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Stability regions of closed loop system with time delay inertial plant of fractional order and fractional order PI controller

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Języki publikacji
EN
Abstrakty
EN
The paper presents the stability problem of control systems composed of a fractional-order PI controller and a inertial plant of a fractional order with time delay. Simple and efficient computational method for determining stability regions in the controller and plant parameters space is given. Knowledge of these regions permits tuning of the fractional-order PI controller. The method proposed is based on the classical D-partition method.
Rocznik
Strony
329--332
Opis fizyczny
Bibliogr. 21 poz., rys.
Twórcy
autor
  • Faculty of Electrical Engineering, Białystok Technical University, 45D Wiejska St., 15-351 Białystok, Poland
Bibliografia
  • [1] K.J. Astr¨om and T. H¨agglund, PID Controllers: Theory, Design, and Tuning, NC: Instrument Society of America, USA, 1995.
  • [2] H. Górecki, Analysis and Synthesis of Time Delay Systems, WNT, Warsaw, 1971, (in Polish).
  • [3] A. O’Dwyer, PI and PID Controller Tuning Rules, Imperial College Press/Word Scientific, London, 2003.
  • [4] G.J. Silva, A. Datta, and S.P. Bhattacharyya, PID Controllers for Time-Delay Systems, Birkhauser, Boston, 2005.
  • [5] A. Datta, M.-T Ho, and S.P. Bhattacharyya, Structure and Synthesis of PID Controllers, Springer-Verlag, London, 2000.
  • [6] J.E. Marshal, H. Górecki, K. Walton, and A. Korytowski, Time Delay Systems – Stability and Performance Criteria with Application, Ellis Horwood, Chichester, 1992.
  • [7] M. Busłowicz and A. Ruszewski, “Stabilization of first order systems with delay using the PI controllers”, Proc. XIV National Conference of Automatics 1, 89–94 (2002), (in Polish).
  • [8] A. Ruszewski, “Stability regions of control systems with multiinertial plant with delay in the parameter space”, Proc. XV National Conference of Automatics 1, 189–192 (2005), (in Polish).
  • [9] A. Ruszewski, Parametric Synthesis of Controllers for Particular Plants with Uncertain Parameters, PhD Dissertation, Faculty of Electrical Engineering, Białystok, 2008, (in Polish).
  • [10] M. Busłowicz, “Stability of linear continuous-time fractional order systems with delays of the retarded type”, Bull. Pol. Ac.: Tech. 56 (4), (2008).
  • [11] D. Matignon, “Stability properties for generalized fractional differential systems”, Proc. ESAIM 145–158 (1998).
  • [12] P. Ostalczyk, Outline of Fractional Order Integral-differential Calculus. Theory and Application in Automatics, Publishing Department of Technical University of Łódz, Łódz, 2008, (in Polish).
  • [13] I. Podlubny, “Fractional-order systems and PIDμ – controllers”, IEEE Trans. on Automatic Control 44, 208–214 (1999).
  • [14] C. Zhao, D. Xue, and Y.Q. Chen, “A fractional order PID tuning algorithm for a class of fractional order plants”, Proc. IEEE Int. Conf. on Mechatronics & Automation 216–221 (2005).
  • [15] Y.Q. Chen, H. Dou, B.M. Vinagre, and C.A. Monje, “A robust tuning method for fractional order PI controllers”, The Second IFAC Symposium on Fractional Derivatives and Applications FDA06, CD-ROM (2006).
  • [16] C.A. Monje, B.M. Vinagre, Y.Q. Chen, V. Feliu, P. Lanusse, and J. Sabatier, “Proposals for fractional PIDμ tuning”, The First IFAC Symposium on Fractional Differentiation and its Applications 38, 369–381 (2004).
  • [17] S.E. Hamamci, “An algorithm for stabilization of fractionalorder time delay systems using fractional-order PID controllers”, IEEE Trans. on Automatic Control 52, 1964–1969 (2007).
  • [18] A. Ruszewski, “Stabilization of fractional-order Strejc’s process model with time delay using fractional-order PI controller”, in Recent Advances in Control and Automation, pp. 103–113, eds: K. Malinowski and L. Rutkowski, Academic Publishing House Exit, Warsaw, 2008.
  • [19] H. Górecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time Delay Systems, PWN-J. Wiley, Warsaw-Chichester, 1989.
  • [20] H. Górecki and A. Korytowski, Advances in Optimization and Stability Analysis of Dynamical Systems, Publishing Department of University of Mining and Metallurgy, Kraków, 1993.
  • [21] M. Busłowicz, “Frequency domain method for stability analysis of linear continuous-time fractional systems”, in Recent Advances in Control and Automation, pp. 83–92, eds.: K. Malinowski and L. Rutkowski, Academic Publishing House Exit, Warsaw, 2008. 332 Bull. Pol. Ac.: Tech. 56(4) 2008
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG8-0011-0005
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