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

Year 2024, , 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

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

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