. After constructing the needed modulating function, a digital fractional order differentiator is proposed in discrete noisy case with some error analysis. Finally, the proposed fractional order differentiator is applied to design a fractional order PID controller for an integer order linear system.","PeriodicalId":308101,"journal":{"name":"2015 54th IEEE Conference on Decision and Control (CDC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"A new model-based fractional order differentiator with application to fractional order PID controllers\",\"authors\":\"Xing Wei, Dayan Liu, D. Boutat\",\"doi\":\"10.1109/CDC.2015.7402796\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper aims at designing a fractional order differentiator based on a integer order linear system with zero initial conditions, where the fractional derivatives of the output are estimated using the output observation corrupted by a non zero-mean noise. Firstly, an integral algebraic formula for the fractional derivatives of the output is exactly obtained in continuous noise free case, using an appropriated modulating function. Unlike the improper integrals in the definitions of the fractional derivatives, the obtained formula is given by a proper integral. Then, an additional condition is added to the used modulating function in order to deal with the non zero-mean noise. After constructing the needed modulating function, a digital fractional order differentiator is proposed in discrete noisy case with some error analysis. Finally, the proposed fractional order differentiator is applied to design a fractional order PID controller for an integer order linear system.\",\"PeriodicalId\":308101,\"journal\":{\"name\":\"2015 54th IEEE Conference on Decision and Control (CDC)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 54th IEEE Conference on Decision and Control (CDC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.2015.7402796\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 54th IEEE Conference on Decision and Control (CDC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2015.7402796","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A new model-based fractional order differentiator with application to fractional order PID controllers
This paper aims at designing a fractional order differentiator based on a integer order linear system with zero initial conditions, where the fractional derivatives of the output are estimated using the output observation corrupted by a non zero-mean noise. Firstly, an integral algebraic formula for the fractional derivatives of the output is exactly obtained in continuous noise free case, using an appropriated modulating function. Unlike the improper integrals in the definitions of the fractional derivatives, the obtained formula is given by a proper integral. Then, an additional condition is added to the used modulating function in order to deal with the non zero-mean noise. After constructing the needed modulating function, a digital fractional order differentiator is proposed in discrete noisy case with some error analysis. Finally, the proposed fractional order differentiator is applied to design a fractional order PID controller for an integer order linear system.