Abstract
To perfectly govern MIMO (Multi-Input Multi-Output) processes, a fully populated matrix controller has been developed due to its flexibility. Taking into account the plant uncertainties, the CRONE (Commande Robuste d’Ordre Non Entier) control approach is used with the non-diagonal quantitative feedback theory (QFT) procedure. The MIMO-QFT robust synthesis methodology has been used in order to generate the appropriate equivalent MISO (Multi-Input Single-Output) system structure from the MIMO plant. For each MISO structure, the CRONE control approach based on third-generation CRONE methodology is used to find the diagonal elements of the controller of the plant while considering the plant uncertainties. The non-diagonal part of the controller is determined to reach the aim of minimizing the coupling effects. After that, a fractional prefilter synthesis approach is developed to find the non-integer prefilter expression satisfying the tracking specifications. A SCARA robot manipulator has been used to verify the designed controller performances.
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References
Oustaloup, A.: Fractional order sinusoidal oscillators: optimization and their use in highly linear F.M. modulation. IEEE Trans. Circuits Syst. 8(10), 1007–1009 (1981)
Oustaloup, A.: The CRONE control. In: Proceedings of the European Control Conference (ECC 91), Grenoble, France, 2–5 July (1991)
Sabatier, J., Oustaloup, A., Garcia Iturricha, A., Lanusse, P.: CRONE control: principles and extension to time-variant plants with asymptotically constant coefficients. Nonlinear Dyn. 29, 363–385 (2002)
Oustaloup, A., Mathieu, B., Lanusse, P.: Intégration non entière complexe et contours d’Isoamortissement. Autom. Prod. Inform. Ind. 29(1), 177–202 (1995)
Lanusse, P.: De la commande CRONE de première génération à la commande CRONE de troisième génération. PhD thesis, Bordeaux I University, France (1994)
Kempfle, S., Schäfer, I., Beyer, H.: Fractional calculus via functional calculus: theory and applications. Nonlinear Dynamics 29(1–4), 99–127 (2002)
Oustaloup, A., Mathieu, B.: La Commande CRONE: du Scalaire Au Multivariable. Hermès, Paris (1999)
Oustaloup, A., Mathieu, B., Lanusse, P., Sabatier, J.: La Commande CRONE. Hermès, Paris (1999)
Lanusse, P., Nelson Gruel, D., Sabatier, J., Lasnier, R., Oustaloup, A.: Synthèse multivariable d’une commande CRONE décentralisée. In: Automatique et Informatique Appliquée. Académie Roumaine, pp. 159–166 (2009)
Melchior, P., Inarn, C., Oustaloup, A.: Path tracking design by fractional prefilter extension to square MIMO systems. In: The Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (ASME 2009), California, USA, 30 August–2 September (2009)
Mohammad, S., Alavi, M., Khaki Sedigh, A., Labibi, B.: Pre-filter design for tracking error specifications in MIMO-QFT. In: The 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC 2005), Seville, Spain, 12–15 December (2005)
Boje, E.: Non-diagonal controllers in MIMO quantitative feedback design. Int. J. Robust Nonlinear Control 12(4), 303–320 (2002)
Zenghui, W., Zengqiang, C., Qinglin, S., Zhuzh, Y.: Multivariable decoupling predictive control based on QFT theory and application in CSTR chemical process. Chin. J. Chem. Eng. 14(6), 765–769 (2006)
Horowitz, I.: Survey of quantitative feedback theory (QFT). Int. J. Robust Nonlinear Control 11(10), 887–921 (2001)
Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control, Analysis and Design. Wiley, New York (1996)
Yousfi, N., Melchior, P., Rekik, C., Derbel, N., Oustaloup, A.: Path tracking design by fractional prefilter using a combined QFT/H∞ design for TDOF uncertain feedback systems. J. Appl. Nonlinear Dyn. 1(3), 239–261 (2012)
Garcia-Sanz, M., Egana, I.: Quantitative non-diagonal controller design for multivariable systems with uncertainty. Int. J. Robust Nonlinear Control 12, 321–333 (2002)
Garcia-Sanz, M., Egana, I., Barreras, M.: Design of quantitative feedback theory non-diagonal controllers for use in uncertain multiple-input multiple-output systems. IEE Proc., Control Theory Appl. 152(2), 177–187 (2005)
Barreras, M., Villegas, C., Garcia-Sanz, M., Kalkkuhl, J.: Robust QFT tracking controller design for a car equipped with 4-wheel steer-by wire. In: Proceedings of the 2006 IEEE International Conference on Control Applications (CCA 2006), Munich, Germany, 4–6 October (2006)
Horowitz, I.: Improved design technique for uncertain multiple input-output feedback systems. Int. J. Control 36, 977–988 (1982)
Franchek, M., Herman, P., Nwokah, O.: Robust non-diagonal controller design for uncertain multivariable regulating systems. J. Dyn. Syst. Meas. Control 119, 80–85 (1997)
Oustaloup, A., Mathieu, B., Lanusse, P.: The CRONE control of resonant plants: application to a flexible transmission. Eur. J. Control 1(2), 113–121 (1995)
Lanusse, P., Oustaloup, A., Mathieu, B.: Robust control of LTI square MIMO plants using two CRONE control design approaches. In: IFAC Symposium on Robust Control Design (ROCOND 2000), Prague, Czech Republic, 11–13 September (2000)
CRONE Research Group: CRONE Control Design Module User’s Guide. Version 4.0 (2010)
Nelson Gruel, D., Lanusse, P., Oustaloup, A.: Decentralized CRONE control of multivariable system with time-delay. In: New Trends in Nanotechnology and Fractional Calculus Applications, pp. 377–391. Springer, Berlin (2009)
Nelson Gruel, D., Lanusse, P., Oustaloup, A.: Robust control design for multivariable plants with time-delays. Chem. Eng. J. 146, 414–427 (2009)
Orsoni, B., Melchior, P., Oustaloup, A.: Davidson–Cole transfer function in path tracking design. In: The 6th IEEE European Control Conference (IEEE-ECC 2001), Porto, Portugal, 4–7 September (2001)
Garcia-Sanz, M., Egaña, I., Villanueva, J.: Interval modeling of a SCARA robot for robust control. In: The 10th Mediterranean Conference on Control and Automation (MED 2002), Lisbon, Portugal, 9–13 July (2002)
Oustaloup, A., Melchior, P., Lanusse, P., Cois, O., Dancla, F.: The CRONE toolbox for Matlab. In: IEEE International Symposium on Computer-Aided Control-System Design (CACSD 2000), Anchorage, USA, 25–27 September, (2000)
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Yousfi, N., Melchior, P., Rekik, C. et al. Path tracking design based on Davidson–Cole prefilter using a centralized CRONE controller applied to multivariable systems. Nonlinear Dyn 71, 701–712 (2013). https://doi.org/10.1007/s11071-012-0695-5
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DOI: https://doi.org/10.1007/s11071-012-0695-5