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Doğrusal Olmayan Manyetik Levitasyon Sisteminin Kontrolü için PID ve LQR Kontrolcülerinin Performans Karşılaştırılması

Year 2023, Volume: 25 Issue: 74, 339 - 350, 15.05.2023

Yusuf Karabacak , Ali Yaşar , İsmail Saritas

https://doi.org/10.21205/deufmd.2023257407

Abstract

Manyetik Levitasyon Sistemi (MLS), düşük enerji tüketimi ve minimum sürtünme gibi avantajlarından dolayı mühendislik alanında güncel bir çalışma haline gelmiştir. MLS'ler doğrusal olmayan kararsız sistemlerdir. Yapının karmaşıklığı ve kontrollerin zorluğu nedeniyle bu sistemler üzerinde birçok gelişmiş kontrol teorisi uygulanabilmekte ve kontrolörlerin performansı değerlendirilebilmektedir. Bu makalede, MATLAB ortamında matematiksel olarak modellenen MLS üzerinde, Oransal–İntegral–Türev (PID) ve Lineer-Quadratic Regulator (LQR) denetleyici yöntemleri uygulanmıştır. Bulunan sonuçlarda denetleyici performansları karşılaştırılmıştır. PID ve LQR kontrol yöntemlerinin MLS için uygulanabilirliği konusunda elde edilen sonuçlar değerlendirilmiştir. Ayrıca kontrolörlerin sistem performansı bakımından beş parametre ile karşılaştırılmıştır. Bunlar yükselme zamanı, yerleşme zamanı, maksimum aşma, aşma ve kararlı durum hatasıdır. LQR kontrolör, PID kontrolöre kıyasla büyük bir kararlılık ve homojen yanıt üretmiştir.

Keywords

Magnetic Levitation System PID Control LQR Control

References

  • [1] M. Ono, S. Koga, and H. Ohtsuki, “Japan’s superconducting maglev train,” IEEE Instrum. Meas. Mag., vol. 5, no. 1, pp. 9–15, 2002.
  • [2] D. M. Rote and Y. Cai, “Review of dynamic stability of repulsive-force maglev suspension systems,” IEEE Trans. Magn., vol. 38, no. 2, pp. 1383–1390, 2002.
  • [3] M.-Y. Chen, M.-J. Wang, and L.-C. Fu, “A novel dual-axis repulsive maglev guiding system with permanent magnet: Modeling and controller design,” IEEE/ASME Trans. mechatronics, vol. 8, no. 1, pp. 77–86, 2003.
  • [4] J. de Boeij, M. Steinbuch, and H. Gutiérrez, “Real-time control of the 3-DOF sled dynamics of a null-flux Maglev system with a passive sled,” IEEE Trans. Magn., vol. 42, no. 5, pp. 1604–1610, 2006.
  • [5] C.-M. Huang, J.-Y. Yen, and M.-S. Chen, “Adaptive nonlinear control of repulsive maglev suspension systems,” Control Eng. Pract., vol. 8, no. 12, pp. 1357–1367, 2000.
  • [6] A. Zomorodian, M. B. Menhaj, Z. Daghooghi, and I. Saboori, “A real time digital controller for magnetic levitation system,” in 2007 2nd IEEE Conference on Industrial Electronics and Applications, 2007, pp. 1013–1018.
  • [7] Y. Karabacak, İ. A. OZKAN, and İ. SARİTAS, “Estimation of li-ion battery state of charge using adaptive neural fuzzy inference system (ANFIS),” Int. J. Energy Appl. Technol., vol. 7, no. 3, pp. 88–94.
  • [8] E. Lughofer and M. Sayed-Mouchaweh, “Adaptive and on-line learning in non-stationary environments,” Evolving Systems, vol. 6, no. 2. Springer, pp. 75–77, 2015.
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  • [10] J. A. Meda-Campaña, J. Rodríguez-Valdez, T. Hernández-Cortés, R. Tapia-Herrera, and V. Nosov, “Analysis of the fuzzy controllability property and stabilization for a class of T–S fuzzy models,” IEEE Trans. Fuzzy Syst., vol. 23, no. 2, pp. 291–301, 2014.
  • [11] M. Sayed-Mouchaweh and E. Lughofer, “Decentralized fault diagnosis approach without a global model for fault diagnosis of discrete event systems,” Int. J. Control, vol. 88, no. 11, pp. 2228–2241, 2015.
  • [12] Q. B. Jin and Q. Liu, “IMC-PID design based on model matching approach and closed-loop shaping,” ISA Trans., vol. 53, no. 2, pp. 462–473, 2014.
  • [13] A. Besançon-Voda, “Iterative auto-calibration of digital controllers: Methodology and applications,” Control Eng. Pract., vol. 6, no. 3, pp. 345–358, 1998.
  • [14] R.-E. Precup and S. Preitl, “PI and PID controllers tuning for integral-type servo systems to ensure robust stability and controller robustness,” Electr. Eng., vol. 88, no. 2, pp. 149–156, 2006.
  • [15] V. J. Ginter and J. K. Pieper, “Robust gain scheduled control of a hydrokinetic turbine,” IEEE Trans. Control Syst. Technol., vol. 19, no. 4, pp. 805–817, 2010.
  • [16] I. Ahmad, M. Shahzad, and P. Palensky, “Optimal PID control of magnetic levitation system using genetic algorithm,” in 2014 IEEE International Energy Conference (ENERGYCON), 2014, pp. 1429–1433.
  • [17] E. V. Kumar and J. Jerome, “LQR based optimal tuning of PID controller for trajectory tracking of magnetic levitation system,” Procedia Eng., vol. 64, pp. 254–264, 2013.
  • [18] M. H. A. Yaseen and H. J. Abd, “Modeling and control for a magnetic levitation system based on SIMLAB platform in real time,” Results Phys., vol. 8, pp. 153–159, 2018.
  • [19] S. Çeven and A. Albayrak, “Çift ters sarkaç sisteminin kontrolü için PID ve LQR kontrolcü tasarımlarının modellenmesi,” Avrupa Bilim ve Teknol. Derg., pp. 323–330, 2020.
  • [20] Y. Karabacak and A. Uysal, “An embedded controller application with regenerative braking for the electric vehicle,” Elektron. ir Elektrotechnika, vol. 26, no. 1, pp. 10–17, 2020.
  • [21] F. Duran, S. Ceven, and R. Bayir, “Drive mode estimation for electric vehicles via fuzzy logic,” in 2018 22nd International Conference Electronics, 2018, pp. 1–5.
  • [22] S. Çeven, A. Albayrak, and R. Bayır, “Real-time range estimation in electric vehicles using fuzzy logic classifier,” Comput. Electr. Eng., vol. 83, p. 106577, 2020.
  • [23] Y. Karabacak and A. Uysal, “Fuzzy logic controlled brushless direct current motor drive design and application for regenerative braking,” in 2017 International Artificial Intelligence and Data Processing Symposium (IDAP), 2017, pp. 1–7.
  • [24] K. Anurag and S. Kamlu, “Design of LQR-PID controller for linearized magnetic levitation system,” in 2018 2nd International Conference on Inventive Systems and Control (ICISC), 2018, pp. 444–447. [25] L. Liu, J. D. Yau, J. Qin, and S. Urushadze, “Optimal dynamic control for a maglev vehicle moving on multi-span guideway girders,” J. Mech., vol. 37, pp. 373–379, 2022.
  • [26] Š. Chamraz, M. Huba, and K. Žáková, “Stabilization of the magnetic levitation system,” Appl. Sci., vol. 11, no. 21, p. 10369, 2021.
  • [27] M. H. A. Yaseen, “A comparative study of stabilizing control of a planer electromagnetic levitation using PID and LQR controllers,” Results Phys., vol. 7, pp. 4379–4387, 2017.
  • [28] M. Khatri, P. Dahiya, and A. Chaturvedi, “Performance Enhancement of Suspension System of an Electric Vehicle Using Nature Inspired Meta-Heuristic Optimization Algorithm,” in Ubiquitous Intelligent Systems, Springer, 2022, pp. 157–170.
  • [29] S. Yadav, S. K. Verma, and S. K. Nagar, “Optimized PID controller for magnetic levitation system,” Ifac-PapersOnLine, vol. 49, no. 1, pp. 778–782, 2016.
  • [30] O. Cem, M. DAŞKIN, A. Turan, and Ö. Özgüven, “Manyetik levitasyon sistemleri için ağırlıklı geometrik merkez yöntemi ile PI-PD kontrolcü tasarımı,” Mühendis ve Makina, vol. 62, no. 704, pp. 556–579, 2021.
  • [31] E. M. GÖKER and K. ERKAN, “Yeni Artı (+) Tip 4 Kutuplu Temassız Taşıyıcı Sistemin Tasarımı ve Manyetik Kuvvet Analizleri,” Avrupa Bilim ve Teknol. Derg., no. 35, pp. 373–379.
  • [32] F. KORKMAZ and H. KARCI, “Doğrusal Sistemlerin Model Bağımsız Kontrolü,” Harran Üniversitesi Mühendislik Derg., vol. 5, no. 2, pp. 122–133.
  • [33] T. Deepa et al., “Comparative Study of Different Controllers for Levitating Ferromagnetic Material,” Adv. Mater. Sci. Eng., vol. 2022, 2022.
  • [34] C. Choubey and J. Ohri, “Tuning of LQR-PID controller to control parallel manipulator,” Neural Comput. Appl., vol. 34, no. 4, pp. 3283–3297, 2022.
  • [35] D. Pandey, S. Yadav, and S. Mishra, “Optimal LQR and Smith Predictor Based PID Controller Design for NMP System,” in Mobile Radio Communications and 5G Networks, Springer, 2022, pp. 211–222.
  • [36] P. Rai and B. Pratap, “Design of Robust Controller for Enhanced Performance of 2-DOF Torsion System,” in Communication and Control for Robotic Systems, Springer, 2022, pp. 465–480.
  • [37] H. Calgan and M. Demirtas, “A robust LQR-FOPIλDµ controller design for output voltage regulation of stand-alone self-excited induction generator,” Electr. Power Syst. Res., vol. 196, p. 107175, 2021.
  • [38] A. S. Elkhatem and S. N. Engin, “Robust LQR and LQR-PI control strategies based on adaptive weighting matrix selection for a UAV position and attitude tracking control,” Alexandria Eng. J., vol. 61, no. 8, pp. 6275–6292, 2022.
  • [39] A. Uysal, S. Gokay, E. Soylu, T. Soylu, and S. Çaşka, “Fuzzy proportional-integral speed control of switched reluctance motor with MATLAB/Simulink and programmable logic controller communication,” Meas. Control, vol. 52, no. 7–8, pp. 1137–1144, 2019.
  • [40] I. Ahmad and M. A. Javaid, “Nonlinear model & controller design for magnetic levitation system,” Recent Adv. signal Process. Robot. Autom., pp. 324–328, 2010.
  • [41] B. C. Kuo, Automatic Control Systems. 1999.
  • [42] A. Isidori, Nonlinear control systems: an introduction. Springer, 1985.

Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System

Year 2023, Volume: 25 Issue: 74, 339 - 350, 15.05.2023

Yusuf Karabacak , Ali Yaşar , İsmail Saritas

https://doi.org/10.21205/deufmd.2023257407

Abstract

Magnetic Levitation System (MLS) has become a current study in the field of engineering due to its advantages such as low energy consumption and minimum friction. MLSs are nonlinear unstable systems. Due to the complexity of the structure and the difficulty of the controls, many advanced control theories can be applied on these systems and the performance of the controllers can be evaluated. In this article, Proportional-Integral-Derivative (PID) and Linear-Quadratic Regulator (LQR) controller methods are applied on MLS mathematically modeled in MATLAB environment. Controller performances were compared in the results found. The results obtained on the applicability of PID and LQR control methods for MLS were evaluated. In addition, the system performance of the controllers was compared with five parameters. These are rise time, settling time, maximum overshoot, overshoot and steady-state error. LQR controller produced great stability and homogeneous response compared to PID controller.

Keywords

Magnetic Levitation System PID Control LQR Control Non-linear System Control

References

  • [1] M. Ono, S. Koga, and H. Ohtsuki, “Japan’s superconducting maglev train,” IEEE Instrum. Meas. Mag., vol. 5, no. 1, pp. 9–15, 2002.
  • [2] D. M. Rote and Y. Cai, “Review of dynamic stability of repulsive-force maglev suspension systems,” IEEE Trans. Magn., vol. 38, no. 2, pp. 1383–1390, 2002.
  • [3] M.-Y. Chen, M.-J. Wang, and L.-C. Fu, “A novel dual-axis repulsive maglev guiding system with permanent magnet: Modeling and controller design,” IEEE/ASME Trans. mechatronics, vol. 8, no. 1, pp. 77–86, 2003.
  • [4] J. de Boeij, M. Steinbuch, and H. Gutiérrez, “Real-time control of the 3-DOF sled dynamics of a null-flux Maglev system with a passive sled,” IEEE Trans. Magn., vol. 42, no. 5, pp. 1604–1610, 2006.
  • [5] C.-M. Huang, J.-Y. Yen, and M.-S. Chen, “Adaptive nonlinear control of repulsive maglev suspension systems,” Control Eng. Pract., vol. 8, no. 12, pp. 1357–1367, 2000.
  • [6] A. Zomorodian, M. B. Menhaj, Z. Daghooghi, and I. Saboori, “A real time digital controller for magnetic levitation system,” in 2007 2nd IEEE Conference on Industrial Electronics and Applications, 2007, pp. 1013–1018.
  • [7] Y. Karabacak, İ. A. OZKAN, and İ. SARİTAS, “Estimation of li-ion battery state of charge using adaptive neural fuzzy inference system (ANFIS),” Int. J. Energy Appl. Technol., vol. 7, no. 3, pp. 88–94.
  • [8] E. Lughofer and M. Sayed-Mouchaweh, “Adaptive and on-line learning in non-stationary environments,” Evolving Systems, vol. 6, no. 2. Springer, pp. 75–77, 2015.
  • [9] J. A. Iglesias and I. Škrjanc, “Applications, results and future direction (EAIS 12),” Evolving Systems, vol. 5, no. 1. Springer, pp. 1–2, 2014.
  • [10] J. A. Meda-Campaña, J. Rodríguez-Valdez, T. Hernández-Cortés, R. Tapia-Herrera, and V. Nosov, “Analysis of the fuzzy controllability property and stabilization for a class of T–S fuzzy models,” IEEE Trans. Fuzzy Syst., vol. 23, no. 2, pp. 291–301, 2014.
  • [11] M. Sayed-Mouchaweh and E. Lughofer, “Decentralized fault diagnosis approach without a global model for fault diagnosis of discrete event systems,” Int. J. Control, vol. 88, no. 11, pp. 2228–2241, 2015.
  • [12] Q. B. Jin and Q. Liu, “IMC-PID design based on model matching approach and closed-loop shaping,” ISA Trans., vol. 53, no. 2, pp. 462–473, 2014.
  • [13] A. Besançon-Voda, “Iterative auto-calibration of digital controllers: Methodology and applications,” Control Eng. Pract., vol. 6, no. 3, pp. 345–358, 1998.
  • [14] R.-E. Precup and S. Preitl, “PI and PID controllers tuning for integral-type servo systems to ensure robust stability and controller robustness,” Electr. Eng., vol. 88, no. 2, pp. 149–156, 2006.
  • [15] V. J. Ginter and J. K. Pieper, “Robust gain scheduled control of a hydrokinetic turbine,” IEEE Trans. Control Syst. Technol., vol. 19, no. 4, pp. 805–817, 2010.
  • [16] I. Ahmad, M. Shahzad, and P. Palensky, “Optimal PID control of magnetic levitation system using genetic algorithm,” in 2014 IEEE International Energy Conference (ENERGYCON), 2014, pp. 1429–1433.
  • [17] E. V. Kumar and J. Jerome, “LQR based optimal tuning of PID controller for trajectory tracking of magnetic levitation system,” Procedia Eng., vol. 64, pp. 254–264, 2013.
  • [18] M. H. A. Yaseen and H. J. Abd, “Modeling and control for a magnetic levitation system based on SIMLAB platform in real time,” Results Phys., vol. 8, pp. 153–159, 2018.
  • [19] S. Çeven and A. Albayrak, “Çift ters sarkaç sisteminin kontrolü için PID ve LQR kontrolcü tasarımlarının modellenmesi,” Avrupa Bilim ve Teknol. Derg., pp. 323–330, 2020.
  • [20] Y. Karabacak and A. Uysal, “An embedded controller application with regenerative braking for the electric vehicle,” Elektron. ir Elektrotechnika, vol. 26, no. 1, pp. 10–17, 2020.
  • [21] F. Duran, S. Ceven, and R. Bayir, “Drive mode estimation for electric vehicles via fuzzy logic,” in 2018 22nd International Conference Electronics, 2018, pp. 1–5.
  • [22] S. Çeven, A. Albayrak, and R. Bayır, “Real-time range estimation in electric vehicles using fuzzy logic classifier,” Comput. Electr. Eng., vol. 83, p. 106577, 2020.
  • [23] Y. Karabacak and A. Uysal, “Fuzzy logic controlled brushless direct current motor drive design and application for regenerative braking,” in 2017 International Artificial Intelligence and Data Processing Symposium (IDAP), 2017, pp. 1–7.
  • [24] K. Anurag and S. Kamlu, “Design of LQR-PID controller for linearized magnetic levitation system,” in 2018 2nd International Conference on Inventive Systems and Control (ICISC), 2018, pp. 444–447. [25] L. Liu, J. D. Yau, J. Qin, and S. Urushadze, “Optimal dynamic control for a maglev vehicle moving on multi-span guideway girders,” J. Mech., vol. 37, pp. 373–379, 2022.
  • [26] Š. Chamraz, M. Huba, and K. Žáková, “Stabilization of the magnetic levitation system,” Appl. Sci., vol. 11, no. 21, p. 10369, 2021.
  • [27] M. H. A. Yaseen, “A comparative study of stabilizing control of a planer electromagnetic levitation using PID and LQR controllers,” Results Phys., vol. 7, pp. 4379–4387, 2017.
  • [28] M. Khatri, P. Dahiya, and A. Chaturvedi, “Performance Enhancement of Suspension System of an Electric Vehicle Using Nature Inspired Meta-Heuristic Optimization Algorithm,” in Ubiquitous Intelligent Systems, Springer, 2022, pp. 157–170.
  • [29] S. Yadav, S. K. Verma, and S. K. Nagar, “Optimized PID controller for magnetic levitation system,” Ifac-PapersOnLine, vol. 49, no. 1, pp. 778–782, 2016.
  • [30] O. Cem, M. DAŞKIN, A. Turan, and Ö. Özgüven, “Manyetik levitasyon sistemleri için ağırlıklı geometrik merkez yöntemi ile PI-PD kontrolcü tasarımı,” Mühendis ve Makina, vol. 62, no. 704, pp. 556–579, 2021.
  • [31] E. M. GÖKER and K. ERKAN, “Yeni Artı (+) Tip 4 Kutuplu Temassız Taşıyıcı Sistemin Tasarımı ve Manyetik Kuvvet Analizleri,” Avrupa Bilim ve Teknol. Derg., no. 35, pp. 373–379.
  • [32] F. KORKMAZ and H. KARCI, “Doğrusal Sistemlerin Model Bağımsız Kontrolü,” Harran Üniversitesi Mühendislik Derg., vol. 5, no. 2, pp. 122–133.
  • [33] T. Deepa et al., “Comparative Study of Different Controllers for Levitating Ferromagnetic Material,” Adv. Mater. Sci. Eng., vol. 2022, 2022.
  • [34] C. Choubey and J. Ohri, “Tuning of LQR-PID controller to control parallel manipulator,” Neural Comput. Appl., vol. 34, no. 4, pp. 3283–3297, 2022.
  • [35] D. Pandey, S. Yadav, and S. Mishra, “Optimal LQR and Smith Predictor Based PID Controller Design for NMP System,” in Mobile Radio Communications and 5G Networks, Springer, 2022, pp. 211–222.
  • [36] P. Rai and B. Pratap, “Design of Robust Controller for Enhanced Performance of 2-DOF Torsion System,” in Communication and Control for Robotic Systems, Springer, 2022, pp. 465–480.
  • [37] H. Calgan and M. Demirtas, “A robust LQR-FOPIλDµ controller design for output voltage regulation of stand-alone self-excited induction generator,” Electr. Power Syst. Res., vol. 196, p. 107175, 2021.
  • [38] A. S. Elkhatem and S. N. Engin, “Robust LQR and LQR-PI control strategies based on adaptive weighting matrix selection for a UAV position and attitude tracking control,” Alexandria Eng. J., vol. 61, no. 8, pp. 6275–6292, 2022.
  • [39] A. Uysal, S. Gokay, E. Soylu, T. Soylu, and S. Çaşka, “Fuzzy proportional-integral speed control of switched reluctance motor with MATLAB/Simulink and programmable logic controller communication,” Meas. Control, vol. 52, no. 7–8, pp. 1137–1144, 2019.
  • [40] I. Ahmad and M. A. Javaid, “Nonlinear model & controller design for magnetic levitation system,” Recent Adv. signal Process. Robot. Autom., pp. 324–328, 2010.
  • [41] B. C. Kuo, Automatic Control Systems. 1999.
  • [42] A. Isidori, Nonlinear control systems: an introduction. Springer, 1985.
There are 41 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Yusuf Karabacak 0000-0001-9864-7512

Ali Yaşar 0000-0001-9012-7950

İsmail Saritas 0000-0002-5743-4593

Early Pub Date May 12, 2023
Publication Date May 15, 2023
Published in Issue Year 2023 Volume: 25 Issue: 74

Cite

APA Karabacak, Y., Yaşar, A., & Saritas, İ. (2023). Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, 25(74), 339-350. https://doi.org/10.21205/deufmd.2023257407
AMA Karabacak Y, Yaşar A, Saritas İ. Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System. DEUFMD. May 2023;25(74):339-350. doi:10.21205/deufmd.2023257407
Chicago Karabacak, Yusuf, Ali Yaşar, and İsmail Saritas. “Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi 25, no. 74 (May 2023): 339-50. https://doi.org/10.21205/deufmd.2023257407.
EndNote Karabacak Y, Yaşar A, Saritas İ (May 1, 2023) Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 25 74 339–350.
IEEE Y. Karabacak, A. Yaşar, and İ. Saritas, “Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System”, DEUFMD, vol. 25, no. 74, pp. 339–350, 2023, doi: 10.21205/deufmd.2023257407.
ISNAD Karabacak, Yusuf et al. “Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 25/74 (May 2023), 339-350. https://doi.org/10.21205/deufmd.2023257407.
JAMA Karabacak Y, Yaşar A, Saritas İ. Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System. DEUFMD. 2023;25:339–350.
MLA Karabacak, Yusuf et al. “Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, vol. 25, no. 74, 2023, pp. 339-50, doi:10.21205/deufmd.2023257407.
Vancouver Karabacak Y, Yaşar A, Saritas İ. Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System. DEUFMD. 2023;25(74):339-50.

Dokuz Eylül Üniversitesi, Mühendislik Fakültesi Dekanlığı Tınaztepe Yerleşkesi, Adatepe Mah. Doğuş Cad. No: 207-I / 35390 Buca-İZMİR.