Performance comparison of different Smith Predictor controller structures

Abstract

Industrial processes have significant time delays due to their long-time constants and the inclusion of integrators. This can lead to undesirable conditions such as high overshoot, oscillation, and instability. The Smith Predictor, developed by O. J. M. Smith, is an effective controller structure for controlling processes with time delays. This study compares the performance of four different Smith Predictor structures previously presented in the literature. To ensure the comparisons are objective, the controller parameters for all predictor models were determined using a Genetic Algorithm (GA)-based optimization method under the same optimization settings. Three different long-time-delay systems were considered in the study: the first is a fourth-order system with no roots at the origin, the second is a fifth-order system with one root at the origin and the others discrete, and the third is a second-order, two-pole system containing a pole at the origin. Based on the findings, the Smith Predictor structure was determined to offer the best control performance among the four structures examined for time-delay systems.

Keywords

• Smith predictictor
• time-delay systems
• genetic algorithm optimization

Farklı Smith Öngörücü kontrolör yapılarının performans karşılaştırması

Abstract

Endüstriyel süreçler, geniş zaman sabiteleri ve entegratör içermeleri nedeniyle ciddi zaman gecikmesine sahiptirler. Bu ise yüksek aşım oranı, salınım ve kararsızlık gibi istenmeyen durumları ortaya çıkarabilmektedir. O. J. M. Smith tarafından geliştirilen Smith Öngörücüsü, zaman gecikmesi içeren proseslerin kontrolünde etkili bir kontrolör yapısıdır. Bu çalışmada, daha önce literatürde sunulmuş dört farklı Smith Öngörücüsü yapısının performansları karşılaştırılmaktadır. Karşılaştırmaların nesnel olabilmesi için tüm öngörücü modellerinde kontrolör parametreleri, Genetik Algoritma (GA) temelli optimizasyon yöntemi ile aynı optimizasyon ayarları altında belirlenmiştir. Çalışmada üç farklı uzun zaman gecikmeli sistem dikkate alınmıştır: İlkinde dördüncü dereceden ve orijinde kök bulundurmayan bir sistem, ikincisinde beşinci dereceden, bir kökü orijinde ve diğerleri ayrık olan bir sistem, üçüncüsünde ise ikinci dereceden, orijinde bir kutup içeren iki kutuplu bir sistem ele alınmaktadır. Elde edilen bulgular ile zaman gecikmeli sistemler için incelenen dört yapıdan en iyi kontrol performansını sunan Smith Öngörücüsü yapısı belirlenmiştir.

Keywords

• Smith öngörücü
• zaman gecikmeli sistemler
• genetik algoritma optimizasyonu

References

1. [1] J Y. İçmez and M. S. Can, “Smith Predictor Controller Design Using the Direct Synthesis Method for Unstable Second-Order and Time-Delay Systems,” Processes, vol. 11, no. 3, p. 941, 2023, doi: 10.3390/pr11030941.
2. [2] A. Rao, “Analytical design of modified Smith predictor in a two-degrees-of-freedom control scheme for second order unstable processes with time delay,” ISA Transactions, vol. 47, no. 4, pp. 407–419, 2008, doi: 10.1016/S0019-0578(07)60118-9.
3. [3] V. L. Korupu and M. Muthukumarasamy, “A comparative study of various Smith predictor configurations for industrial delay processes,” Chemical Product and Process Modeling, vol. 17, no. 6, pp. 701–732, 2022, doi: 10.1515/cppm-2021-0026.
4. [4] I. Kaya, “A PI-PD controller design for control of unstable and integrating processes,” ISA Transactions, vol. 42, no. 1, pp. 111–121, 2003, doi: 10.1016/S0019-0578(07)60118-9.
5. [5] I. Kaya, “PI-PD controllers for controlling stable processes with inverse response and dead time,” Electrical Engineering, vol. 98, no. 1, pp. 55–65, 2016, doi: 10.1007/s00202-015-0352-3.
6. [6] D. G. Padhan and S. Majhi, “Modified Smith predictor based cascade control of unstable time delay processes,” ISA Transactions, vol. 51, no. 1, pp. 95–104, 2012, doi: 10.1016/j.isatra.2011.08.002.
7. [7] O. J. M. Smith, “A controller to overcome dead time,” ISA J., vol. 6, no. 2, pp. 28–33, 1959. [Online]. Available: https://cir.nii.ac.jp/crid/1572543025873489664
8. [8] F. Alyoussef and I. Kaya, “Tuning proportional–integral controllers based on new analytical methods for finding centroid of stability locus for stable/unstable first-order plus dead-time processes,” Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng., 2021, doi: 10.1177/09596518211048028.

9. [9] P. Ioannou, K. Gousman, R. Rooney, D. Boskovic, S. Yu, R. K. Mehra, M. Gopinathan, J. D. Boskovic, and C. Rago, “Stability analysis and observer design for neutral delay systems,” IEEE Trans. Autom. Control, vol. 47, no. 3, pp. 969–976, 2002, doi: 10.1109/TAC.2002.989144.
10. [10] A. S. Rao and M. Chidambaram, “Analytical design of modified Smith predictor in a two-degrees-of-freedom control scheme for second order unstable processes with time delay,” ISA Transactions, vol. 47, no. 4, pp. 407–419, 2008, doi: 10.1016/S0019-0578(07)60118-9.
11. [11] M. Ajmeri and A. Ali, “Modified Smith predictor and controller for unstable first order processes,” in Proc. Indian Control Conf. (ICC), IEEE, 2017, doi: 10.1109/INDIANCC.2017.7846507.
12. [12] J. E. Normey-Rico and E. F. Camacho, Control of Dead-Time Processes. London, U.K.: Springer, 2007.
13. [13] T. Liu, W. Zhang, and D. Gu, “Analytical design of two-degree-of-freedom control scheme for open-loop unstable processes with time delay,” J. Process Control, vol. 15, no. 5, pp. 559–572, 2005, doi: 10.1016/S0959-1524(04)00114-3.
14. [14] W. Zhang, Y. Sun, and X. Xu, “Two degree-of-freedom Smith predictor for processes with time delay,” Automatica, vol. 34, no. 10, pp. 1279–1282, 1998.
15. [15] C. Mejía, et al., “A modified Smith predictor for processes with variable delay,” in Proc. IEEE 4th Colombian Conf. Automatic Control (CCAC), 2019.
16. [16] N. S. Özbek and I. Eker, “A fractional fuzzy PI-PD based modified Smith predictor for controlling of FOPDT process,” in Proc. 5th Int. Conf. Electronic Devices, Systems and Applications (ICEDSA), 2016.
17. [17] C. Mejía, E. Salazar, and O. Camacho, “A comparative experimental evaluation of various Smith predictor approaches for a thermal process with large dead time,” Alexandria Eng. J., vol. 61, no. 12, pp. 9377–9394, 2022.
18. [18] F. N. Deniz, et al., “Stability region analysis in Smith predictor configurations using a PI controller,” Trans. Inst. Meas. Control, vol. 37, no. 5, pp. 606–614, 2015.
19. [19] S. E. Hamamci, I. Kaya, and D. P. Atherton, “Smith predictor design by CDM,” in Proc. Eur. Control Conf. (ECC), 2001.
20. [20] V. Kachitvichyanukul, “Comparison of three evolutionary algorithms: GA, PSO, and DE,” Ind. Eng. Manag. Syst., vol. 11, no. 3, pp. 215–223, 2012.
21. [21] I. Erlich, G. Venayagamoorthy, and N. Worawat, “A mean-variance optimization algorithm,” in Proc. IEEE Congr. Evol. Comput., Barcelona, Spain, 2010, pp. 1–6.
22. [22] M. J. Kochenderfer and T. A. Wheeler, Algorithms for Optimization. Cambridge, MA, USA: MIT Press, 2019.
23. [23] B. Friedland, Advanced Control System Design. New York, NY, USA: McGraw-Hill, 1996.
24. [24] J. K. Parker, A. R. Khoogar, and D. E. Goldberg, “Inverse kinematics of redundant robots using genetic algorithms,” in Proc. IEEE Int. Conf. Robotics and Automation, 1989, pp. 271–276.
25. [25] J. H. Holland, “Genetic algorithms and adaptation,” in Adaptive Control of Ill-Defined Systems. Boston, MA, USA: Springer, 1984, pp. 317–333.
26. [26] M. Mitchell, An Introduction to Genetic Algorithms. Cambridge, MA, USA: MIT Press, 1998.
27. [27] R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms. Hoboken, NJ, USA: John Wiley & Sons, 2004.
28. [28] S. N. Sivanandam and S. N. Deepa, Introduction to Genetic Algorithms. Berlin, Germany: Springer, 2008.