Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia

IMPACT FACTOR 2018: 3.514
5-year IMPACT FACTOR: 3.524

CiteScore 2018: 3.44

SCImago Journal Rank (SJR) 2018: 1.891
Source Normalized Impact per Paper (SNIP) 2018: 1.808

Mathematical Citation Quotient (MCQ) 2018: 1.08

See all formats and pricing
More options …
Volume 14, Issue 4


PLC implementation of a crone controller

Patrick Lanusse / Jocelyn Sabatier
Published Online: 2011-09-29 | DOI: https://doi.org/10.2478/s13540-011-0031-7


Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parametrization of open loop transfer function which is optimized in a robustness context. A CRONE Control-System-Design Toolbox for MATLAB has been developed for several years. It is composed of 4 main units. The “CRONE CSD Guided Start” unit is the starting one as it helps to choose which 1st, 2nd or 3rd Generation CRONE CSD unit needs to be used. Controllers are often implemented using Hardware in the Loop development kits or Digital Signal Processors. In this paper, we propose to design a robust controller for an hydraulic system and then to implement it into a Programmable Logic Controller (PLC).

MSC: 93Cxx; 93B52; 47N70; 26A33; 58E25; 93D09

Keywords: CRONE control; CSD toolbox; Programmable Logic Controller (PLC) implementation

  • [1] K.J. Åström, Model uncertainty and robust control design, In: Proc. of the Cosy Workshop - ESF Course, IEEE Control Systems Society (1999), 63–100. Google Scholar

  • [2] H.W. Bode, Network Analysis and Feedback Amplifier Design, Van Nostrand (1945). Google Scholar

  • [3] P. Lanusse, A. Oustaloup, B. Mathieu, Third generation CRONE control, In: Proc. of the IEEE/SMC’93 Conference, IEEE Control Systems Society, Vol. 2 (1993), 149–155. Google Scholar

  • [4] P. Lanusse, De la commande CRONE de première génération à la commande CRONE de troisi`eme generation, PhD Thesis, Bordeaux I University - France (1994). Google Scholar

  • [5] P. Lanusse, A. Oustaloup, D. Sutter, Multi-scalar CRONE control of multivariable plants, In: Proc. of WAC’96 - ISIAC Symposia, TSIPress (1996). Google Scholar

  • [6] P. Lanusse, A. Oustaloup, B. Mathieu, Robust control of LTI square MIMO plants using two CRONE control design approaches, In: Proc. of the IFAC Symposium on Robust Control Design ”ROCOND 2000”, Elsevier (2000), 379–384. Google Scholar

  • [7] D. Nelson-Gruel, P. Lanusse, A. Oustaloup, Decentralized CRONE control of m × n multivariable system with time-delay, In: Proc. of the 3rd IFAC Workshop on Fractional Differentiation and its Applications (FDA’08), IFAC (2008). Google Scholar

  • [8] A. Oustaloup, Systèmes asservis linéaires d’ordre fractionnaire, Masson Ed., Paris (1983). Google Scholar

  • [9] A. Oustaloup, La commande CRONE, Hermes Ed., Paris (1991). Google Scholar

  • [10] A. Oustaloup, P. Lanusse, B. Mathieu, Robust control of SISO plants: the CRONE control, In: Proc. of the ECC’95 Conference, Kluwer Academic Publishers (1995). Google Scholar

  • [11] A. Oustaloup, B. Mathieu, P. Lanusse, The CRONE control of resonant plants: Application to a flexible transmission, European Journal of Control 1, No 2 (1995), 113–121. CrossrefGoogle Scholar

  • [12] V. Pommier-Budinger, P. Lanusse, Y. Janat, A. Oustaloup, CRONE control of MIMO plants, In: Proc. of the ECC-CDC Conference, IEEE Control Systems Society (2005). Google Scholar

  • [13] V. Pommier-Budinger, Y. Janat, D. Nelson-Gruel, P. Lanusse, A. Oustaloup, Fractional active robust control: Control of lightly-damped plants using the isodamping contours and the CRONE approach, Journal Européen des Systèmes Automatisés (JESA) 42, No 6–7–8 (2008), 1015–1036. http://dx.doi.org/10.3166/jesa.42.1015-1035CrossrefGoogle Scholar

  • [14] J. Sabatier, A. Oustaloup, A. Garcia Iturricha, P. Lanusse, CRONE Control: Principles and extension to time varying systems with asymptotically constant coefficients, Nonlinear Dynamics: An Intern. J. of Nonlinear Dynamics and Chaos in Engineering Systems 29, No 1–4 (2002), 363–385. Google Scholar

  • [15] J. Sabatier, A. Oustaloup, A. Garcia Iturricha, F. Levron, CRONE control of continuous linear time periodic systems: Application to a testing bench, ISA Transactions 42, No 3 (2003), 421–436. http://dx.doi.org/10.1016/S0019-0578(07)60144-XCrossrefGoogle Scholar

  • [16] J. Sabatier, A. Garcia Iturricha, M. Moze, A. Oustaloup, Application of CRONE control to a sampled time varying system with periodic coefficients Journal of Dynamic Systems, Measurement and Control 30, No 6 (2008), 1005–1017. Web of ScienceGoogle Scholar

  • [17] J. Sabatier, M. Moze, P. Lanusse, A. Oustaloup, Recursive distributions of poles and zeros for linear phase variations, Journal of Vibration and Control 14 (2008), 1557–1571. http://dx.doi.org/10.1177/1077546307087430Web of ScienceCrossrefGoogle Scholar

About the article

Published Online: 2011-09-29

Published in Print: 2011-12-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 14, Issue 4, Pages 505–522, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-011-0031-7.

Export Citation

© 2011 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Yuquan Chen, Yiheng Wei, Xi Zhou, and Yong Wang
Nonlinear Dynamics, 2017, Volume 89, Number 2, Page 1011
Seshu Kumar Damarla and Madhusree Kundu
Fractional Calculus and Applied Analysis, 2015, Volume 18, Number 5
Eduardo A. Yucra, Juan I. Yuz, and Graham C. Goodwin
IEEE Transactions on Automatic Control, 2013, Volume 58, Number 9, Page 2383
Ivo Petráš
Fractional Calculus and Applied Analysis, 2012, Volume 15, Number 2
Mohammad Tavazoei
Fractional Calculus and Applied Analysis, 2014, Volume 17, Number 2
Zhuang Jiao and YangQuan Chen
Fractional Calculus and Applied Analysis, 2012, Volume 15, Number 1

Comments (0)

Please log in or register to comment.
Log in