Robustness and Stability Margins of Linear Quadratic Regulators

Aref Shahmansoorian; Sahar Jamebozorg

doi:doi:10.11648/j.acis.20150303.12

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Robustness and Stability Margins of Linear Quadratic Regulators

Aref Shahmansoorian, Sahar Jamebozorg

Published in Automation, Control and Intelligent Systems (Volume 3, Issue 3)

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), 2024. 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

Aref Shahmansoorian

EE Department, Imam Khomeini International University, Qazvin, Iran
Sahar Jamebozorg

EE Department, Imam Khomeini International University, Qazvin, Iran

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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}
}

Copy | Download

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  -

Copy | Download