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| Error quantification of the normalised right graph symbol for an errors-in-variables system |
| L.Geng,S.Cui,Z.Xia |
|
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| (Tianjin Key Laboratory of Information
Sensing and Intelligent Control, School
of Automation and Electrical Engineering,
Tianjin University of Technology and Education, Tianjin 300222,
China) |
|
| 摘要: |
| This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol (NRGS) for an errors-in-variables (EIV) system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from \textit{a priori} and \textit{a posteriori} information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and ${\rm H}_\infty$-norm of their NRGSs' difference. The obtained NRGS perturbation model set paves the way for robust controller design using an ${\rm H}_\infty$ loop-shaping method because it is a standard form of the well-known NCF (normalized coprime factor) perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method. |
| 关键词: Error quantification, errors-in-variables, normalized right graph symbol |
| DOI： |
| Received:December 24, 2014Revised:July 10, 2015 |
| 基金项目: |
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| Error quantification of the normalised right graph symbol for an errors-in-variables system |
| L. Geng,S. Cui,Z. Xia |
| (Tianjin Key Laboratory of InformationSensing and Intelligent Control, Schoolof Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222,China) |
| Abstract: |
| This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol (NRGS) for an errors-in-variables (EIV) system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from \textit{a priori} and \textit{a posteriori} information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and ${\rm H}_\infty$-norm of their NRGSs' difference. The obtained NRGS perturbation model set paves the way for robust controller design using an ${\rm H}_\infty$ loop-shaping method because it is a standard form of the well-known NCF (normalized coprime factor) perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method. |
| Key words: Error quantification, errors-in-variables, normalized right graph symbol |
