{"title":"Stability conditions when using theforward difference method","authors":"Seppo J. Ovaska, Olli Vainio","doi":"10.1016/0921-5956(91)80027-D","DOIUrl":null,"url":null,"abstract":"<div><p>The forward difference method, also known as Euler's method, generates discretetime transfer functions that lead to compact implementations that are desirable for several industrial control applications. However, the potential of Euler's method is usually overlooked because some control literature gives misleading information on the stability of the z-domain poles obtained by Euler's method. In this paper, we derive analytical expressions for the minimum sampling rate that guarantees stability, and the optimum sampling rate that minimizes the modulus of a stable <em>z</em>-domain pole.</p></div>","PeriodicalId":100666,"journal":{"name":"Industrial Metrology","volume":"2 1","pages":"Pages 85-90"},"PeriodicalIF":0.0000,"publicationDate":"1991-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0921-5956(91)80027-D","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Industrial Metrology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/092159569180027D","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
The forward difference method, also known as Euler's method, generates discretetime transfer functions that lead to compact implementations that are desirable for several industrial control applications. However, the potential of Euler's method is usually overlooked because some control literature gives misleading information on the stability of the z-domain poles obtained by Euler's method. In this paper, we derive analytical expressions for the minimum sampling rate that guarantees stability, and the optimum sampling rate that minimizes the modulus of a stable z-domain pole.
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