Stability region analysis in Smith predictor configurations using a PI controller

Abstract

This paper deals with the stabilization problem of Smith predictor structures using a PI controller. Stability regions that include all stabilizing parameters of a PI controller for the case of perfect matching between the plant and model and for mismatched case are obtained. The models of the plant are assumed to be FOPDT (first-order plus dead time) and SOPDT (second-order plus dead time) transfer functions. Thus, the aim of this study is to determine all stabilizing PI controllers for the Smith predictor scheme and to compare the stability regions obtained for perfectly matched and mismatched models. It is observed that the stability regions obtained for both cases are quite different and the stability regions for FOPDT and SOPDT models are broader than the stability region of the actual model. Furthermore, an approach is presented to find different models of an actual system using the stability region and it is shown that the stability region of these models can fit the stability region of actual system. A simulation example is provided to illustrate the results.

Keywords

Model identification Smith predictor structure stability boundary locus stability region

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References

Abe

Yamanaka

(2003) Smith predictor control and internal model control –a tutorial. In: SICE Annual Conference, Fukui, Japan.

Ackermann

Kaesbauer

(2003) Stable polyhedra in parameter space. Automatica 39: 937–943.

Astrom

Hagglund

(1995) PID Controllers: Theory, Design, and Tuning. Research Triangle Park, NC: Instrument Society of America.

Astrom

Hagglund

(2001) The future of PID control. Control Engineering Practice 9: 1163–1175.

Benouarets

Atherton

(1994) Autotuning design methods for a Smith predictor control scheme. In: UKACC International Conference on Control’94, pp. 795–800.

Deniz

Tan

Hamamci

. (2013) Smith Öngörücüsü Yapılarıİçin Kararlılık Bölgesi Analizi, TOK’13 Otomatik Kontrol Türk Milli Komitesi Otomatik Kontrol Ulusal Toplantısı, Malatya, Türkiye.

Hamamci

(2012) PI and PID stabilization of neutral and retarded systems with time delay. Turkish Journal of Electrical Engineering & Computer Sciences 20(Sup.1): 1189–1205.

Hang

Wang

Cao

(1995) Self-tuning Smith predictors for processes with long dead time. International Journal of Adaptive Control and Signal Processing 9: 255–270.

Datta

Bhattacharyya

(1996) A new approach to feedback stabilization. In: Proceedings of the 35th CDC, pp. 4643–4648.

10.

Datta

Bhattacharyya

(1997) A linear programming characterization of all stabilizing PID controllers. In: Proceedings of American Control Conference, Albuquerque, NM.

11.

Kaya

Atherton

(1999) A new PI-PD Smith predictor for control of processes with long dead time. In: Proceedings of the 14th IFAC World Congress IFAC’99, pp. 283–288.

12.

Kaya

Atherton

(2001) Parameter estimation from relay autotuning with asymmetric limit cycle data. Journal of Process Control 11: 429–439.

13.

Kaya

(2003) Obtaining controller parameters for a new PI-PD Smith predictor using autotuning. Journal of Process Control 13(5): 465–472.

14.

Kaya

(2004) IMC based automatic tuning method for PID controllers in Smith predictor configuration. Computers & Chemical Engineering 28: 281–290.

15.

Morari

Zafiriou

(1989) Robust Process Control. Englewood Cliffs, NJ: Prentice-Hall.

16.

Normey-Rico

Camacho

(2007) Control of Dead-time Processes. London: Springer.

17.

Palmor

Blan

(1994) An auto-tuner for Smith dead time compensator. International Journal of Control 60(1): 117–135.

18.

Rivera

Morari

Sigurd

(1986) Internal model control: PID controller design. Industrial Chemistry in Process Design and Development 25(1): 252–265.

19.

Smith

OJM

(1959) A controller to overcome dead time. ISA Journal 6: 28–33.

20.

Soylemez

Munro

Baki

(2003) Fast calculation of stabilizing PID controllers. Automatica 39: 121–126.

21.

Tan

Kaya

Yeroglu

. (2006) Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Conversion and Management 47: 3045–3058.

22.

Tan

(2005) Computation of stabilizing PI and PID controllers for processes with time delay. ISA Transactions 44: 213–223.

23.

Thompson

(1985) Model reduction for closed-loop performance. Transactions of the Institute of Measurement and Control 7(3): 127–132.

24.

Thompson

(1989) Control Systems Engineering and Design. Harlow: Longman Scientific & Technical.

25.

Vodencarevic

(2010) Design of PLC-based Smith predictor for controlling processes with long dead time. IMECs 2010, Hong Kong.

26.

Zhang

(2001) Analytical design and analysis of mismatched Smith predictor. ISA Transactions 40: 133–138.