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Error quantification of the normalized right graph symbol for an errors-in-variables system

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Abstract

This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol (NRGS) for an errorsin- 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 a priori and 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 H∞-norm of their NRGSs’ difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H∞ 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.

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Authors and Affiliations

  1. Tianjin Key Laboratory of Information Sensing and Intelligent Control, School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin, 300222, China

    Lihui Geng, Shigang Cui & Zeyu Xia

Authors
  1. Lihui Geng
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  2. Shigang Cui
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  3. Zeyu Xia
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Corresponding author

Correspondence to Lihui Geng.

Additional information

This work was supported in part by the National Natural Science Foundation of China (Nos. 61203119, 61304153), the Key Program of Tianjin Natural Science Foundation, China (No. 14JCZDJC36300) and the Tianjin University of Technology and Education funded project (No. RC14-48).

Lihui GENG received the B.E., the M.E. and the Ph.D. degrees from Tianjin University of Commerce, Hebei University of Technology and Tsinghua University in 2000, 2003 and 2011, respectively. Currently, he is an associate professor at the School of Automation and Electrical Engineering, Tianjin University of Technology and Education. His research interests include system identification and its engineering applications.

Shigang CUI received the M.E. and the Ph.D. degrees both from Tianjin University in 1991 and 2004, respectively. Currently, he is a professor at the School of Automation and Electrical Engineering, Tianjin University of Technology and Education. In addition to being a director of this school, he has also served as a director of Tianjin Key Laboratory of Information Sensing and Intelligent Control. His research interests cover robot control and applications.

Zeyu XIA received the B.E. degree from the Department of Computer Engineering, Anhui Economic Management Cadres’ Institute in 2007. Currently, he is pursuing the M.E. degree at the School of Automation and Electrical Engineering, Tianjin University of Technology and Education. His research interests are system identification and control.

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Geng, L., Cui, S. & Xia, Z. Error quantification of the normalized right graph symbol for an errors-in-variables system. Control Theory Technol. 13, 238–244 (2015). https://doi.org/10.1007/s11768-015-4183-6

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  • DOI: https://doi.org/10.1007/s11768-015-4183-6

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