Araştırma Makalesi
BibTex RIS Kaynak Göster

Ters Sarkaç Sisteminin Doğrusal Olmayan Kontrolü

Yıl 2020, Cilt: 35 Sayı: 1, 27 - 38, 31.03.2020
https://doi.org/10.21605/cukurovaummfd.764516

Öz

Sunulan bir ters sarkaç sistemi için doğrusal olmayan kontrol çalışmasıdır. Ters sarkaç sistemi eksik tahrikli, karma evreye sahip ve oldukça kararsız bir sistemin en önemli örneğidir. Bu araştırma makalesinin amacı, ters sarkaç sistemi için doğrusal olmayan kontrol yasaları elde etmektir. İlk olarak, ters sarkaçların dinamik denklemleri Lagrange denklemleri kullanılarak türetilir ve daha sonra kararsız dik pozisyon etrafında lineer karalılık noktaları bulunur. Diğer adımda analizler için doğrusal kararlılık teorileri ve Lyapunov metodunu kullanır. Doğrusal olmayan kayan kipli kontrol ve geri beslemeli doğrusallaştırmış kontrol yasaları türetilir. Geri beslemeli doğrusallaştırmış kontrol yasası doğrusal olmayan sistemi eşdeğer bir doğrusal sisteme dönüştürmek için kullanılır, böylece uygun bir geri besleme kontrol yasaları önerilebilir. Başlangıç koşullarından kararlılık ve referans takibi bu makalede incelenmiştir. Önerilen doğrusal olmayan kontrol stratejilerinin kontrol performansı MATLAB/ Simulink programı ile gösterilmiştir.

Kaynakça

  • 1. Chanchareon, R., Sangveraphunsiri, V., Chantranuwathana, S., 2006. Tracking Control of an Inverted Pendulum Using Computed Feedback Linearization Technique. In 2006 IEEE Conference on Robotics, Automation and Mechatronics 1-6, IEEE.
  • 2. Du, L., Cao, F., 2015. Nonlinear Controller Design of the Inverted Pendulum System based on Extended State Observer. In 2015 International Conference on Automation, Mechanical Control and Computational Engineering. Atlantis Press.
  • 3. Zare, A., Lotfi, T., Gordan, H., Dastranj, M., 2012. Robust Control of Inverted Pendulum Using Fuzzy Sliding Mode Control and Particle Swarm Optimization Pso Algorithm. International Journal of Scientific & Engineering Research, 3(10), 1-5.
  • 4. Brisilla, R.M., Sankaranarayanan, V., 2015. Nonlinear Control of Mobile Inverted Pendulum. Robotics and Autonomous Systems, 70, 145-155.
  • 5. Stellet, J. Control of an Inverted Pendulum.
  • 6. Anderson, C.W., 1989. Learning to Control an Inverted Pendulum Using Neural Networks. IEEE Control Systems Magazine, 9(3), 31-37.
  • 7. Gani, A., Kececioglu, O.F., Acikgoz, H., Sekkeli, M., 2017. Fuzzy Logic Controller Design Based on Sugeno Inference Method for Nonlinear Inverted Pendulum Dynamical System. Sigma Journal of Engineering and Natural Sciences-Sigma Muhendislik ve Fen Bilimleri Dergisi, 8(1), 19-30.
  • 8. Şen, M.A., Bilgiç, H.H., Kalyoncu, M., 2016. Çift Ters Sarkaç Sisteminin Denge ve Konum Kontrolü için Arı Algoritması ile Lqr Kontrolcü Parametrelerinin Tayini. Mühendis ve Makina, 57(679), 53-62.
  • 9. Bilgic, H.H., Sen, M.A., Kalyoncu, M., 2016. Tuning of LQR Controller for an Experimental Inverted Pendulum System Based on the Bees Algorithm. Journal of Vibroengineering, 18(6), 3684-3694.
  • 10. Köse, E., Abaci, K., Kizmaz, H., Aksoy, S., Yalçin, M.A., 2013. Sliding Mode Control Based on Genetic Algorithm for WSCC Systems Include of SVC. Elektronika ir Elektrotechnika, 19(4), 25-28.
  • 11. Köse, E., 2017. Controller Design by Using Non-linear Control Methods for Satellite Chaotic System. Electrical Engineering, 99(2), 763-773.
  • 12. Irfan, S., Mehmood, A., Razzaq, M.T., Iqbal, J. 2018. Advanced Sliding Mode Control Techniques for Inverted Pendulum: Modelling and Simulation. Engineering Science and Technology, an International Journal, 21(4), 753-759.
  • 13. Grossimon, P., Barbieri, E., Drakunov, S., 1996. Sliding Mode Control of an Inverted Pendulum, System Theory, Proceedings of the Twenty-Eighth Southeastern Symposium, ISBN 0-8186-7352-4, pp.248-252, 31 Mar - 02 Apr 1996 IEEE.
  • 14. Naik, M., Cochran, D., 2012. System Identification of an Inverted Pendulum ona Cart using Compressed Sensing, Signals, Systems and Computers (ASILOMAR), 2012 Conference Record of the Forth Sixth Asilomar Conference, pp.426-430, 4-7 Nov 2012 IEEE.
  • 15. de Jesús Rubio, J., 2018. Robust Feedback Linearization for Nonlinear Processes Control. ISA Transactions, 74, 155-164.
  • 16. Moreno-Valenzuela, J., Aguilar-Avelar, C., 2018. Feedback Linearization Control of the IWP. In Motion Control of Underactuated Mechanical Systems, 141-158, Springer, Cham.
  • 17. Bugeja, M., 2003. Non-linear Swing-up and Stabilizing Control of an Inverted Pendulum System. In The IEEE Region 8 EUROCON 2003. Computer as a Tool. 2, 437-441, IEEE.

Non-linear Control of Inverted Pendulum

Yıl 2020, Cilt: 35 Sayı: 1, 27 - 38, 31.03.2020
https://doi.org/10.21605/cukurovaummfd.764516

Öz

Presented is a study of non-linear control for an inverted pendulum system. The inverted pendulum system is a great example of an underactuated, non-minimum phase, and highly unstable system. The objective of this research paper is to derive non-linear control laws for an inverted pendulum system. First, dynamic equations of the inverted pendulum are derived by utilizing the Lagrange's equations and then it is linearized around an unstable upright position. Secondly, the corresponding analysis uses the standard linear stability arguments and the traditional Lyapunov method. The non-linear sliding mode control and feedback linearization control laws are then derived The feedback linearization control law is used to transform the non-linear system into an equivalent linear system such that a suitable feedback control law can be proposed. The stabilization of the initial condition and reference tracking is studied in this paper. I demonstrate the effectiveness of the proposed non-linear control strategies using MATLAB/Simulink software.

Kaynakça

  • 1. Chanchareon, R., Sangveraphunsiri, V., Chantranuwathana, S., 2006. Tracking Control of an Inverted Pendulum Using Computed Feedback Linearization Technique. In 2006 IEEE Conference on Robotics, Automation and Mechatronics 1-6, IEEE.
  • 2. Du, L., Cao, F., 2015. Nonlinear Controller Design of the Inverted Pendulum System based on Extended State Observer. In 2015 International Conference on Automation, Mechanical Control and Computational Engineering. Atlantis Press.
  • 3. Zare, A., Lotfi, T., Gordan, H., Dastranj, M., 2012. Robust Control of Inverted Pendulum Using Fuzzy Sliding Mode Control and Particle Swarm Optimization Pso Algorithm. International Journal of Scientific & Engineering Research, 3(10), 1-5.
  • 4. Brisilla, R.M., Sankaranarayanan, V., 2015. Nonlinear Control of Mobile Inverted Pendulum. Robotics and Autonomous Systems, 70, 145-155.
  • 5. Stellet, J. Control of an Inverted Pendulum.
  • 6. Anderson, C.W., 1989. Learning to Control an Inverted Pendulum Using Neural Networks. IEEE Control Systems Magazine, 9(3), 31-37.
  • 7. Gani, A., Kececioglu, O.F., Acikgoz, H., Sekkeli, M., 2017. Fuzzy Logic Controller Design Based on Sugeno Inference Method for Nonlinear Inverted Pendulum Dynamical System. Sigma Journal of Engineering and Natural Sciences-Sigma Muhendislik ve Fen Bilimleri Dergisi, 8(1), 19-30.
  • 8. Şen, M.A., Bilgiç, H.H., Kalyoncu, M., 2016. Çift Ters Sarkaç Sisteminin Denge ve Konum Kontrolü için Arı Algoritması ile Lqr Kontrolcü Parametrelerinin Tayini. Mühendis ve Makina, 57(679), 53-62.
  • 9. Bilgic, H.H., Sen, M.A., Kalyoncu, M., 2016. Tuning of LQR Controller for an Experimental Inverted Pendulum System Based on the Bees Algorithm. Journal of Vibroengineering, 18(6), 3684-3694.
  • 10. Köse, E., Abaci, K., Kizmaz, H., Aksoy, S., Yalçin, M.A., 2013. Sliding Mode Control Based on Genetic Algorithm for WSCC Systems Include of SVC. Elektronika ir Elektrotechnika, 19(4), 25-28.
  • 11. Köse, E., 2017. Controller Design by Using Non-linear Control Methods for Satellite Chaotic System. Electrical Engineering, 99(2), 763-773.
  • 12. Irfan, S., Mehmood, A., Razzaq, M.T., Iqbal, J. 2018. Advanced Sliding Mode Control Techniques for Inverted Pendulum: Modelling and Simulation. Engineering Science and Technology, an International Journal, 21(4), 753-759.
  • 13. Grossimon, P., Barbieri, E., Drakunov, S., 1996. Sliding Mode Control of an Inverted Pendulum, System Theory, Proceedings of the Twenty-Eighth Southeastern Symposium, ISBN 0-8186-7352-4, pp.248-252, 31 Mar - 02 Apr 1996 IEEE.
  • 14. Naik, M., Cochran, D., 2012. System Identification of an Inverted Pendulum ona Cart using Compressed Sensing, Signals, Systems and Computers (ASILOMAR), 2012 Conference Record of the Forth Sixth Asilomar Conference, pp.426-430, 4-7 Nov 2012 IEEE.
  • 15. de Jesús Rubio, J., 2018. Robust Feedback Linearization for Nonlinear Processes Control. ISA Transactions, 74, 155-164.
  • 16. Moreno-Valenzuela, J., Aguilar-Avelar, C., 2018. Feedback Linearization Control of the IWP. In Motion Control of Underactuated Mechanical Systems, 141-158, Springer, Cham.
  • 17. Bugeja, M., 2003. Non-linear Swing-up and Stabilizing Control of an Inverted Pendulum System. In The IEEE Region 8 EUROCON 2003. Computer as a Tool. 2, 437-441, IEEE.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Serdar Coşkun Bu kişi benim

Yayımlanma Tarihi 31 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 35 Sayı: 1

Kaynak Göster

APA Coşkun, S. (2020). Non-linear Control of Inverted Pendulum. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 35(1), 27-38. https://doi.org/10.21605/cukurovaummfd.764516
AMA Coşkun S. Non-linear Control of Inverted Pendulum. cukurovaummfd. Mart 2020;35(1):27-38. doi:10.21605/cukurovaummfd.764516
Chicago Coşkun, Serdar. “Non-Linear Control of Inverted Pendulum”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35, sy. 1 (Mart 2020): 27-38. https://doi.org/10.21605/cukurovaummfd.764516.
EndNote Coşkun S (01 Mart 2020) Non-linear Control of Inverted Pendulum. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35 1 27–38.
IEEE S. Coşkun, “Non-linear Control of Inverted Pendulum”, cukurovaummfd, c. 35, sy. 1, ss. 27–38, 2020, doi: 10.21605/cukurovaummfd.764516.
ISNAD Coşkun, Serdar. “Non-Linear Control of Inverted Pendulum”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35/1 (Mart 2020), 27-38. https://doi.org/10.21605/cukurovaummfd.764516.
JAMA Coşkun S. Non-linear Control of Inverted Pendulum. cukurovaummfd. 2020;35:27–38.
MLA Coşkun, Serdar. “Non-Linear Control of Inverted Pendulum”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, c. 35, sy. 1, 2020, ss. 27-38, doi:10.21605/cukurovaummfd.764516.
Vancouver Coşkun S. Non-linear Control of Inverted Pendulum. cukurovaummfd. 2020;35(1):27-38.