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Root Locus Practical Sketching Rules for Fractional‐Order Systems

Author

Listed:
  • António M. Lopes
  • J. A. Tenreiro Machado

Abstract

For integer‐order systems, there are well‐known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional‐order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer‐order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Suggested Citation

  • António M. Lopes & J. A. Tenreiro Machado, 2013. "Root Locus Practical Sketching Rules for Fractional‐Order Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:102068
    DOI: 10.1155/2013/102068
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    References listed on IDEAS

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    1. Farshad Merrikh-Bayat & Mahdi Afshar, 2008. "Extending the Root‐Locus Method to Fractional‐Order Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2008(1).
    2. Farshad Merrikh-Bayat & Mahdi Afshar, 2008. "Extending the Root-Locus Method to Fractional-Order Systems," Journal of Applied Mathematics, Hindawi, vol. 2008, pages 1-13, June.
    3. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    4. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    5. Deng, W.H. & Li, C.P., 2005. "Chaos synchronization of the fractional Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 61-72.
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    1. Yiheng Wei & Hamid Reza Karimi & Jinwen Pan & Qing Gao & Yong Wang, 2014. "Observation of a Class of Disturbance in Time Series Expansion for Fractional Order Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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