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Vol: 50(64) No: 1 / March 2005      

Improving Disturbance Rejection by Means of a Double Parameterization of the Symmetrical Optimum Method
Zsuzsa Preitl
Budapest University of Technology and Economics, Budapest, Hungary, phone: +40-256-403229, e-mail: zsuzsa.preitl@aut.upt.ro


Keywords: PI(PID) controller design, symmetrical optimum, load disturbance rejection, increase of robustness.

Abstract
The paper presents a new efficient tuning method for PI, PID controllers, based on the Symmetrical Optimum (SO) Criterion [1]. The method, dedicated to benchmark type plants with one time constant much larger than the others, is based on a double parameterization of the SO Criterion: - one that extends the optimization relations; - a second one that characterizes the ratio between the largest and smallest time constant. Compared with the tuning methods based on pole-zero cancellation, this method ensures better performances as far as load disturbance rejection is concerned. By fixing adequately one of the parameters, also the sensitivity of the system can be reduced (increase of robustness). Also with adequate measures a desired reference tracking can be ensured. The main application domain of the presented results is servo-driving systems (electrical) with large inertia.

References
[1] C. Kessler, “Das symmetrische Optimum”, Regelungstechnik vol. 6, no.11, pp.395 – 400, no. 12, pp.432 – 436, 1958.
[2] K. J. Åstrom and T. Hägglund, PID Controllers. Theory, Design and Tuning, Research Triangle Park, North Carolina, 1995.
[3] J. Quevedo and T. Escobet (Editors), IFAC Workshop on Digital Control. Past, Present and Future of PID Control – PID’00, Preprints, Terrassa, Spain, 2000.
[4] A. O’Dwyer, “A summary of PI and PID controller tuning rules for processes with time delay, Part 1, Part 2”, Prep. of IFAC Workshop on Digital Control, Terrassa, Spain, pp.175 – 180, 242-247, 2000.
[5] A. O’Dwyer, Handbook of PI and PID Controller Tuning Rules, Imperial College Press, 2003.
[6] A. Leva, “Autotuning process controller with improved load disturbance rejection”, Journal of Process Control, vol. 15, pp. 223 – 234, 2005.
[7] A. Leva, “Simple model-based PID autotuners with rapid relay identification”, Preprints of 16th IFAC World Congress, Prague, Czech Republic, Electronic format, Paper ID – 01931, 2005.
[8] C. Kessler, “Uber die Vorasberechnung optimal abgestimmter Regelkreise Teil III: die optimale Einstellung des Regler nach dem Betragsoptimum”, Rt., vol. 3, no. 2, pp. 40 – 49, 1955.
[9] D. Vrančić, J. Kocijan, and S. Strmčnik, “Improving PID controller disturbance rejection by means of Magnitude Optimum”, Proc. of 4th Asian Control Conference, Singapore, pp. 214 – 2145, 2002.
[10] R. Gorez and P. Klàn, “Nonmodel-based explicit design relations for PID controllers”, Preprints of IFAC workshop on Digital Control, Terrassa, Spain, pp.141 – 148, 2000.
[11] K. J. Åstrom, H. Panagopoulos, and T. Hägglund, “Design of PI controllers based on non-convex optimization, Automatica, vol. 34, no. 5, pp.585 – 601, 1998.
[12] Zs. Preitl, “PI and PID controller tuning method for a class of systems”, Proc. of SACCS-2001 - 7th International Symposium on Automatic Control and Computer Science, Iasi, Romania, e-format, 2001.
[13] Z. Shafei and A. T. Shenton, “Frequency-domain design of PID controllers for stable and unstable systems with time delay”, Automatica, vol. 33, pp. 2223 – 2232, 1997.
[14] W. Krajewski, A. Lepschy, and U. Viaro, “Design PI controllers for robust stability and performance”, IEEE Trans. on Control System Techology, vol. 12, no. 6, pp.973 – 983, 2004.
[15] K. J. Åstrom and T. Hägglund, “Benchmark systems for PID control”, Preprints of IFAC workshop on Digital Control, Terrassa, Spain, pp.181 – 182, 2000.
[16] O. Föllinger, Regelungstechnik, Elitera Verlag, Berlin, 1972 (also later editions).
[17] J. -P. Richard, “Time-delay systems: an overview of some recent advances and open problems”, Automatica, vol. 39, pp. 1667 – 1694, 2003.
[18] T. L. Dragomir and o., System Theory and Control Engineering, vol. I, II, Inst. Politehnic “Traian Vuia” Timisoara Publisher, 1979 (in Romanian).
[19] A. A. Voda and I. D. Landau, “Applications of the KLV method for the auto-calibration of PID controllers”, Proc. 2nd IEEE Conference on Control Applications, Vancouver, British Columbia, pp.829 – 834, 1993.
[20] S. Preitl and R. -E. Precup, “An extension of tuning relations after Symmetrical Optimum Method for PI and PID controllers”, Automatica, vol. 35, no. 10, pp. 1731 – 1736, 1999.
[21] M. Lelič, PID Controllers in Nineties, Corning Incorporated Science and Technology Division, Corning, NY, 1999.
[22] Zs. Preitl, “Ǘj tervezési módszer vizsgálata frekvencia-tartományban, PI és PID szabályozók beálitása részére”, Proc. Of Enelko Conference, Cluj-Napoca, Romania, pp. 136 – 141, 2001.
[23] St. Preitl, Zs. Preitl, and R. -E. Precup, “Low cost fuzzy controllers for classes of second-order systems, Preprints of 15th IFAC World Congress b'02, Barcelona, Spain, Paper code: 416, 2002.
[24] Preitl Zs., Controller Development by Algebraic Methods. Analysis and Matlab-Simulink programs, (in Romanian) Master thesis, “Politehnica” University of Timisoara, 2003.
[25] Zs. Preitl and T. Levendowszki, “Computer aided design of Two-Degree-Of-Freedom (2DF) controllers”, Buletinul Stiintific al Universitatii “Politehnica” din Timisoara, Romania, Seria Automatica si Calculatoare, vol.48 (62), pp. 70 – 75, 2003.
[26] J. Ackermann, Robuste Regelung, Springer Verlag, Berlin Heidelberg, New-York, 1993.
[27] M. Morari and E. Zafiriou, Robust Process Control, Prentice-Hall Inc., 1989.
[28] E. Rosenwasser and R. Yusupov, Sensitivity of Automatic Control Structure, CRC Press LLC, USA, 2000.
[29] R. Prokop, P. Husak, and Z. Prokopova, “Robust PID-like controllers –design and tuning”, Prep. of IFAC Workshop on Digital Control, Terrassa, Spain, pp.320 – 325, 2000.
[30] A. Leva and F. Schiavo, “Low-cost flexible speed control experiments”, Preprints of 16th IFAC World Congress, Prague, Czech Republic, Electronic format, Paper Th-Edd-TO/1, 2005.