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2013 | 11 | 6 | 868-880
Tytuł artykułu

Posicast control of a class of fractional-order processes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The number of studies on the control of fractional-order processes-processes having dynamics described by differential equations of arbitrary order-has been increasing in the past two decades and it is now ubiquitous. Various methods have emerged and have been proven to effectively control such processes-usually resulting in fractional-order controllers similar to their conventional integer-order counterparts, which include, but are not limited to fractional PID and fractional lead-lag controllers. However, such methods require a lot of computational effort and fractional-order controllers could be challenging when it comes to their synthesis and implementation. In this paper, we propose a simple yet effective delay-based controller with the use of the Posicast control methodology in controlling the overshoot of a fractional-order process of the class $$\mathcal{P}:\left\{ {P\left( s \right) = {1 \mathord{\left/ {\vphantom {1 {\left( {as^\alpha + b} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {as^\alpha + b} \right)}}} \right\}$$ having orders 1 < α < 2. Such controllers have proven to be easy to implement because they only require delays and summers. In this paper, the Posicast control methodology introduced in the past few years is modified to minimize the overshoot of the processes step response to a level that is acceptable in control engineering and automation practices. Furthermore, proof of the existence of overshoot for such class of processes, as well as the determination of the peak-time of the open-loop response of a fractional-order process of the class P is presented. Validation through numerical simulations for a class of fractional-order processes are presented in this paper.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
6
Strony
868-880
Opis fizyczny
Daty
wydano
2013-06-01
online
2013-10-09
Twórcy
  • Department of Computer Technology, College of Computer Studies, De La Salle University Manila, 2401 Taft Ave., Malate Manila, 1004, Philippines, emm.gonzalez@delasalle.ph
autor
  • Electrical & Computer Engineering Department, Auburn University, Auburn, AL, USA
  • Institute of Control and Informatization of Production Processes, B.E.R.G. Faculty, Technical University of Kosice, B. Nemcovej 3, 042 00, Kosice, Slovak Republic
autor
  • Institute of Control and Informatization of Production Processes, B.E.R.G. Faculty, Technical University of Kosice, B. Nemcovej 3, 042 00, Kosice, Slovak Republic
autor
  • Institute of Control and Informatization of Production Processes, B.E.R.G. Faculty, Technical University of Kosice, B. Nemcovej 3, 042 00, Kosice, Slovak Republic
Bibliografia
  • [1] L. Dorcak, Numerical models for the simulation of the fractional-order control systems (The Acedemy of Science Insitute of Experimental Physics, UEF-04-94, Kosice, Slovak Republic, 1994) 12
  • [2] L. Dorcak, J. Terpak, M. Papajova, Identification of the fractional-order systems, 8th International Scientific-Technical Conference on Process Control, Kouty nad Desnou, June 9–12, 2008, University of Pardubice, Pardubice, Czech Republic, (2008)
  • [3] L. Dorcak, J. Valsa, J. Terpak, P. Horovcak, E. Gonzalez, Modeling and identification of fractional-order dynamical systems, 11th International Multidisciplinary Scientific Geo-Conference & Expo on Modern Management of Mine Producing, Geology and Environmental Protection - SGEM 2011, June 20–25, Bulgaria ISSN 1314-2704 (Published by STEF92 Technology Ltd., 14 Kl. Ohrdiski Blvd., Sofia, Bulgaria, 2011) 553
  • [4] K. B. Oldham, J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Abitrary Order (Dover Publications, Inc, New York, 2002)
  • [5] A. Oustaloup, From fractality to non integer derivation through recursivity, a property common to these two concepts: a fundamental idea for a new process control strategy, Proceedings of the 12th IMACS World Congress, Scientific. Publishing Co, Paris, July 18–22, 1988, Paris, France, 3 (1988) 203
  • [6] A. Oustaloup, F. Levron, B. Mathieu, F. M. Nanot, IEEE T. Circuits-I 47(1), 25 (2000) http://dx.doi.org/10.1109/81.817385[Crossref]
  • [7] A. Oustaloup, La Commande CRONE: Commande Robuste d’Ordre Non Entier, (Hermes, Paris, 1991)
  • [8] I. Petras, L. Dorcak, Fractional Calc. App. Anal. Int. J. Theor. App. 6(2), 205 (2003)
  • [9] Y. Chen, I. Petras, D. Xue, Fractional order control - a tutorial, IEEE, Americal Control Conference, St. Louis, MO, USA, June 10–12, (2009) 1397
  • [10] C. A. Monje, Y. Chen, B. M. Vinagre, D. Xue, V. Feliu, Fractional-Order Systems and Controls in Advances in Industrial Control (Springer-Verlag, London, 2010) http://dx.doi.org/10.1007/978-1-84996-335-0[Crossref]
  • [11] A. Oustaloup, M. Bansard, First generation CRONE control, Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, IEEE, Le Touquet, Oct. 17–20, 1993, Le Touquet, France, 2 (1993) 130
  • [12] R. S. Barbosa, J. A. Tenreiro Machado, I. M. Ferreira, Nonlinear Dynam. 38, 305 (2004) http://dx.doi.org/10.1007/s11071-004-3763-7[Crossref]
  • [13] H. W. Bode, AT&T Tech. J. 19, 421 (1940)
  • [14] H. W. Bode, Network Analysis and Feedback Amplifier Design (Van Nostard, Princeton New Jersey, 1945)
  • [15] V. Bhambhani, Y. Chen, Experimental study of fractional order proportional integral (FOPI) controller for water level control, Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008, December 9–11, 2008, Cancun, Mexico, 1791 (2008)
  • [16] Y. Luo, Y. Chen, C. Y. Wang, Y. G. Pi, J. Process Contr. 20, 823 (2010) http://dx.doi.org/10.1016/j.jprocont.2010.04.011[Crossref]
  • [17] C. A. Monje, B. M. Vinagre, Y. Chen, Vicente Feliu, Nonlinear Dynam. 38(1–2), 361 (2004)
  • [18] C. Y. Wang, Y. Luo, Y. Chen, Fractional order proportional integral (FOPI) and [proportional integral] (FO[PI]) controller design for first order plus time delay (FOPTD) systems, Chinese Control and Decision Conference, IEEE, Guilin, Chine, June 17–19, 2009
  • [19] Y. Jin, Y. Luo, C. Wang, Y. Chen, Fractional order proportional derivative (FOPD) and FO[PD]_controller design for networked position servo systems, Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2009), ASME, San Diego, California, August 30–September 2, 2009
  • [20] H. Li, Y. Chen, A fractional order proportional and derivative (FOPD) controller tuning algorithm, Chinese Control and Decision Conference, IEEE, Yantai, Shandong, China, 2–4 July 2008, 4059
  • [21] H. Li, Y. Luo, Y. Chen, IEEE T. Control Syst. Tech. 18(2), 516 (2009) http://dx.doi.org/10.1109/TCST.2009.2019120[Crossref]
  • [22] Y. Luo, Y. Chen, Fractional-order [proportional derivative]_controller for robust motion control: tuning procedure and validation, 2009 American Control Conference, IEEE, St. Louise, USA (2009) 1412
  • [23] Y. Luo, Y. Chen, Automatica 45, 2446 (2009) http://dx.doi.org/10.1016/j.automatica.2009.06.022[Crossref]
  • [24] Y. Chen, K. L. Moore, IEEE T. Syst. Man. Cy. B. 35(1), 23 (2005) http://dx.doi.org/10.1109/TSMCB.2004.837950[Crossref]
  • [25] L. Dorcak, J. Terpak, M. Papajova, Acta Montanistica Slovaca 12(4), 285 (2007)
  • [26] C. A. Monje, B. M. Vinagre, V. Feliu, Y. Chen, On autotuning of fractional order PI_Dμ controllers, Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications, IFAC, Porto, Portugal, July 19–21, 2006
  • [27] C. A. Monje, B. M. Vinagre, G. E. Santamaria, I. Tejado, Auto-tuning of fractional order PI λD μ controllers using PLC, Proceedings of the 14th IEEE international conference on Emerging technologies & factory automation (IEEE Press Piscataway, NJ, USA, 2009) 1095
  • [28] I. Podlubny, L. Dorcak, I. Kostial, On fractional derivatives, fractional-order dynamic systems and controllers, Proceedings of the 36th Conference on Decision & Control, IEEE, San Diego, California, (1997) 4985 http://dx.doi.org/10.1109/CDC.1997.649841[Crossref]
  • [29] C. A. Monje, A. J. Calderon, B. M. Vinagre, V. Feliu, The fractional order lead compensator, Second IEEE International Conference on Computational Cybernetics, IEEE, Vienna University of Technology, Aug.30–Sept.1, 2004, Vienna (2004), 347
  • [30] C. A. Monje, B. M. Vinagre, A. J. Calderon, V. Feliu, Y. Chen, Auto-tuning of fractional lead-lag compensators (IFAC, Prague, 2005)
  • [31] E. A. Gonzalez, Posicast control in power electronics, Proceedings of the AUN/SEED-Net Fieldwise Seminar in Power Systems 2007, Hotel Intercontinental Manila, Philippines, Mar. 21–22, 2007, (AUN/SEEDNet, Manila, Philippines, 2007)
  • [32] E. A. Gonzalez, L. Dorcak, Robust I λI controller for a class of stable fractional-order systems, 3rd AUN/SEED-Net Regional Conference in Mechanical and Aerospace Technology, Pasay City, Traders Hotel, Pasay City, Philippines, Mar. 4–5, (AUN/SEEDNet - RCMeAe, Pasay City, Philippines, 2011)
  • [33] E. A. Gonzalez, L. Dorcak, C. B. Co, Stabilization with fractional-order frequency-dependent amplifiers for a class of continuous-time systems with time delay, 5th ERDT Conference, Sep. 10, (ERDT, Philippines, 2010)
  • [34] E. A. Gonzalez, L. Dorcak, C. B. Co, Guaranteed phase margin stabilization of a class of integerorder dynamical systems using frequency-dependent fractional-order differentiators, 5th ERDT Conference, Sep. 10, (ERDT, Philippines, 2010)
  • [35] L. Dorcak, J. Terpak, I. Petras, F. Dorcakova, Acta Montanistica Slovaca 12(3), 231 (2007)
  • [36] I. Podlubny, I. Petras, B. M. Vinagre, P. O’Leary, L.Dorcak, Nonlinear Dynam. 29(1–4), 281 (2002) http://dx.doi.org/10.1023/A:1016556604320[Crossref]
  • [37] Y. Chen, K. L. Moore, IEEE T. Circuits-I 49, 363 (2002) http://dx.doi.org/10.1109/81.989172[Crossref]
  • [38] R. Yadav, M. Gupta, Design of fractional order differentiators and integrators using indirect discretization approach, International Conference on Advances in Recent Technologies in Communication and Computing (ARTCom), IEEE, Kottayam, India, Oct. 16–17, (2010) 126
  • [39] R. Yadav, M. Gupta, Design of fractional order differentiators and integrators using indirect discretization scheme, India International Conference on Power Electronics (IICPE), IEEE, New Delhi, India, June 21–24, (2010) 1
  • [40] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and Numerical Methods (World Scientific Publishing Company, Singapore, 2012
  • [41] P. L. Butzer, U. Westphal, In. R. Hilfer (Ed.), An introduction to fractional calculus, Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000), 1
  • [42] J. A. Tenreiro Machado, V. Kiryakova, F. Mainardi, Commun. Nonlinear Sci. Num. Simul. 16, 1140 (2011) http://dx.doi.org/10.1016/j.cnsns.2010.05.027[Crossref]
  • [43] O. J. M. Smith, P. IRE 45, 1249 (1957) http://dx.doi.org/10.1109/JRPROC.1957.278530[Crossref]
  • [44] G. Cook, IEEE T. Automat. Contr. AC-11, 556 (1966)
  • [45] G. Cook, Control of flexible structures via Posicast, Proceedings of the 1986 Southeastern Symposium on Systems Theory, IEEE Computer Society (Knoxville, TN, April 7–8, 1986), 31 (1986)
  • [46] G. Cook, J. Dyn. Syst.-T. 115(2), 309 (1993) http://dx.doi.org/10.1115/1.2899037[Crossref]
  • [47] N. C. Singer, W. P. Seering, J. Dyn. Syst.-T. ASME 112, 76 (1990) http://dx.doi.org/10.1115/1.2894142[Crossref]
  • [48] R. A. Fowell, U.S. Patent 5610848, Hughes Aircraft Company, Mar. 11, 1997
  • [49] E. A. Gonzalez, J. Y. Hung, C. B. Co, Posicast control of two-term fractional-order systems, 5th International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management (HNICEM), Manila, Philippines, Mar. 9–13, (HINCEM, Pasay City, 2011)
  • [50] J. Y. Hung, Application of Posicast principles in feedback control, 2002 IEEE International Symposium on Industrial Electronics, IEEE, L’Aquila, Italy (2002) 500
  • [51] J. Y. Hung, IEEE T. Ind. Electron. 50(1), 94 (2003) http://dx.doi.org/10.1109/TIE.2002.804979[Crossref]
  • [52] J. Y. Hung, IEEE Multidiscip. Eng. Educ. Mag. 2(1), 7 (2007)
  • [53] P. C. Loh, C. J. Gajanayake, Don M. Vilathgamuwa, F. Blaabjerg, IEEE T. Power Electr. 23(4), 2035 (2008) http://dx.doi.org/10.1109/TPEL.2008.924590[Crossref]
  • [54] Y. Yildiz, A. Annaswamy, I. V. Kolmanovsky, D. Yanakiev, Automatica 46, 279 (2010) http://dx.doi.org/10.1016/j.automatica.2009.11.008[Crossref]
  • [55] O. J. M. Smith, Feedback Control Systems (New York, McGraw-Hill, 1958) 331
  • [56] W. R. LePage, Complex Variables and the Laplace Transform for Engineers (New York, McGraw-Hill, 1961)
  • [57] M. S. Tavazoei, M. Haeri, Math. Comput. Simulat. 79, 1566 (2009) http://dx.doi.org/10.1016/j.matcom.2008.07.003[Crossref]
  • [58] D. Matignon, Stability result for fractional differential equations with applications to control processing, Computational Engineering in Systems Applications, Lille, France, IMACS, (IEEE SMC 2, 1996)
  • [59] I. Podlubny, Fractional Differential Equations, in Mathematics in Science and Engineering, 198 (Academic Press, San Diego, California, 1999)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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