Manyetik Levitasyon Sistemleri İçin Ağırlıklı Geometrik Merkez Yöntemi ile PI-PD Kontrolcü Tasarımı

Year 2021, Volume: 62 Issue: 704, 556 - 579, 22.09.2021

Cem Onat Mahmut Daşkın Abdullah Turan Ömerülfaruk Özgüven

https://doi.org/10.46399/muhendismakina.877649

Cited By: 2

Abstract

Manyetik levitasyon sistemleri, mühendislik sistemlerinde sürtünmeyi en aza indiren çözümler sunduğundan, güncel mühendislik çalışmalarına tabidirler. Bu çalışmada, yeni bir PI-PD kontrolcü tasarım prosedürü sunulmuştur. PI-PD kontrolcüleri, bir PI (iç çevrim) ve bir PD (dış çevrim) kombinasyonundan oluşur. İç çevrimin amacı, açık çevrim kararsız sistemi kararlı kılmaktır. Dış çevrimin amacı, kapalı çevrim sisteminin toplam performans gereksinimlerini sağlamaktır. Tasarım prosedürü, kontrolcü parametreleri düzleminde kararlılık sınır eğrisi kullanılarak çizilen kararlı bölgenin elde edilmesine ve bu bölgenin ağırlıklı geometrik merkezinin (AGM) hesaplanmasına dayanır. Tasarım prosedüründe, ilk olarak, iç çevrim için PD kontrolcü parametrelerinin düzlemindeki kararlı bölge ve bunun ağırlıklı geometrik merkezi hesaplanır. İç çevrim, belirtilen AGM kontrol parametreleri kullanılarak tek bir bloğa indirgenir ve ardından prosedür, farklı tasarımlarda faz ve kazanç marjı performans gereksinimlerini uygulayan bir test fonksiyonu kullanılarak dış çevrim PI denetleyicisi için tekrarlanır. Deneysel çalışma, önerilen metodoloji ile tasarlanan PI-PD kontrolcünün literatürde bulunan alternatiflere göre daha üstün performans sergilediğini göstermektedir.

Keywords

PI-PD kontrol;, kararsız sistem,, maglev;, ağırlıklı geometrik merkez.

Supporting Institution

İnönü Üniversitesi Bilimsel Araştırma Birimi (BAP)

Project Number

FDK-2017-886

Thanks

Bu çalışma, İnönü Üniversitesi Bilimsel Araştırma Birimi (BAP) tarafından desteklenmiştir.

PI-PD Controller Design for Magnetic Levitation Systems Via Weighted Geometrical Center Method

Abstract

Since magnetic levitation systems offer solutions that minimize friction in engineering systems, they are subject to current engineering studies. In this study, a new PI-PD controller design procedure has been presented. A PI-PD controller consists of a combination of a PI (inner loop) and a PD (outer loop). The purpose of the inner loop is to stabilize the open loop unstable system. The purpose of the outer loop is to provide the total performance requirements of the closed loop system. The design procedure is based on obtaining the stability area plotted using the stability boundary curve in the control parameters plane, and then calculating the weighted geometrical center (WGC) of the stability region. In the design procedure, first, the stable region in the plane of the PD controller parameters for the inner loop and its weighted geometrical center are computed. The inner loop is reduced to a single block by using specified WGC control parameters, and then the procedure is repeated for the outer loop PI controller by using of a test function imposing the phase and gain margin performance requirements in different designs. Experimental study shows that the PI-PD controller, which is designed with the suggested methodology, exhibits superior performance compared to the alternatives available in the literature.

Keywords

PI-PD controller;, unstable system;, maglev;, weighted geometrical center.

Project Number

FDK-2017-886

References

• 1. Yaghoubi, H. 2013. "The most important maglev applications," Journal of Engineering, vol. 2013, p. 1-19.
• 2. Maslen, E. H.,Schweitzer, G. 2009. "Magnetic bearings: theory, design, and application to rotating machinery," Berlin Heidelberg, Germany.
• 3. Yoshida, K.,Zhang, X. 2005. "Propulsion and guidance control in ropeless linear elevator with pitching motion," 2005 International Conference on Electrical Machines and Systems, vol. 3, p. 1887-1892.
• 4. Zhang, Y., Liu, S., Guan, Y., Li, H.,Fan, Y. 2010. "The axial position sensing and signal processing in maglev artificial heart pump," 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), p. 396-400.
• 5. Ahmad, I.,Javaid, M. A. 2010. "Nonlinear model & controller design for magnetic levitation system," Recent advances in signal processing, robotics and automation, p. 324-328.
• 6. Kumar, T., Shimi, S., Karanjkar, D.,Rana, S. 2014. "Modeling, simulation and control of single actuator magnetic levitation system," 2014 Recent Advances in Engineering and Computational Sciences (RAECS), p. 1-6.
• 7. Green, S. A.,Craig, K. C. 1998. "Robust, digital, nonlinear control of magnetic-levitation systems," Journal of Dynamics, Measurement, and Control, vol.120, no.4, p. 488-495.
• 8. Kim, C.,Kim, K. 1994. "Gain scheduled control of magnetic bearings technology," Proc. American Contr. Conf, p. 3127-3131.
• 9. El Rifai, O. M.,Youcef-Toumi, K. 1998. "Achievable performance and design trade-offs in magnetic levitation control," AMC'98-Coimbra. 1998 5th International Workshop on Advanced Motion Control. Proceedings (Cat. No. 98TH8354), p. 586-591.
• 10. Lairi, M.,Bloch, G. 1999. "A neural network with minimal structure for maglev system modeling and control," Proceedings of the 1999 IEEE International Symposium on Intelligent Control Intelligent Systems and Semiotics (Cat. No. 99CH37014), p. 40-45.
• 11. Swain, S. K., Sain, D., Mishra, S. K.,Ghosh, S. 2017. "Real time implementation of fractional order PID controllers for a magnetic levitation plant," AEU-International Journal of Electronics and Communications, vol. 78, p. 141-156.
• 12. Sain, D., Swain, S. K.,Mishra, S. K. 2017. "Real-time implementation of robust set-point weighted PID controller for magnetic levitation system," International Journal on Electrical Engineering and Informatics, vol. 9, no. 2, p. 272.
• 13. Sain, D. 2019. "Real-Time implementation and performance analysis of robust 2-DOF PID controller for Maglev system using pole search technique," Journal of Industrial Information Integration, vol. 15, p. 183-190.
• 14. Duka, A.-V., Dulău, M.,Oltean, S.-E. 2016. "IMC based PID control of a magnetic levitation system," Procedia Technology, vol. 22, p. 592-599.
• 15. Pandey, S. K.,Laxmi, V. 2014. "PID control of magnetic levitation system based on derivative filter," 2014 Annual International Conference on Emerging Research Areas: Magnetics, Machines and Drives (AICERA/iCMMD), p. 1-5.
• 16. Ahmad, I., Shahzad, M., Palensky, P. 2014. "Optimal PID control of magnetic levitation system using genetic algorithm," 2014 IEEE International Energy Conference (ENERGYCON), p. 1429-1433.
• 17. Kumar, E. V., Jerome, J. 2013. "LQR based optimal tuning of PID controller for trajectory tracking of magnetic levitation system," Procedia Engineering, vol. 64, p. 254-264.
• 18. Gandhi, R. V.,Adhyaru, D. M. 2018. "Pre-fuzzy-PID controller for effective control of electromagnetic levitation system," 2018 Indian Control Conference (ICC), p. 113-118.
• 19. Lin, C.-M., Lin, M.-H.,Chen, C.-W. 2011. "SoPC-based adaptive PID control system design for magnetic levitation system," IEEE Systems journal, vol. 5, no. 2, p. 278-287.
• 20. Onat, C. 2019. "A new design method for PI–PD control of unstable processes with dead time," ISA transactions, vol. 84, p. 69-81.
• 21. Ali, H. I.,Saeed, A. H. 2016. "Robust PI-PD controller design for systems with parametric uncertainties," Engineering & Technology Journal, vol. 34.
• 22. Sain, D., Swain, S. K.,Mishra, S. K. 2018. "Real time implementation of optimized I-PD controller for the magnetic levitation system using Jaya algorithm," IFAC-PapersOnLine, vol. 51, no. 1, p. 106-111.
• 23. Sain, D., Swain, S. K.,Mishra, S. K. 2016. "TID and I-TD controller design for magnetic levitation system using genetic algorithm," Perspectives in Science, vol. 8, p. 370-373.
• 24. Onat, C. 2013. "A new concept on PI design for time delay systems: weighted geometrical center," International Journal of Innovative Computing, information and control, vol. 9, no. 4, p. 1539-1556.
• 25. Ozyetkin, M. M., Onat, C.,Tan, N. 2020. "PI‐PD controller design for time delay systems via the weighted geometrical center method," Asian Journal of Control, vol. 22, no. 5, p. 1811-1826.
• 26. Hamamci, S. E.,Tan, N. 2006. "Design of PI controllers for achieving time and frequency domain specifications simultaneously," ISA transactions, vol. 45, no. 4, p. 529-543.
• 27. Ho, M.-T., Datta, A.,Bhattacharyya, S. 1996. "A new approach to feedback stabilization," Proceedings of 35th IEEE Conference on Decision and Control, vol. 4, p. 4643-4648.
• 28. Ho, M.-T., Datta, A.,Bhattacharyya, S. 1997. "A linear programming characterization of all stabilizing PID controllers," Proceedings of the 1997 American Control Conference (Cat. No. 97CH36041), vol. 6, p. 3922-3928.
• 29. Ghosh, A., Krishnan, T. R., Tejaswy, P., Mandal, A., Pradhan, J. K.,Ranasingh, S. 2014. "Design and implementation of a 2-DOF PID compensation for magnetic levitation systems," ISA transactions, vol. 53, no. 4, p. 1216-1222.
• 30. Onat, C. 2014. "WGC based robust and gain scheduling PI controller design for condensing boilers," Advances in Mechanical Engineering, vol. 6, p. 659051.
• 31. Kharitonov, V. 1979. "Asymptotic Stability of Equillibrium Position of a Family of Systems of Linear Differential Equations," Differential equations, p. 1483-1485.
• 32. Ozyetkin, M. M., Onat, C.,Tan, N. 2018. "PID tuning method for integrating processes having time delay and inverse response," IFAC-PapersOnLine, vol. 51, no. 4, p. 274-279.
• 33. Onat, C., Hamamci, S. E.,Obuz, S. 2012. "A practical PI tuning approach for time delay systems," IFAC Proceedings Volumes, vol. 45, no. 14, p. 102-107.