Abstract
In this paper, we propose to use a fractional order model to predict the process output in Smith predictor. The parameters of the model are determined by minimizing the error between its output and one of the processes using a genetic algorithm. After determining the model’s parameters, a fractional PID controller is proposed to improve the controlled system performances. The parameters of the controller are also determined in an optimal way by minimizing the position error taking into account the sensitivity and the complementary sensitivity conditions. Applications on a dead time and multiple lags processes have been performed, where the simulation results show that the proposed Smith predictor enhance the closed loop control system.
Similar content being viewed by others
References
Ho, W.K., Hang, C.C., Cao, L.S.: Tuning of PID controllers based on gain and phase margin specifications. Automatica 31(3), 497–502 (1995)
Smith, O.J.M.: Closer control of loops with dead time. Chem. Eng. Prog. 53, 217–219 (1957)
Åstrom, K.J., Hang, C.C., Lim, B.C.: A new Smith predictor for controlling a process with an integrator and long dead time. IEEE Trans. Autom. Control 39, 343–345 (1994)
Zhang, W., Xu, X.: Analytical design and analysis of mismatched Smith predictor. ISA Trans. 40(2), 133–138 (2001)
Feliu-Batlle, V., Rivas Pérez, R., Castillo, F.J., Sanchez Rodriguez, L.: Smith predictor based robust fractional order control: application to water distribution in a main irrigation canal pool. J. Process Control 19, 506–519 (2009)
Jesus Isabel, S., Tenreiro Machado, J.A.: Fractional control of heat diffusion systems. Nonlinear Dyn. 54(3), 263–282 (2008)
Rapaić, M.R., Jeličić, Z.D.: Optimal control of a class of fractional heat diffusion systems. Nonlinear Dyn. 62(1–2), 39–51 (2010)
Castillo, F.J., Feliua, V., Rivas, R., Sánchez, L.: Design of a class of fractional controllers from frequency specifications with guaranteed time domain behavior. Comput. Math. Appl. 59, 1656–1666 (2010)
Boudjehem, D., Boudjehem, B.: A fractional model predictive control for fractional order systems. In: Baleanu, D. (ed.) Fractional Dynamics and Control 1st, pp. 49–57. Springer, Berlin (2012)
Monje Concepción, A., Calderon Antonio, J., Vinagre Blas, M., Chen, Y., Feliu, V.: On fractional PIλ controllers: some tuning rules for robustness to plant uncertainties. Nonlinear Dyn. 38(1–4), 369–381 (2004)
Boudjehem, B., Boudjehem, D.: Parameter tuning of a fractional-order PI controller using the ITAE criteria. In: Baleanu, D. (ed.) Fractional Dynamics and Control 1st, pp. 49–57. Springer, Berlin (2012)
Podlubny, I.: Fractional-order systems and PI Λ D μ controllers. IEEE Trans. Autom. Control 44, 208–214 (1999)
Wang, Q.G., Bi, Q., Zhang, Y.: Re-design of Smith predictor systems for performance enhancement. ISA Trans. 39(1), 79–92 (2000)
Tenreiro Machado, J.A.: Optimal tuning of fractional controllers using genetic algorithms. Nonlinear Dyn. 62(1–2), 447–452 (2010)
Tenreiro Machado, J.A.: Fractional order modelling of fractional-order holds. Nonlinear Dyn. 70(1), 789–796 (2012)
Valério, D., da Costa, J.S.: Tuning of fractional PID controllers with Ziegler–Nichols-type rules. Signal Process. 86, 2771–2784 (2006)
Shantanu, D.: Functional Fractional Calculus for System Identification and Controls. Springer, Berlin (2008)
Rao, A.S., Rao, V.S.R., Chidambaram, M.: Set point weighted modified Smith predictor for integrating and double integrating processes with time delay. ISA Trans. 46(1), 59–71 (2007)
Baiyu, O., Lei, S., Chunlei, C.: Tuning of fractional PID controllers by using radial basis function neural network. In: Poceed. of IEEE International Conference on Control and Automation, pp. 1239–1244 (2010)
Jesus Isabel, S., Tenreiro Machado, J.A.: Fractional control with a Smith predictor. J. Comput. Nonlinear Dyn. 6(3), 031014 (2011)
Clarke, T., Achar, B.N.N., Hanneken, J.W.: Mittag–Leffler functions and transmission lines. J. Mol. Liq. 114, 159–163 (2004)
Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations to Methods of Their Solution and Some of Their Applications. Academic Press, San Diego (1999)
Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)
Oldham, K.B., Spanier, J.: The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press, San Diego (1974)
Oustaloup, A.: La Commande CRONE: Commande Robuste D’ordre Non Entier. Hermès, Paris (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Boudjehem, D., Sedraoui, M. & Boudjehem, B. A fractional model for robust fractional order Smith predictor. Nonlinear Dyn 73, 1557–1563 (2013). https://doi.org/10.1007/s11071-013-0885-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-013-0885-9