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Robustness and Stability Margins of Linear Quadratic Regulators

Received: 9 May 2015     Accepted: 29 May 2015     Published: 11 June 2015
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Abstract

In this paper, It is showed that however we can mention the guaranteed gain margin of -6 to +∞ and also phase margin of -〖60〗^° to +〖60〗^° for single input systems as the well-known robustness properties of linear quadratic regulators (LQR). But determining the robustness of closed-loop system from the range of gain and phase margins is not corrected. By an example, this matter is explained.

Published in Automation, Control and Intelligent Systems (Volume 3, Issue 3)
DOI 10.11648/j.acis.20150303.12
Page(s) 36-38
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Linear Quadratic Regulators, Robustness, Gain Margins, Phase Margins

References
[1] Horowitz, Isaac M. Synthesis of feedback systems. Elsevier, 2013.
[2] N. A. Lehtomaki, N. R. Sandell, Jr, and M. Athans, "Robustness results in linear-quadratic Gaussian based multivariable control designs", IEEE Trans. Automatic Control, Vol. AC-26. pp. 75-93, Feb. 1981.
[3] B.D.O. Anderson, "The inverse problem of optimal control", Stanford Electronics Laboratories, Stanford, CA, Tech. Rep. SEL-66-038 (T. R. no.6560-3), Apr. 1966.
[4] B. D. O. Anderson and J. B. Moore, Linear Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1971.
[5] R. E. Kalman, "When is a linear control system optimal?", Trans. ASME Ser. D: J. Basic Engineering, Vol. 86, pp. 51-60, Mar. 1964.
[6] E. Soroka, U. Shaked, "On the robustness of LQ regulators", IEEE Trans, Automatic Control, Vol. AC-29, no. 7, pp. 664-665, 1984.
[7] J. C. Doyle, ‘Guaranteed margins for LQG regulators. “IEEE Truns. Auromur. Conrr., vol. AC-23. pp. 756-757. Aug. 1978.
[8] A. Khaki-Sedigh, Analysis and design of Multivariable Control Systems, , K. N. Toosi University Press, 2011.
[9] Anderson, Brian DO, and John B. Moore. Optimal control: linear quadratic methods. Courier Corporation, 2007.
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  • APA Style

    Aref Shahmansoorian, Sahar Jamebozorg. (2015). Robustness and Stability Margins of Linear Quadratic Regulators. Automation, Control and Intelligent Systems, 3(3), 36-38. https://doi.org/10.11648/j.acis.20150303.12

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    ACS Style

    Aref Shahmansoorian; Sahar Jamebozorg. Robustness and Stability Margins of Linear Quadratic Regulators. Autom. Control Intell. Syst. 2015, 3(3), 36-38. doi: 10.11648/j.acis.20150303.12

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    AMA Style

    Aref Shahmansoorian, Sahar Jamebozorg. Robustness and Stability Margins of Linear Quadratic Regulators. Autom Control Intell Syst. 2015;3(3):36-38. doi: 10.11648/j.acis.20150303.12

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  • @article{10.11648/j.acis.20150303.12,
      author = {Aref Shahmansoorian and Sahar Jamebozorg},
      title = {Robustness and Stability Margins of Linear Quadratic Regulators},
      journal = {Automation, Control and Intelligent Systems},
      volume = {3},
      number = {3},
      pages = {36-38},
      doi = {10.11648/j.acis.20150303.12},
      url = {https://doi.org/10.11648/j.acis.20150303.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20150303.12},
      abstract = {In this paper, It is showed that however we can mention the guaranteed gain margin of -6 to +∞ and also phase margin of -〖60〗^° to +〖60〗^° for single input systems as the well-known robustness properties of linear quadratic regulators (LQR). But determining the robustness of closed-loop system from the range of gain and phase margins is not corrected. By an example, this matter is explained.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Robustness and Stability Margins of Linear Quadratic Regulators
    AU  - Aref Shahmansoorian
    AU  - Sahar Jamebozorg
    Y1  - 2015/06/11
    PY  - 2015
    N1  - https://doi.org/10.11648/j.acis.20150303.12
    DO  - 10.11648/j.acis.20150303.12
    T2  - Automation, Control and Intelligent Systems
    JF  - Automation, Control and Intelligent Systems
    JO  - Automation, Control and Intelligent Systems
    SP  - 36
    EP  - 38
    PB  - Science Publishing Group
    SN  - 2328-5591
    UR  - https://doi.org/10.11648/j.acis.20150303.12
    AB  - In this paper, It is showed that however we can mention the guaranteed gain margin of -6 to +∞ and also phase margin of -〖60〗^° to +〖60〗^° for single input systems as the well-known robustness properties of linear quadratic regulators (LQR). But determining the robustness of closed-loop system from the range of gain and phase margins is not corrected. By an example, this matter is explained.
    VL  - 3
    IS  - 3
    ER  - 

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Author Information
  • EE Department, Imam Khomeini International University, Qazvin, Iran

  • EE Department, Imam Khomeini International University, Qazvin, Iran

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