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An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System

Yıl 2024, Cilt: 3 Sayı: 3, 337 - 349, 31.10.2024
https://doi.org/10.62520/fujece.1445734

Öz

The rotary inverted pendulum system (RIP), which is highly favored in control applications, is examined in this work. By determining the coordinates of the Rip elements' centers of gravity, the system's total kinetic and potential energies were determined. The kinetic and potential energy expressions were used to generate the Lagrangian function. Expressions providing the system's equations of motion were discovered by taking the Lagrangian approach into consideration. The motor's equations, which will initiate the system, have also been considered. Through the use of state variables and a Matlab program, the system's pendulum angle was managed by using a moving sliding surface and the traditional sliding mode control technique. Based on the dynamics, the slip surface's slope was computed. The sliding surface's slope was computed based on the system's dynamics. The genetic algorithm was utilized to determine the ideal values for the coefficients employed in the control structure. The findings showed that the inaccuracy was roughly zero and that the pendulum angle took around 1.5 seconds to reach the intended reference value. Furthermore, it noted that the motor torque and current values are 12 Nm and 2.5 amps, respectively. The findings show that the motor values are reasonably similar to the values seen in real-world applications. Control in real-time applications won't be an issue if the motor is chosen based on these values.

Kaynakça

  • M. Bugeja, "Non-linear swing-up and stabilizing control of an inverted pendulum system," The IEEE Region 8 EUROCON 2003. Computer as a Tool., Ljubljana, Slovenia, pp. 437-441, vol. 2, 2003.
  • W. Zhong and H. Rock, "Energy and passivity based control of the double inverted pendulum on a cart," in Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01), Mexico City, Mexico, pp. 896-901, 2001.
  • J. Krishen and V. M. Becerra, "Efficient fuzzy control of a rotary inverted pendulum based on LQR mapping," in Proceedings of the 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, Munich, Germany, pp. 2701-2706, 2006.
  • S. Awtar, N. King, T. Allen, I. Bang, M. Hagan, D. Skidmore, K. Craig, "Inverted pendulum systems: rotary and arm-driven - a mechatronic system design case study," Mechat., vol. 12, no. 2, pp. 357-370, 2002.
  • Q. Yan, "Output tracking of underactuated rotary inverted pendulum by nonlinear controller," in Proceedings of the 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), Maui, HI, USA, vol. 3, pp. 2395-2400, 2003.
  • T. C. Kuo, Y. J. Huang, and B. W. Hong, "Adaptive PID with sliding mode control for the rotary inverted pendulum system," in Proceedings of the 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Singapore, pp. 1804-1809, 2009.
  • J. Nuo and H. Wang, "Nonlinear Control of an Inverted Pendulum System based on Sliding mode method," ACTA Analy. Funct. Appl., vol. 9, no. 3, pp. 234-237, 2008.
  • J. Krishen and V. M. Becerra, "Efficient fuzzy control of a rotary inverted pendulum based on LQR mapping," in Proceedings of the 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, Munich, Germany, pp. 2701-2706, 2006.
  • O. Altinoz, A. Tolga, E. Yilmaz, and G. W. Weber, "Chaos particle swarm optimized PID controller for the inverted pendulum system," in Proceedings of the 2nd international conference on engineering optimization, 2010.
  • S. Toshiharu and K. Fujimoto, "Controller design for an inverted pendulum based on approximate linearization," International Journal of Robust and Nonlinear Control: IFAC‐Affiliated Journal, vol. 8, no. 7, pp. 585-597, 1998.
  • M. A. Khanesar, M. Teshnehlab, and M. A. Shoorehdeli, "Fuzzy Sliding Mode Control of Rotary Inverted Pendulum," in Proceedings of the 2007 IEEE International Conference on Computational Cybernetics, Gammarth, Tunisia, pp. 57-62, 2007.
  • W. Wang, "Adaptive fuzzy sliding mode control for inverted pendulum," in Proceedings of the 2009 International Symposium on Computer Science and Computational Technology (ISCSCI 2009), Academy Publisher, pp. 231, 2009.
  • A. Bogdanov, "Optimal control of a double inverted pendulum on a cart," Oregon Health and Science University, Tech. Rep. CSE-04-006, OGI School of Science and Engineering, Beaverton, OR, 2004.
  • I. Hassanzadeh and S. Mobayen, "PSO-based controller design for rotary inverted pendulum system," Jour. of Appl. Sci., vol. 8, no. 16, pp. 2907-2912, 2008.
  • V. Sukontanakarn and M. Parnichkun, "Real-time optimal control for rotary inverted pendulum," American Journal of Applied Sciences, vol. 6, no. 6, pp. 1106, 2009.
  • M. Aydın, O. Yakut, and H. Tutumlu, "Implementation of the network-based moving sliding mode control algorithm to the rotary inverted pendulum system," Jour. of Eng. and Techn., vol. 3, no. 1, pp. 31-40, 2009.
  • S. Horikawa, T. Furuhashi, and Y. Uchikawa, "Fuzzy control for inverted pendulum using fuzzy neural networks," J. Rob. and Mechat., vol. 7, no. 1, pp. 36-44, 1995.
  • I. H. Zadeh and S. Mobayen, "PSO-based controller for balancing rotary inverted pendulum," J. Appl. Sci., vol. 16, pp. 2907-2912, 2008.
  • S. D. Sanjeewa and M. Parnichkun, "Control of rotary double inverted pendulum system using LQR sliding surface based sliding mode controller," Jour. of Con. and Dec., vol. 9, no. 1, pp. 89-101, 2022.
  • A. Ma'arif, M. A. M. Vera, M. S. Mahmoud, S. Ladaci, A. Çakan, and J. N. Parada, "Backstepping sliding mode control for inverted pendulum system with disturbance and parameter uncertainty," Jour. of Robotics and Con. (JRC), vol. 3, no. 1, pp. 86-92, 2022.
  • R. Hernández and F. Jurado, "Adaptive Neural Sliding Mode Control of an Inverted Pendulum Mounted on a Ball System," in Proceedings of the 2018 15th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico City, Mexico, pp. 1-6, 2018.
  • S. Irfan, A. Mehmood, M. T. Razzaq, and J. Iqbal, "Advanced sliding mode control techniques for inverted pendulum: Modelling and simulation," Eng. Sci. and Techn., an Inter. Jour., vol. 21, no. 4, pp. 753-759, 2018.
  • K. D. Young, V. I. Utkin, and U. A. Ozguner, "Control engineer’s guide to sliding mode control," IEEE Transactions on Control Systems Technology, vol. 7, no. 3, pp. 328-342, 1999.
  • C. Edwards and S. K. Spurgeon, Sliding Mode Control: Theory and Applications, New York: Taylor and Francis, 1998.
  • Chuan-Kang Ting, "On the Mean Convergence Time of Multi-parent Genetic Algorithms without Selection," in Advances in Artificial Life, Springer, Berlin, Heidelberg, pp. 403-412, 2005.
  • K. Nath and L. Dewan, "A comparative analysis of linear quadratic regulator and sliding mode control for a rotary inverted pendulum," in Proceedings of the 2018 International Conference on Recent Trends in Electrical, Control and Communication, pp. 302-307, 2018.

Hareketli Kayma Yüzeyli DC Motor Modelli Klasik Kayan Kipli Kontrolün Dönel Ters Sarkaç Sistemine Uygulanması

Yıl 2024, Cilt: 3 Sayı: 3, 337 - 349, 31.10.2024
https://doi.org/10.62520/fujece.1445734

Öz

Bu çalışmada kontrol uygulamalarında çok tercih edilen dönel ters sarkaç sistemi (DTS) ele alınmıştır. DTS elemanlarının ağırlık merkezi koordinatları bulunarak sistemin toplam kinetik ve potansiyel enerjileri elde edilmiştir. Kinetik ve potansiyel enerji ifadeleri kullanılarak Lagrange fonksiyonu oluşturulmuştur. Lagrange yöntemi dikkate alınarak sistemin hareket denklemlerini veren ifadeler bulunmuştur. Ayrıca sistemi harekete geçirecek olan motorun denklemleri dikkate alınmıştır. Durum değişkenleri kullanılarak Matlab da yazılan program yardımıyla sistemin sarkaç açısı, kayma yüzeyi hareketli klasik kayan kipli kontrol yöntemiyle kontrol edilmiştir. Kayma yüzeyinin eğimi sistemin dinamiklerine bağlı olarak hesaplatılmıştır. Kontrol yapısında kullanılan katsayıların optimum değerleri genetik algoritma yardımıyla bulunmuştur. Sonuçlardan sarkaç açısının istenilen referans değere yaklaşık 1.5 sn civarında ulaştığı ve hatanın yaklaşık sıfır olduğu görülmüştür. Ayrıca motor tork değerinin 12 Nm seviyelerinde ve motor akım değerinin 2.5 amper seviyelerinde olduğu gözlemlenmiştir. Motor değerlerinin pratik uygulamalardaki değerlere yakın makul seviyelerde olduğu sonuçlardan elde edilmiştir. Elde edilen bu değerlere göre motor seçimi yapıldığında gerçek zamanlı uygulamalarda kontrol için sorun yaşanmayacaktır.

Kaynakça

  • M. Bugeja, "Non-linear swing-up and stabilizing control of an inverted pendulum system," The IEEE Region 8 EUROCON 2003. Computer as a Tool., Ljubljana, Slovenia, pp. 437-441, vol. 2, 2003.
  • W. Zhong and H. Rock, "Energy and passivity based control of the double inverted pendulum on a cart," in Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01), Mexico City, Mexico, pp. 896-901, 2001.
  • J. Krishen and V. M. Becerra, "Efficient fuzzy control of a rotary inverted pendulum based on LQR mapping," in Proceedings of the 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, Munich, Germany, pp. 2701-2706, 2006.
  • S. Awtar, N. King, T. Allen, I. Bang, M. Hagan, D. Skidmore, K. Craig, "Inverted pendulum systems: rotary and arm-driven - a mechatronic system design case study," Mechat., vol. 12, no. 2, pp. 357-370, 2002.
  • Q. Yan, "Output tracking of underactuated rotary inverted pendulum by nonlinear controller," in Proceedings of the 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), Maui, HI, USA, vol. 3, pp. 2395-2400, 2003.
  • T. C. Kuo, Y. J. Huang, and B. W. Hong, "Adaptive PID with sliding mode control for the rotary inverted pendulum system," in Proceedings of the 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Singapore, pp. 1804-1809, 2009.
  • J. Nuo and H. Wang, "Nonlinear Control of an Inverted Pendulum System based on Sliding mode method," ACTA Analy. Funct. Appl., vol. 9, no. 3, pp. 234-237, 2008.
  • J. Krishen and V. M. Becerra, "Efficient fuzzy control of a rotary inverted pendulum based on LQR mapping," in Proceedings of the 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, Munich, Germany, pp. 2701-2706, 2006.
  • O. Altinoz, A. Tolga, E. Yilmaz, and G. W. Weber, "Chaos particle swarm optimized PID controller for the inverted pendulum system," in Proceedings of the 2nd international conference on engineering optimization, 2010.
  • S. Toshiharu and K. Fujimoto, "Controller design for an inverted pendulum based on approximate linearization," International Journal of Robust and Nonlinear Control: IFAC‐Affiliated Journal, vol. 8, no. 7, pp. 585-597, 1998.
  • M. A. Khanesar, M. Teshnehlab, and M. A. Shoorehdeli, "Fuzzy Sliding Mode Control of Rotary Inverted Pendulum," in Proceedings of the 2007 IEEE International Conference on Computational Cybernetics, Gammarth, Tunisia, pp. 57-62, 2007.
  • W. Wang, "Adaptive fuzzy sliding mode control for inverted pendulum," in Proceedings of the 2009 International Symposium on Computer Science and Computational Technology (ISCSCI 2009), Academy Publisher, pp. 231, 2009.
  • A. Bogdanov, "Optimal control of a double inverted pendulum on a cart," Oregon Health and Science University, Tech. Rep. CSE-04-006, OGI School of Science and Engineering, Beaverton, OR, 2004.
  • I. Hassanzadeh and S. Mobayen, "PSO-based controller design for rotary inverted pendulum system," Jour. of Appl. Sci., vol. 8, no. 16, pp. 2907-2912, 2008.
  • V. Sukontanakarn and M. Parnichkun, "Real-time optimal control for rotary inverted pendulum," American Journal of Applied Sciences, vol. 6, no. 6, pp. 1106, 2009.
  • M. Aydın, O. Yakut, and H. Tutumlu, "Implementation of the network-based moving sliding mode control algorithm to the rotary inverted pendulum system," Jour. of Eng. and Techn., vol. 3, no. 1, pp. 31-40, 2009.
  • S. Horikawa, T. Furuhashi, and Y. Uchikawa, "Fuzzy control for inverted pendulum using fuzzy neural networks," J. Rob. and Mechat., vol. 7, no. 1, pp. 36-44, 1995.
  • I. H. Zadeh and S. Mobayen, "PSO-based controller for balancing rotary inverted pendulum," J. Appl. Sci., vol. 16, pp. 2907-2912, 2008.
  • S. D. Sanjeewa and M. Parnichkun, "Control of rotary double inverted pendulum system using LQR sliding surface based sliding mode controller," Jour. of Con. and Dec., vol. 9, no. 1, pp. 89-101, 2022.
  • A. Ma'arif, M. A. M. Vera, M. S. Mahmoud, S. Ladaci, A. Çakan, and J. N. Parada, "Backstepping sliding mode control for inverted pendulum system with disturbance and parameter uncertainty," Jour. of Robotics and Con. (JRC), vol. 3, no. 1, pp. 86-92, 2022.
  • R. Hernández and F. Jurado, "Adaptive Neural Sliding Mode Control of an Inverted Pendulum Mounted on a Ball System," in Proceedings of the 2018 15th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico City, Mexico, pp. 1-6, 2018.
  • S. Irfan, A. Mehmood, M. T. Razzaq, and J. Iqbal, "Advanced sliding mode control techniques for inverted pendulum: Modelling and simulation," Eng. Sci. and Techn., an Inter. Jour., vol. 21, no. 4, pp. 753-759, 2018.
  • K. D. Young, V. I. Utkin, and U. A. Ozguner, "Control engineer’s guide to sliding mode control," IEEE Transactions on Control Systems Technology, vol. 7, no. 3, pp. 328-342, 1999.
  • C. Edwards and S. K. Spurgeon, Sliding Mode Control: Theory and Applications, New York: Taylor and Francis, 1998.
  • Chuan-Kang Ting, "On the Mean Convergence Time of Multi-parent Genetic Algorithms without Selection," in Advances in Artificial Life, Springer, Berlin, Heidelberg, pp. 403-412, 2005.
  • K. Nath and L. Dewan, "A comparative analysis of linear quadratic regulator and sliding mode control for a rotary inverted pendulum," in Proceedings of the 2018 International Conference on Recent Trends in Electrical, Control and Communication, pp. 302-307, 2018.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Makine Teorisi ve Dinamiği
Bölüm Research Articles
Yazarlar

Muhammet Aydın 0000-0003-2746-9477

Oğuz Yakut 0000-0002-0986-1435

Yayımlanma Tarihi 31 Ekim 2024
Gönderilme Tarihi 1 Mart 2024
Kabul Tarihi 11 Temmuz 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 3 Sayı: 3

Kaynak Göster

APA Aydın, M., & Yakut, O. (2024). An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System. Firat University Journal of Experimental and Computational Engineering, 3(3), 337-349. https://doi.org/10.62520/fujece.1445734
AMA Aydın M, Yakut O. An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System. FUJECE. Ekim 2024;3(3):337-349. doi:10.62520/fujece.1445734
Chicago Aydın, Muhammet, ve Oğuz Yakut. “An Application of DC Motor Modelled Classical Sliding Mode Control With Moving Sliding Surface to Rotary Inverted Pendulum System”. Firat University Journal of Experimental and Computational Engineering 3, sy. 3 (Ekim 2024): 337-49. https://doi.org/10.62520/fujece.1445734.
EndNote Aydın M, Yakut O (01 Ekim 2024) An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System. Firat University Journal of Experimental and Computational Engineering 3 3 337–349.
IEEE M. Aydın ve O. Yakut, “An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System”, FUJECE, c. 3, sy. 3, ss. 337–349, 2024, doi: 10.62520/fujece.1445734.
ISNAD Aydın, Muhammet - Yakut, Oğuz. “An Application of DC Motor Modelled Classical Sliding Mode Control With Moving Sliding Surface to Rotary Inverted Pendulum System”. Firat University Journal of Experimental and Computational Engineering 3/3 (Ekim 2024), 337-349. https://doi.org/10.62520/fujece.1445734.
JAMA Aydın M, Yakut O. An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System. FUJECE. 2024;3:337–349.
MLA Aydın, Muhammet ve Oğuz Yakut. “An Application of DC Motor Modelled Classical Sliding Mode Control With Moving Sliding Surface to Rotary Inverted Pendulum System”. Firat University Journal of Experimental and Computational Engineering, c. 3, sy. 3, 2024, ss. 337-49, doi:10.62520/fujece.1445734.
Vancouver Aydın M, Yakut O. An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System. FUJECE. 2024;3(3):337-49.