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Decoupled Backstepping Sliding Mode Control of a Ball and Beam System

Year 2020, Volume: 35 Issue: 3, 659 - 668, 30.09.2020
https://doi.org/10.21605/cukurovaummfd.846402

Abstract

In this study, a decoupled backstepping sliding mode controller is designed for a ball and beam system as an example of underactuated mechanical systems. The decoupled backstepping sliding mode control method which is a combination of backstepping and sliding mode with a decoupling algorithm is considered to control a ball and beam system. The stability of the system is guaranteed by the design procedure of the controller which is based on the Lyapunov theorem. The effectiveness of the designed controller is verified by simulation tests. Simulation results show that the decoupled backstepping sliding method provides a robust control signal under external disturbances compared to the conventional decoupled sliding mode control method.

References

  • 1. Oryschuk, P., Salerno, A., Al-Husseini, A.M., Angeles, J., 2009. Experimental Validation of an Underactuated Two-wheeled Mobile Robot. IEEE/ASME Transactions on Mechatronics, 14(2), 252–257.
  • 2. Woods, S.A., Bauer, R.J., Seto, M.L., 2012. Automated Ballast Tank Control System for Autonomous Underwater Vehicles. IEEE Journal of Oceanic Engineering, 37(4), 727–739.
  • 3. Olfati-Saber, R., 2001. Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles. Doktora Tezi, Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science, 316.
  • 4. Choukchou-Braham, A., Cherki, B., Djemaï, M., Busawon, K., 2013. Analysis and Control of Underactuated Mechanical Systems. Springer-Verlag, New York.
  • 5. Liu, Y., Yu, H., 2013. A Survey of Underactuated Mechanical Systems. IET Control Theory and Applications, 7(7), 921–935.
  • 6. Huang, X., Ralescu, A. L., Gao, H., Huang, H., 2019. A Survey on the Application of Fuzzy Systems for Underactuated Systems. Journal of Systems and Control Engineering, 233(3), 217–244.
  • 7. She, J., Zhang, A., Lai, X., Wu, M., 2012. Global Stabilization of 2-DOF Underactuated Mechanical Systems-an Equivalent-input- disturbance Approach. Nonlinear Dynamics, 69(1–2), 495–509.
  • 8. Shah, I., Rehman, F.U., 2018. Smooth Second Order Sliding Mode Control of a Class of Underactuated Mechanical Systems. IEEE Access, 6(c), 7759–7771.
  • 9. Mehedi, I.M., Al-Saggaf, U.M., Mansouri, R., Bettayeb, M., 2019. Two Degrees of Freedom Fractional Controller Design: Application to the Ball and Beam System. Measurement: Journal of the International Measurement Confederation, 135, 13–22.
  • 10. Yang, J., Wang, Z.H., 2010. Adaptive Robust Dissipative Design on Stability Control for Ball and Beam System. International Conference on Computer and Automation Engineering, ICCAE 2010, 4, 68–71.
  • 11. Guinaldo, M., Vargas, H., Sánchez, J., Sanz, E., Dormido, S., 2009. Web-based Control Laboratory: The Ball and Beam System. IFAC Proceedings Volumes 8, 174–179.
  • 12. Choudhary, M.K., Naresh Kumar, G., 2016. ESO Based LQR Controller for Ball and Beam System. IFAC-PapersOnLine, 49(1), 607–610.
  • 13. Hirschorn, R.M., 2002. Incremental Sliding Mode Control of the Ball and Beam. IEEE Transactions on Automatic Control, 47(10), 1696-1700.
  • 14. Meenakshipriya, B., Kalpana, K., 2014. Modelling and Control of Ball and Beam System Using Coefficient Diagram Method (CDM) Based PID Controller. IFAC Proceedings Volumes, 3, 620–626.
  • 15. Moezi, S. A., Zakeri, E., Eghtesad, M., 2019. Optimal Adaptive Interval Type-2 Fuzzy Fractional-order Backstepping Sliding Mode Control Method for Some Classes of Nonlinear Systems. ISA Transactions, 93, 23–39.
  • 16. Freeman, R.A., Kokotović, P., 1996. Robust Nonlinear Control Design. Birkhäuser, Boston.
  • 17. Krstic, M., Kokotovic, P.V., Kanellakopoulos, I., 1995. Nonlinear and Adaptive Control Design. Wiley, New York.
  • 18. Madani, T., Benallegue, A., 2006. Backstepping Control for a Quadrotor Helicopter. IEEE International Conference on Intelligent Robots and Systems, 3255–3260.
  • 19. Liu, S., Liu, Y., Wang, N., Liu, S., Liu, Y., Wang, N., Wang, N., 2017. Nonlinear Disturbance Observer-based Backstepping Finite-time Sliding Mode Tracking Control of Underwater Vehicles with System Uncertainties and External Disturbances. Nonlinear Dynamics, 88, 465–476.
  • 20. Pan, Y., Wang, H., Li, X., Yu, H., 2018. Adaptive Command-Filtered Backstepping Control of Robot Arms with Compliant Actuators. IEEE Transactions on Control Systems Technology, 26(3), 1149–1156.
  • 21. Bouabdallah, S., Siegwart, R., 2005. Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor. IEEE International Conference on Robotics and Automation, 2247–2252.
  • 22. Coban, R., 2017. Backstepping Sliding Mode Tracking Controller Design and Experimental Application to an Electromechanical System. Control Engineering and Applied Informatics, 19(3), 88–96.
  • 23. Utkin, V., 1977. Variable Structure Systems with Sliding Modes. IEEE Transactions on Automatic Control, 22(2), 212–222.
  • 24. Utkin, V., 1992. Sliding Modes in Control and Optimization. Springer, Berlin.
  • 25. Edwards, C., Spurgeon, S., 1998. Sliding Mode Control. CRC Press, London.
  • 26. Lee, H., Utkin, V.I., 2007. Chattering Suppression Methods in Sliding Mode Control Systems. Annual Reviews in Control, 31(2), 179–188.
  • 27. Lo, J. C., Kuo, Y. H., 1998. Decoupled Fuzzy Sliding-mode Control. IEEE Transactions on Fuzzy Systems, 6(3), 426–435.
  • 28. Ata, B., Coban, R., 2019. Decoupled Backstepping Sliding Mode Control of Underactuated Systems with Uncertainty: Experimental Results. Arabian Journal for Science and Engineering, 44(8), 7013–7021.
  • 29. Hauser, J., Sastry, S., Kokotovic, P., 1992. Nonlinear Control Via Approximate Input- output Linearization: The Ball and Beam Example. IEEE Transactions on Automatic Control, 37(3), 392-398.
  • 30. Coban, R., Ata, B., 2017. Decoupled Sliding Mode Control of an Inverted Pendulum on a Cart: An Experimental Study. 2017 IEEE International Conference on Advanced Intelligent Mechatronics, 993–997.
  • 31. Lu, C.H., Hwang, Y.R., Shen, Y.T., 2011. Backstepping Sliding Mode Tracking Control of a Vane-type Air Motor X–Y Table Motion System. ISA Transactions, 50(2), 278–286.

Bir Top ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü

Year 2020, Volume: 35 Issue: 3, 659 - 668, 30.09.2020
https://doi.org/10.21605/cukurovaummfd.846402

Abstract

Bu çalışmada, eksik eyleyicili mekanik sistemlerin bir örneği olan top ve çubuk sistemi için bir ayrıklaştırılmış geri adımlamalı kayan kipli kontrol kuralı tasarlanmıştır. Kayan kipli kontrol ve geri adımlamalı kontrol yöntemlerini birleştiren ve bir ayrıklaştırma algoritması ile bu yöntemin eksik eyleyicili sistemlere uygulanmasını sağlayan ayrıklaştırılmış geri adımlamalı kayan kipli kontrol yöntemi top ve çubuk sisteminin kontrolünde kullanılmıştır. Kontrolörün tasarım yöntemi Lyapunov teoremine dayandığı için sistemin kararlılığı garanti altına alınmıştır. Tasarlanan kontrolörün etkinliği benzetim çalışmaları ile test edilmiştir. Benzetim bulguları ayrıklaştırılmış geri adımlamalı kayan kipli kontrol yönteminin geleneksel ayrıklaştırılmış kayan kipli kontrol yöntemi ile karşılaştırıldığında dış bozuculara karşı etkili bir kontrol sinyali ürettiğini göstermiştir.

References

  • 1. Oryschuk, P., Salerno, A., Al-Husseini, A.M., Angeles, J., 2009. Experimental Validation of an Underactuated Two-wheeled Mobile Robot. IEEE/ASME Transactions on Mechatronics, 14(2), 252–257.
  • 2. Woods, S.A., Bauer, R.J., Seto, M.L., 2012. Automated Ballast Tank Control System for Autonomous Underwater Vehicles. IEEE Journal of Oceanic Engineering, 37(4), 727–739.
  • 3. Olfati-Saber, R., 2001. Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles. Doktora Tezi, Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science, 316.
  • 4. Choukchou-Braham, A., Cherki, B., Djemaï, M., Busawon, K., 2013. Analysis and Control of Underactuated Mechanical Systems. Springer-Verlag, New York.
  • 5. Liu, Y., Yu, H., 2013. A Survey of Underactuated Mechanical Systems. IET Control Theory and Applications, 7(7), 921–935.
  • 6. Huang, X., Ralescu, A. L., Gao, H., Huang, H., 2019. A Survey on the Application of Fuzzy Systems for Underactuated Systems. Journal of Systems and Control Engineering, 233(3), 217–244.
  • 7. She, J., Zhang, A., Lai, X., Wu, M., 2012. Global Stabilization of 2-DOF Underactuated Mechanical Systems-an Equivalent-input- disturbance Approach. Nonlinear Dynamics, 69(1–2), 495–509.
  • 8. Shah, I., Rehman, F.U., 2018. Smooth Second Order Sliding Mode Control of a Class of Underactuated Mechanical Systems. IEEE Access, 6(c), 7759–7771.
  • 9. Mehedi, I.M., Al-Saggaf, U.M., Mansouri, R., Bettayeb, M., 2019. Two Degrees of Freedom Fractional Controller Design: Application to the Ball and Beam System. Measurement: Journal of the International Measurement Confederation, 135, 13–22.
  • 10. Yang, J., Wang, Z.H., 2010. Adaptive Robust Dissipative Design on Stability Control for Ball and Beam System. International Conference on Computer and Automation Engineering, ICCAE 2010, 4, 68–71.
  • 11. Guinaldo, M., Vargas, H., Sánchez, J., Sanz, E., Dormido, S., 2009. Web-based Control Laboratory: The Ball and Beam System. IFAC Proceedings Volumes 8, 174–179.
  • 12. Choudhary, M.K., Naresh Kumar, G., 2016. ESO Based LQR Controller for Ball and Beam System. IFAC-PapersOnLine, 49(1), 607–610.
  • 13. Hirschorn, R.M., 2002. Incremental Sliding Mode Control of the Ball and Beam. IEEE Transactions on Automatic Control, 47(10), 1696-1700.
  • 14. Meenakshipriya, B., Kalpana, K., 2014. Modelling and Control of Ball and Beam System Using Coefficient Diagram Method (CDM) Based PID Controller. IFAC Proceedings Volumes, 3, 620–626.
  • 15. Moezi, S. A., Zakeri, E., Eghtesad, M., 2019. Optimal Adaptive Interval Type-2 Fuzzy Fractional-order Backstepping Sliding Mode Control Method for Some Classes of Nonlinear Systems. ISA Transactions, 93, 23–39.
  • 16. Freeman, R.A., Kokotović, P., 1996. Robust Nonlinear Control Design. Birkhäuser, Boston.
  • 17. Krstic, M., Kokotovic, P.V., Kanellakopoulos, I., 1995. Nonlinear and Adaptive Control Design. Wiley, New York.
  • 18. Madani, T., Benallegue, A., 2006. Backstepping Control for a Quadrotor Helicopter. IEEE International Conference on Intelligent Robots and Systems, 3255–3260.
  • 19. Liu, S., Liu, Y., Wang, N., Liu, S., Liu, Y., Wang, N., Wang, N., 2017. Nonlinear Disturbance Observer-based Backstepping Finite-time Sliding Mode Tracking Control of Underwater Vehicles with System Uncertainties and External Disturbances. Nonlinear Dynamics, 88, 465–476.
  • 20. Pan, Y., Wang, H., Li, X., Yu, H., 2018. Adaptive Command-Filtered Backstepping Control of Robot Arms with Compliant Actuators. IEEE Transactions on Control Systems Technology, 26(3), 1149–1156.
  • 21. Bouabdallah, S., Siegwart, R., 2005. Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor. IEEE International Conference on Robotics and Automation, 2247–2252.
  • 22. Coban, R., 2017. Backstepping Sliding Mode Tracking Controller Design and Experimental Application to an Electromechanical System. Control Engineering and Applied Informatics, 19(3), 88–96.
  • 23. Utkin, V., 1977. Variable Structure Systems with Sliding Modes. IEEE Transactions on Automatic Control, 22(2), 212–222.
  • 24. Utkin, V., 1992. Sliding Modes in Control and Optimization. Springer, Berlin.
  • 25. Edwards, C., Spurgeon, S., 1998. Sliding Mode Control. CRC Press, London.
  • 26. Lee, H., Utkin, V.I., 2007. Chattering Suppression Methods in Sliding Mode Control Systems. Annual Reviews in Control, 31(2), 179–188.
  • 27. Lo, J. C., Kuo, Y. H., 1998. Decoupled Fuzzy Sliding-mode Control. IEEE Transactions on Fuzzy Systems, 6(3), 426–435.
  • 28. Ata, B., Coban, R., 2019. Decoupled Backstepping Sliding Mode Control of Underactuated Systems with Uncertainty: Experimental Results. Arabian Journal for Science and Engineering, 44(8), 7013–7021.
  • 29. Hauser, J., Sastry, S., Kokotovic, P., 1992. Nonlinear Control Via Approximate Input- output Linearization: The Ball and Beam Example. IEEE Transactions on Automatic Control, 37(3), 392-398.
  • 30. Coban, R., Ata, B., 2017. Decoupled Sliding Mode Control of an Inverted Pendulum on a Cart: An Experimental Study. 2017 IEEE International Conference on Advanced Intelligent Mechatronics, 993–997.
  • 31. Lu, C.H., Hwang, Y.R., Shen, Y.T., 2011. Backstepping Sliding Mode Tracking Control of a Vane-type Air Motor X–Y Table Motion System. ISA Transactions, 50(2), 278–286.
There are 31 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Barış Ata

Publication Date September 30, 2020
Published in Issue Year 2020 Volume: 35 Issue: 3

Cite

APA Ata, B. (2020). Bir Top ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 35(3), 659-668. https://doi.org/10.21605/cukurovaummfd.846402
AMA Ata B. Bir Top ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü. cukurovaummfd. September 2020;35(3):659-668. doi:10.21605/cukurovaummfd.846402
Chicago Ata, Barış. “Bir Top Ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35, no. 3 (September 2020): 659-68. https://doi.org/10.21605/cukurovaummfd.846402.
EndNote Ata B (September 1, 2020) Bir Top ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35 3 659–668.
IEEE B. Ata, “Bir Top ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü”, cukurovaummfd, vol. 35, no. 3, pp. 659–668, 2020, doi: 10.21605/cukurovaummfd.846402.
ISNAD Ata, Barış. “Bir Top Ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35/3 (September 2020), 659-668. https://doi.org/10.21605/cukurovaummfd.846402.
JAMA Ata B. Bir Top ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü. cukurovaummfd. 2020;35:659–668.
MLA Ata, Barış. “Bir Top Ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, vol. 35, no. 3, 2020, pp. 659-68, doi:10.21605/cukurovaummfd.846402.
Vancouver Ata B. Bir Top ve Çubuk Sisteminin Ayrıklaştırılmış Geri Adımlamalı Kayan Kipli Kontrolü. cukurovaummfd. 2020;35(3):659-68.