PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS

Hilal İrgan; Nusret Tan

doi:10.17482/uumfd.1318643

Research Article

PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS

Year 2024, Volume: 29 Issue: 1, 225 - 244, 22.04.2024

Hilal İrgan Nusret Tan

https://doi.org/10.17482/uumfd.1318643

Abstract

This study focuses on designing PI controllers for time-delay systems using various model order reduction techniques to reduce complexity. The stability boundary locus method was used to determine PI parameters that stabilizing reduced order models. After the PI parameters have been determined using the weighted geometric center method, the calculated controller parameters have been implemented in the original system. In this way, the efficiency of the controller design is effectively demonstrated through the reduction techniques. In addition, the study investigated the effectiveness of reduction methods with increasing time delay and adding an integrator to the system. The importance of these results is that they demonstrate the use of model order reduction techniques in the design of controllers for time-delay systems and reveal the advantages of these methods.

Keywords

Time-Delay, Weighted Geometrical Center, Model Order Reduction

References

1. Åström, K. J. and Hägglund, T. (1995) PID Controllers: Theory, Design, and Tuning (2nd ed.), Research Triangle Park, North Carolina: ISA - The Instrumentation, Systems and Automation Society.
2. Bagis, A. and Senberger, H. (2017) ABC algorithm based PID controller design for higher order oscillatory systems, Elektronika ir Elektrotechnika, 23(6). doi:10.5755/j01.eie.23.6.19688
3. Chen, T., Chang, C. and Han, K. (1979) Reduction of transfer functions by the stability-equation method, Journal of the Franklin Institute, 308(4), 389-404. doi:10.1016/0016-0032(79)90066-8
4. Cohen, G. and Coon, G. (1953) Theoretical consideration of retarded control, Transactions of the American Society of Mechanical Engineers, 75(5), 827-834. doi:10.1115/1.4015451
5. Dogruer, T. and Tan, N. (2018) Design of PI controller using optimization method in fractional order control systems, IFAC-PapersOnLine, 51(4), 841-846. doi:10.1016/j.ifacol.2018.06.124
6. Garg, M. (2017) Model order reduction and approximation analysis for control system design, 4th International Conference on Signal Processing, Computing and Control (ISPCC), Solan, India, doi:10.1109/ISPCC.2017.8269725
7. Gutman, P., Mannerfelt, C. and Molander, P. (1982) Contributions to the model reduction problem, IEEE Transactions on Automatic Control, 27(2), 454-455. doi:10.1109/TAC.1982.1102930
8. Huang, H.-P., Jeng, J.-C. and Luo, K.-Y. (2005) Auto-tune system using single-run relay feedback test and model-based controller design, Journal of process control, 15(6), 713-727. doi:10.1016/j.jprocont.2004.11.004
9. Irgan, H. and Tan, N. (2022), Model Derecesi İndirgeme Yöntemleri Kullanılarak Zaman Gecikmeli Sistemlerde Ağırlıklı Geometrik Merkez Yöntemi ile PI Kontrolör Tasarımı International Conference on Electrical and Electronics Engineering (ELECO), Bursa, Turkey.
10. Kaya, I. (2021) Optimal PI–PD controller design for pure integrating processes with time delay, Journal of Control, Automation and Electrical Systems, 32(3), 563-572. doi:10.1007/s40313-021-00692- 2
11. Kaya, I. and Peker, F. (2020) Optimal I‐PD controller design for setpoint tracking of integrating processes with time delay, IET Control Theory & Applications, 14(18), 2814-2824. doi:10.1049/iet- cta.2019.1378
12. Komarasamy, R., Albhonso, N. and Gurusamy, G. (2012) Order reduction of linear systems with an improved pole clustering, Journal of vibration and control, 18(12), 1876-1885. doi:10.1177/1077546311426592
13. Krishnamurthy, V. and Seshadri, V. (1978) Model reduction using the Routh stability criterion, IEEE Transactions on Automatic control, 23(4), 729-731. doi:10.1109/TAC.1978.1101805
14. Malwatkar, G., Sonawane, S. and Waghmare, L. (2009) Tuning PID controllers for higher-order oscillatory systems with improved performance, ISA transactions, 48(3), 347-353. doi:10.1016/j.isatra.2009.04.005
15. Monje, C. A., Chen, Y., Vinagre, B. M., Xue, D. and Feliu-Batlle, V. (2010) Fractional-order systems and controls: fundamentals and applications: Springer Science & Business Media. doi:10.1007/978-1- 84996-335-0
16. Onat, C. (2013) A new concept on PI design for time delay systems: weighted geometrical center, International Journal of Innovative Computing, information and control, 9(4), 1539-1556.
17. Onat, C., Hamamci, S. E. and Obuz, S. (2012) A practical PI tuning approach for time delay systems, IFAC Proceedings Volumes, 45(14), 102-107. doi:10.3182/20120622-3-US-4021.00027
18. Ozyetkin, M., Onat, C. and Tan, N. (2018) PID tuning method for integrating processes having time delay and inverse response, IFAC-PapersOnLine, 51(4), 274-279. doi:10.1016/j.ifacol.2018.06.077
19. Özbek, N. (2018). Control of time-delayed systems with experimental applications. Doctorate thesis, Çukurova University Graduate School of Natural and Applied Sciences, Adana.
20. Özyetkin, M. M., Onat, C. and Tan, N. (2012) Zaman Gecikmeli Sistemler için Denetçi Tasarımı, Otomatik Kontrol Ulusal Toplantısı TOK-2012, Niğde,
21. Özyetkin, M. M. and Toprak, A. (2016) Ağırlıklı geometrik merkez metodu ile pratik PI-PD kontrolör tasarımı, Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi, 7(3), 595-605.
22. Pai, N.-S., Chang, S.-C. and Huang, C.-T. (2010) Tuning PI/PID controllers for integrating processes with deadtime and inverse response by simple calculations, Journal of process control, 20(6), 726-733. doi:10.1016/j.jprocont.2010.04.003
23. Parmar, G., Mukherjee, S. and Prasad, R. (2007) Reduced order modelling of linear dynamic systems using particle swarm optimized eigen spectrum analysis, International Journal of Electrical and Computer Engineering, 1(1), 73-80. doi:10.5281/zenodo.1083457
24. Peker, F. and Kaya, I. (2022) Maximum sensitivity (Ms)-based I-PD controller design for the control of integrating processes with time delay, International Journal of Systems Science, 1-20. doi:10.1080/00207721.2022.2122759
25. Prajapati, A. K. and Prasad, R. (2020) A new model reduction method for the linear dynamic systems and its application for the design of compensator, Circuits, Systems, and Signal Processing, 39(5), 2328-2348. doi:10.1007/s00034-019-01264-1
26. Rahimian, M. A. and Tavazoei, M. S. (2012) Application of stability region centroids in robust PI stabilization of a class of second-order systems, Transactions of the Institute of Measurement and Control, 34(4), 487-498. doi:10.1177/0142331211400117
27. Sikander, A. and Prasad, R. (2017) A new technique for reduced-order modelling of linear time-invariant system, IETE Journal of Research, 63(3), 316-324. doi:10.1080/03772063.2016.1272436
28. Sinha, A. and Pal, J. (1990) Simulation based reduced order modelling using a clustering technique, Computers & Electrical Engineering, 16(3), 159-169. doi:10.1016/0045-7906(90)90020-G
29. Tan, N. (2005) Computation of stabilizing PI and PID controllers for processes with time delay, ISA transactions, 44(2), 213-223. doi:10.1016/s0019-0578(07)90000-2
30. Tan, N., Kaya, I., Yeroglu, C. and Atherton, D. P. (2006) Computation of stabilizing PI and PID controllers using the stability boundary locus, Energy Conversion and management, 47(18-19), 3045- 3058. doi:10.1016/j.enconman.2006.03.022
31. Tyreus, B. D. and Luyben, W. L. (1992) Tuning PI controllers for integrator/dead time processes, Industrial & Engineering Chemistry Research, 31(11), 2625-2628. doi:10.1021/ie00011a029
32. Zhong, Q.-C. (2006) Robust control of time-delay systems, London: Springer. doi:10.1007/1-84628-265-9
33. Ziegler, J. G. and Nichols, N. B. (1942) Optimum settings for automatic controllers, trans. ASME, 64(11). doi:10.1115/1.4019264

Farklı Model Derecesi İndirgeme Yöntemleri Kullanılarak Zaman Gecikmeli Sistemler için PI Kontrolör Tasarımı

Year 2024, Volume: 29 Issue: 1, 225 - 244, 22.04.2024

Hilal İrgan Nusret Tan

https://doi.org/10.17482/uumfd.1318643

Abstract

Bu çalışma, karmaşıklığı azaltmak için çeşitli model derecesi azaltma tekniklerini kullanarak zaman gecikmeli sistemlerde PI denetleyicileri tasarlamaya odaklanmıştır. Dereceleri azaltılmış modelleri stabilize eden PI parametrelerini belirlemek için kararlılık sınır eğrisi metodu kullanılmıştır. PI parametreleri ağırlıklı geometrik merkez yöntemi ile elde edildikten sonra, bu kontrolör parametreleri orijinal zaman gecikmeli modellerde uygulanmıştır. Böylece, model derecesi azaltma tekniklerinin uygulanması yoluyla kontrolör tasarımının verimliliği etkili bir şekilde gösterilmiştir. Ayrıca çalışma, artan zaman gecikmesi ve sisteme bir integratör eklenmesi ile model derecesi azaltma yöntemlerinin etkinliğini araştırmıştır. Bu bulguların önemi, zaman gecikmeli sistemlerde kontrolör tasarımında model derecesi azaltma tekniklerinin kullanımının gösterilerek bu yöntemlerin avantajlarının ortaya konmasıdır.

Keywords

Zaman-Gecikmesi, Ağırlıklı Geometrik Merkez, Model Derecesi İndirgeme

References

1. Åström, K. J. and Hägglund, T. (1995) PID Controllers: Theory, Design, and Tuning (2nd ed.), Research Triangle Park, North Carolina: ISA - The Instrumentation, Systems and Automation Society.
2. Bagis, A. and Senberger, H. (2017) ABC algorithm based PID controller design for higher order oscillatory systems, Elektronika ir Elektrotechnika, 23(6). doi:10.5755/j01.eie.23.6.19688
3. Chen, T., Chang, C. and Han, K. (1979) Reduction of transfer functions by the stability-equation method, Journal of the Franklin Institute, 308(4), 389-404. doi:10.1016/0016-0032(79)90066-8
4. Cohen, G. and Coon, G. (1953) Theoretical consideration of retarded control, Transactions of the American Society of Mechanical Engineers, 75(5), 827-834. doi:10.1115/1.4015451
5. Dogruer, T. and Tan, N. (2018) Design of PI controller using optimization method in fractional order control systems, IFAC-PapersOnLine, 51(4), 841-846. doi:10.1016/j.ifacol.2018.06.124
6. Garg, M. (2017) Model order reduction and approximation analysis for control system design, 4th International Conference on Signal Processing, Computing and Control (ISPCC), Solan, India, doi:10.1109/ISPCC.2017.8269725
7. Gutman, P., Mannerfelt, C. and Molander, P. (1982) Contributions to the model reduction problem, IEEE Transactions on Automatic Control, 27(2), 454-455. doi:10.1109/TAC.1982.1102930
8. Huang, H.-P., Jeng, J.-C. and Luo, K.-Y. (2005) Auto-tune system using single-run relay feedback test and model-based controller design, Journal of process control, 15(6), 713-727. doi:10.1016/j.jprocont.2004.11.004
9. Irgan, H. and Tan, N. (2022), Model Derecesi İndirgeme Yöntemleri Kullanılarak Zaman Gecikmeli Sistemlerde Ağırlıklı Geometrik Merkez Yöntemi ile PI Kontrolör Tasarımı International Conference on Electrical and Electronics Engineering (ELECO), Bursa, Turkey.
10. Kaya, I. (2021) Optimal PI–PD controller design for pure integrating processes with time delay, Journal of Control, Automation and Electrical Systems, 32(3), 563-572. doi:10.1007/s40313-021-00692- 2
11. Kaya, I. and Peker, F. (2020) Optimal I‐PD controller design for setpoint tracking of integrating processes with time delay, IET Control Theory & Applications, 14(18), 2814-2824. doi:10.1049/iet- cta.2019.1378
12. Komarasamy, R., Albhonso, N. and Gurusamy, G. (2012) Order reduction of linear systems with an improved pole clustering, Journal of vibration and control, 18(12), 1876-1885. doi:10.1177/1077546311426592
13. Krishnamurthy, V. and Seshadri, V. (1978) Model reduction using the Routh stability criterion, IEEE Transactions on Automatic control, 23(4), 729-731. doi:10.1109/TAC.1978.1101805
14. Malwatkar, G., Sonawane, S. and Waghmare, L. (2009) Tuning PID controllers for higher-order oscillatory systems with improved performance, ISA transactions, 48(3), 347-353. doi:10.1016/j.isatra.2009.04.005
15. Monje, C. A., Chen, Y., Vinagre, B. M., Xue, D. and Feliu-Batlle, V. (2010) Fractional-order systems and controls: fundamentals and applications: Springer Science & Business Media. doi:10.1007/978-1- 84996-335-0
16. Onat, C. (2013) A new concept on PI design for time delay systems: weighted geometrical center, International Journal of Innovative Computing, information and control, 9(4), 1539-1556.
17. Onat, C., Hamamci, S. E. and Obuz, S. (2012) A practical PI tuning approach for time delay systems, IFAC Proceedings Volumes, 45(14), 102-107. doi:10.3182/20120622-3-US-4021.00027
18. Ozyetkin, M., Onat, C. and Tan, N. (2018) PID tuning method for integrating processes having time delay and inverse response, IFAC-PapersOnLine, 51(4), 274-279. doi:10.1016/j.ifacol.2018.06.077
19. Özbek, N. (2018). Control of time-delayed systems with experimental applications. Doctorate thesis, Çukurova University Graduate School of Natural and Applied Sciences, Adana.
20. Özyetkin, M. M., Onat, C. and Tan, N. (2012) Zaman Gecikmeli Sistemler için Denetçi Tasarımı, Otomatik Kontrol Ulusal Toplantısı TOK-2012, Niğde,
21. Özyetkin, M. M. and Toprak, A. (2016) Ağırlıklı geometrik merkez metodu ile pratik PI-PD kontrolör tasarımı, Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi, 7(3), 595-605.
22. Pai, N.-S., Chang, S.-C. and Huang, C.-T. (2010) Tuning PI/PID controllers for integrating processes with deadtime and inverse response by simple calculations, Journal of process control, 20(6), 726-733. doi:10.1016/j.jprocont.2010.04.003
23. Parmar, G., Mukherjee, S. and Prasad, R. (2007) Reduced order modelling of linear dynamic systems using particle swarm optimized eigen spectrum analysis, International Journal of Electrical and Computer Engineering, 1(1), 73-80. doi:10.5281/zenodo.1083457
24. Peker, F. and Kaya, I. (2022) Maximum sensitivity (Ms)-based I-PD controller design for the control of integrating processes with time delay, International Journal of Systems Science, 1-20. doi:10.1080/00207721.2022.2122759
25. Prajapati, A. K. and Prasad, R. (2020) A new model reduction method for the linear dynamic systems and its application for the design of compensator, Circuits, Systems, and Signal Processing, 39(5), 2328-2348. doi:10.1007/s00034-019-01264-1
26. Rahimian, M. A. and Tavazoei, M. S. (2012) Application of stability region centroids in robust PI stabilization of a class of second-order systems, Transactions of the Institute of Measurement and Control, 34(4), 487-498. doi:10.1177/0142331211400117
27. Sikander, A. and Prasad, R. (2017) A new technique for reduced-order modelling of linear time-invariant system, IETE Journal of Research, 63(3), 316-324. doi:10.1080/03772063.2016.1272436
28. Sinha, A. and Pal, J. (1990) Simulation based reduced order modelling using a clustering technique, Computers & Electrical Engineering, 16(3), 159-169. doi:10.1016/0045-7906(90)90020-G
29. Tan, N. (2005) Computation of stabilizing PI and PID controllers for processes with time delay, ISA transactions, 44(2), 213-223. doi:10.1016/s0019-0578(07)90000-2
30. Tan, N., Kaya, I., Yeroglu, C. and Atherton, D. P. (2006) Computation of stabilizing PI and PID controllers using the stability boundary locus, Energy Conversion and management, 47(18-19), 3045- 3058. doi:10.1016/j.enconman.2006.03.022
31. Tyreus, B. D. and Luyben, W. L. (1992) Tuning PI controllers for integrator/dead time processes, Industrial & Engineering Chemistry Research, 31(11), 2625-2628. doi:10.1021/ie00011a029
32. Zhong, Q.-C. (2006) Robust control of time-delay systems, London: Springer. doi:10.1007/1-84628-265-9
33. Ziegler, J. G. and Nichols, N. B. (1942) Optimum settings for automatic controllers, trans. ASME, 64(11). doi:10.1115/1.4019264

There are 33 citations in total.

Details

Primary Language	English
Subjects	Automation Engineering
Journal Section	Research Articles
Authors	Hilal İrgan 0000-0003-0999-2483 Nusret Tan 0000-0002-1285-1991
Early Pub Date	March 28, 2024
Publication Date	April 22, 2024
Submission Date	June 22, 2023
Acceptance Date	January 4, 2024
Published in Issue	Year 2024 Volume: 29 Issue: 1

Cite

APA	İrgan, H., & Tan, N. (2024). PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 29(1), 225-244. https://doi.org/10.17482/uumfd.1318643
AMA	İrgan H, Tan N. PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS. UUJFE. April 2024;29(1):225-244. doi:10.17482/uumfd.1318643
Chicago	İrgan, Hilal, and Nusret Tan. “PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29, no. 1 (April 2024): 225-44. https://doi.org/10.17482/uumfd.1318643.
EndNote	İrgan H, Tan N (April 1, 2024) PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29 1 225–244.
IEEE	H. İrgan and N. Tan, “PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS”, UUJFE, vol. 29, no. 1, pp. 225–244, 2024, doi: 10.17482/uumfd.1318643.
ISNAD	İrgan, Hilal - Tan, Nusret. “PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29/1 (April 2024), 225-244. https://doi.org/10.17482/uumfd.1318643.
JAMA	İrgan H, Tan N. PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS. UUJFE. 2024;29:225–244.
MLA	İrgan, Hilal and Nusret Tan. “PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, vol. 29, no. 1, 2024, pp. 225-44, doi:10.17482/uumfd.1318643.
Vancouver	İrgan H, Tan N. PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS. UUJFE. 2024;29(1):225-44.

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