A Design Method for Stabilizing Modified Smith Predictors for Multiple-Input/Multiple-Output Time-Delay Plants

Abstract:

The modified Smith predictor is well known as an effective time-delay compensator for a plant with large time-delays, and several papers on the modified Smith predictor have been published. The parameterization of all stabilizing modified Smith predictors for single-input/single-output time-delay plants is obtained by Yamada et al. However, they do not examine the parameterization of all stabilizing modified Smith predictors for multiple-input/multiple-output time-delay plants. The purpose of this paper is to expand the result by Yamada et al. and to propose the parameterization of all stabilizing modified Smith predictors for multiple-input/multiple-output time-delay plants. Control characteristics of the control system using obtained parameterization of all stabilizing modified Smith predictors are also given. Finally, a numerical example is illustrated to show the effectiveness of proposed parameterization of all stabilizing modified Smith predictors.

• Periodical: Key Engineering Materials (Volume 459)
• Pages: 221-233
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.459.221
• Online since: December 2010
• Authors: Kou Yamada, Nghia Thi Mai, Yoshinori Ando, Takaaki Hagiwara, Iwanori Murakami, Tatsuya Hoshikawa
• Keywords: Multiple-Input Plant, Multiple-Output Plant, Parameterization, Smith Predictor, Time Delay System

References

[1] O.J.M. Smith, A controller to overcome dead-time, ISA Journal, Vol. 6, pp.28-33. (1959).

[2] S. Sawano, Analog study of process-model control systems, Journal of the Society of Instrument and Control Engineers, Vol. 1, pp.198-203. (1962).

[3] C.C. Hang and F.S. Wong, Modified Smith predictors for the control of processes with dead time, Proc. ISA Annual Conf., pp.33-44. (1979).

[4] K. Watanabe and M. Ito, A process-model control for linear systems with delay, IEEE Transactions on Automatic Control, Vol. 26, pp.1261-1266. (1981).

DOI: 10.1109/tac.1981.1102802

[5] K. Watanabe and M. Sato, A process-model control for multivariable systems with multiple delays in inputs and outputs subject to unmeasurable disturbances, International Journal of Control, Vol. 39, pp.1-17. (1984).

DOI: 10.1080/00207178408933145

[6] A.M. De Paor, A modified Smith predictor and controller for unstable processes with time delay, International Journal of Control, Vol. 41, pp.1025-1036. (1985).

DOI: 10.1080/0020718508961181

[7] P.B. Deshpande and R.H. Ash, Computer process control with advanced control applications, ISA Pub. (1988).

[8] A.M. De Paor and R.P.K. Egan, Extension and partial optimization of a modified Smith predictor and controller for unstable processes with time delay, International Journal of Control, Vol. 50, pp.1315-1326. (1989).

DOI: 10.1080/00207178908953435

[9] K.J. Astrom, C.C. Hang and B.C. Lim, A new Smith predictor for controlling a process with an integrator and long dead-time, IEEE Transactions on Automatic Control, Vol. 39, pp.343-345. (1994).

DOI: 10.1109/9.272329

[10] M.R. Matausek and A.D. Micic, A modified Smith predictor for controlling a process with an integrator and long dead-time, IEEE Transactions on Automatic Control, Vol. 41, pp.1199-1203. (1996).

DOI: 10.1109/9.533684

[11] K. Watanabe, A new modified Smith predictor control for time-delay systems with an integrator, Proceedings of the 2nd Asian Control Conference, Vol. 3, pp.127-130. (1997).

[12] H.J. Kwak, S.W. Sung, I.B. Lee and J.Y. Park, A modified Smith predictor with a new structure for unstable processes, Ind. Eng. Chem. Res., Vol. 38, pp.405-411. (1999).

DOI: 10.1021/ie980515n

[13] G. Zames, Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses, IEEE Transactions on Automatic Control, Vol. 26, pp.301-320. (1981).

DOI: 10.1109/tac.1981.1102603

[14] D.C. Youla, H.A. Jabr and J.J. Bongiorno, Modern Wiener-Hopf design of optimal controllers. Part I, IEEE Transactions on Automatic Control, Vol. 21, pp.3-13. (1976).

DOI: 10.1109/tac.1976.1101139

[15] C.A. Desoer, R.W. Liu, J. Murray and R. Saeks, Feedback system design: The fractional representation approach to analysis and synthesis, IEEE Transactions on Automatic Control, Vol. 25, pp.399-412. (1980).

DOI: 10.1109/tac.1980.1102374

[16] M. Vidyasagar, Control System Synthesis-A factorization approach-, MIT Press. (1985).

[17] M. Morari and E. Zafiriou, Robust Process Control, Prentice-Hall. (1989).

[18] J.J. Glaria and G.C. Goodwin, A parameterization for the class of all stabilizing controllers for linear minimum phase plants, IEEE Transactions on Automatic Control, Vol. 39, pp.433-434. (1994).

DOI: 10.1109/9.272352

[19] K. Yamada, A parameterization for the class of all proper stabilizing controllers for linear minimum phase systems, Preprints of the 9th IFAC/IFORS/IMACS/IFIP/ Symposium on Large Scale Systems: Theory and Applications, pp.578-583. (2001).

DOI: 10.1016/s1474-6670(17)40875-5

[20] E. Nobuyama and T. Kitamori, Spectrum assignment and parameterization of all stabilizing compensators for time-delay systems, Proceedings of the 29th Conference on Decision and Control, Honolulu, Hawaii, pp.3629-3634. (1990).

DOI: 10.1109/cdc.1990.203509

[21] E. Nobuyama and T. Kitamori, Parameterization of all stabilizing compensators in time-delay systems, Transactions of the Society of Instrument and Control Engineers, Vol. 27, pp.1115-1122. (1991).

DOI: 10.9746/sicetr1965.27.1115

[22] K. Yamada, H. Takenaga, T. Hagiwara, Y. Ando and I. Murakami, A design method for stabilizing modified Smith predictor for non-minimum-phase time-delay plants, submitted for publication.