Research Article
BibTex RIS Cite

Ters Sarkaç Sistemi İçin LQR Kontrolcü Tasarımında Genetik Algoritma Optimizasyonu

Year 2020, Ejosat Special Issue 2020 (ISMSIT), 163 - 171, 30.11.2020
https://doi.org/10.31590/ejosat.820337

Abstract

Bu çalışmada kontrol tekniklerinin performanslarını incelemek için sıklıkla tercih edilen ters sarkaç sistemi ele alınmıştır. Ters sarkaç sisteminin doğrusal olmayan yapısı nedeniyle de kontrolü zor bir mühendislik problemidir. Ters sarkaç problemine yönelik sistemin hareket denklemleri çıkartılmış, durum-uzay formunda ifade edilmiş ve tasarım kriterleri belirlenmiştir. Ters sarkaç sisteminde tasarım kriteri olarak arabanın ve sarkacın pozisyonlarını kontrol etmek hedeflenmiştir. Bu hedeflere uygun olarak kontrol tekniği belirlenmiştir. Kontrolcü olarak Lineer Kuadratik Regülatör (LQR) tekniği kullanılmıştır. LQR kontrolcüsü ile birden fazla durum değişkenleri kontrol edilebildiği için ters sarkaç sisteminde tercih edilmiştir. Gerçekleştirilen çalışmada LQR kontrolcüsünün performansını doğrudan etkileyen Q ve R matrisleri Genetik Algoritma ile optimize edilmiştir. Optimize edilmiş LQR kontrolcüsü ve standart LQR kontrolcüsü olarak iki farklı yöntem uygulanmıştır. Genetik Algoritma geniş arama algoritmalarının aksine en iyiye ulaşmak için bir yaklaşımı olmadığından en iyiye ulaşamayabilir fakat zaman kısıtlamalarını dikkate almada en iyi algoritmalardan birisi olduğu için tercih edilmiştir. Ters sarkaç sisteminde yapılan optimizasyonlarda amaç fonksiyonları genellikle referans değere yükselme süresi, oturma süresi ve kalıcı durum hatalarının toplanması olarak kullanılmaktadır. Gerçekleştirilen çalışmada farklı olarak Genetik Algoritmanın uygunluk fonksiyonu için bir öneri sunulmuştur. Bu öneri, arabanın referans pozisyon değeri ile arabanın pozisyon değeri arasındaki farkın minimize edilmesi şeklinde tasarlanmıştır. Genetik Algoritma (GA) uygunluk fonksiyonunun çalışmada önerilen formül ile kullanıldığında kabul edilebilir sonuçlar ürettiği gösterilmiştir. Gerçekleştirilen deneyler sonucunda Genetik Algoritma ile optimizasyonu yapılan LQR kontrolcüsü, deneme yanılma yöntemiyle bulunan değerler ile çalışan LQR kontrolcüsüne göre daha başarılı olduğu gözlemlenmiştir. Aynı zamanda Q ve R matrisleri Genetik Algoritma ile belirlendiği için bu katsayıların belirlenmesinde kaybedilen zamanın önüne geçilmiştir.

References

  • Anderson, C. W. (1989). Learning to Control and Inverted Pendulum Using Neural Networks. IEEE Control Systems Magazine, 9(3), 31-37. https://doi.org/10.1109/37.24809
  • Ata, B., & Çoban, R. (2017). Linear Quadratic Optimal Control of an Inverted Pendulum on a Cart Using Artificial Bee Colony Algorithm: An Experimental Study. 16.
  • Bakarac, P., Klauco, M., & Fikar, M. (2018). Comparison of Inverted Pendulum Stabilization with PID, LQ, and MPC Control. 2018 Cybernetics & Informatics (K&I), 1-6. https://doi.org/10.1109/CYBERI.2018.8337540
  • Anderson, C. W. (1989). Learning to Control and Inverted Pendulum Using Neural Networks. IEEE Control Systems Magazine, 9(3), 31-37. https://doi.org/10.1109/37.24809
  • Ata, B., & Çoban, R. (2017). Linear Quadratic Optimal Control of an Inverted Pendulum on a Cart Using Artificial Bee Colony Algorithm: An Experimental Study. 16.
  • Bakarac, P., Klauco, M., & Fikar, M. (2018). Comparison of Inverted Pendulum Stabilization with PID, LQ, and MPC Control. 2018 Cybernetics & Informatics (K&I), 1-6. https://doi.org/10.1109/CYBERI.2018.8337540
  • Bilgiç, H. H., Şen, M. A., Kalyoncu, M., & Yapıcı, A. (2014). Doğrusal Ters Sarkacın Denge Kontrolü için Yapay Sinir Ağı Tabanlı Bulanık Mantık & LQR Kontrolcü Tasarımı. https://doi.org/10.13140/RG.2.1.4983.7204
  • Control Tutorials for MATLAB and Simulink—Inverted Pendulum: System Modeling. (t.y.). Geliş tarihi 09 Ekim 2020, gönderen http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SystemModeling
  • Ghanbari, A., & Farrokhi, M. (2006). Decentralized Neuro-Fuzzy Controller Design Using Decoupled Sliding-Mode Structure for Two-Dimensional Inverted Pendulum. 2006 IEEE International Conference on Engineering of Intelligent Systems, 1-6. https://doi.org/10.1109/ICEIS.2006.1703155
  • Housner, G. W. (1963). The Behavior of Inverted Pendulum Structures During Earthquakes. Bulletin of the Seismological Society of America, 53(2), 403-417.
  • Mahfouz, A. A., M. K., M., & Salem, F. A. (2013). Modeling, Simulation and Dynamics Analysis Issues of Electric Motor, for Mechatronics Applications, Using Different Approaches and Verification by MATLAB/Simulink. International Journal of Intelligent Systems and Applications, 5(5), 39-57. https://doi.org/10.5815/ijisa.2013.05.06
  • Muskinja, N., & Tovornik, B. (2006). Swinging Up and Stabilization of a Real Inverted Pendulum. Industrial Electronics, IEEE Transactions on, 53, 631-639. https://doi.org/10.1109/TIE.2006.870667
  • Okubanjo, A. A., & Oyetola, O. K. (2019). Dynamic Mathematical Modeling and Control Algorithms Design of an Inverted Pendulum System (IPS). Turkish Journal of Engineering, 1-10. https://doi.org/10.31127/tuje.435028
  • Önen, Ü., Çakan, A., & İLhan, İ. (t.y.). Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. 16.
  • Prasad, L., Tyagi, B., & Gupta, H. (2014). Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input. International Journal of Automation and Computing, 11, 661-670. https://doi.org/10.1007/s11633-014-0818-1
  • Razzaghi, K., & Jalali, A. A. (2012). A New Approach on Stabilization Control of an Inverted Pendulum, Using PID Controller. Advanced Materials Research, 4674-4680. https://doi.org/10.4028/www.scientific.net/AMR.403-408.4674
  • Shehu, M., Ahmad, M. R., Shehu, A., & Alhassan, A. (2015). LQR, Double-PID and Pole Placement Stabilization and Tracking Control of Single Link Inverted Pendulum. 2015 IEEE International Conference on Control System, Computing and Engineering (ICCSCE), 218-223. https://doi.org/10.1109/ICCSCE.2015.7482187
  • Wang, J.-J. (2011). Simulation Studies of Inverted Pendulum Based on PID Controllers. Simulation Modelling Practice and Theory, 19(1), 440-449. https://doi.org/10.1016/j.simpat.2010.08.003
  • Yeung, K. S., & Chen, Y. P. (1990). Sliding Mode Controller Design of a Single-Link Flexible Manipulator Under Gravity. International Journal of Control, 52(1), 101-117. https://doi.org/10.1080/00207179008953526

Genetic Algorithm Optimization in LQR Controller Design for Inverted Pendulum System

Year 2020, Ejosat Special Issue 2020 (ISMSIT), 163 - 171, 30.11.2020
https://doi.org/10.31590/ejosat.820337

Abstract

In this study, the frequently preferred inverted pendulum system is handled to examine the performance of control techniques. It is a difficult engineering problem to control due to the nonlinear nature of the inverted pendulum system. The motion equations of the system for the inverted pendulum problem were extracted, expressed in state-space form, and design criteria were determined. In the inverted pendulum system, it is aimed to control the positions of the cart and the pendulum as a design criterion. The Control technique has been determined by these goals. Linear Quadratic Regulator (LQR) technique is used as the controller. Since multiple state variables can be controlled with the LQR controller, it was preferred in the inverted pendulum system. The Q and R matrices that directly affect the performance of the LQR controller in the work carried out were optimized with the Genetic Algorithm. Two different methods were applied as an optimized LQR controller and standard LQR controller. Unlike the wide search algorithms, the Genetic Algorithm may not reach the best because it does not have an approach to reach the best, but it was preferred because it is one of the best algorithms to consider time constraints. In the optimizations made in the inverted pendulum system, the fitness functions are generally used as the rise time to the reference value, the settling time, and the summation of the steady-state errors. In the study, a different proposal was presented for the fitness function of the Genetic Algorithm. This proposal is designed to minimize the difference between the car's reference position value and the car's current position value. The Genetic Algorithm fitness function has been shown to produce acceptable results when used with the formula suggested in the study. As a result of the experiments carried out, it was observed that the LQR controller, which was optimized with the Genetic Algorithm, was more successful than the LQR controller working with the values found by the trial and error method. At the same time, since the Q and R matrices are determined by the Genetic Algorithm, the time lost in determining these coefficients has been prevented.

References

  • Anderson, C. W. (1989). Learning to Control and Inverted Pendulum Using Neural Networks. IEEE Control Systems Magazine, 9(3), 31-37. https://doi.org/10.1109/37.24809
  • Ata, B., & Çoban, R. (2017). Linear Quadratic Optimal Control of an Inverted Pendulum on a Cart Using Artificial Bee Colony Algorithm: An Experimental Study. 16.
  • Bakarac, P., Klauco, M., & Fikar, M. (2018). Comparison of Inverted Pendulum Stabilization with PID, LQ, and MPC Control. 2018 Cybernetics & Informatics (K&I), 1-6. https://doi.org/10.1109/CYBERI.2018.8337540
  • Anderson, C. W. (1989). Learning to Control and Inverted Pendulum Using Neural Networks. IEEE Control Systems Magazine, 9(3), 31-37. https://doi.org/10.1109/37.24809
  • Ata, B., & Çoban, R. (2017). Linear Quadratic Optimal Control of an Inverted Pendulum on a Cart Using Artificial Bee Colony Algorithm: An Experimental Study. 16.
  • Bakarac, P., Klauco, M., & Fikar, M. (2018). Comparison of Inverted Pendulum Stabilization with PID, LQ, and MPC Control. 2018 Cybernetics & Informatics (K&I), 1-6. https://doi.org/10.1109/CYBERI.2018.8337540
  • Bilgiç, H. H., Şen, M. A., Kalyoncu, M., & Yapıcı, A. (2014). Doğrusal Ters Sarkacın Denge Kontrolü için Yapay Sinir Ağı Tabanlı Bulanık Mantık & LQR Kontrolcü Tasarımı. https://doi.org/10.13140/RG.2.1.4983.7204
  • Control Tutorials for MATLAB and Simulink—Inverted Pendulum: System Modeling. (t.y.). Geliş tarihi 09 Ekim 2020, gönderen http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SystemModeling
  • Ghanbari, A., & Farrokhi, M. (2006). Decentralized Neuro-Fuzzy Controller Design Using Decoupled Sliding-Mode Structure for Two-Dimensional Inverted Pendulum. 2006 IEEE International Conference on Engineering of Intelligent Systems, 1-6. https://doi.org/10.1109/ICEIS.2006.1703155
  • Housner, G. W. (1963). The Behavior of Inverted Pendulum Structures During Earthquakes. Bulletin of the Seismological Society of America, 53(2), 403-417.
  • Mahfouz, A. A., M. K., M., & Salem, F. A. (2013). Modeling, Simulation and Dynamics Analysis Issues of Electric Motor, for Mechatronics Applications, Using Different Approaches and Verification by MATLAB/Simulink. International Journal of Intelligent Systems and Applications, 5(5), 39-57. https://doi.org/10.5815/ijisa.2013.05.06
  • Muskinja, N., & Tovornik, B. (2006). Swinging Up and Stabilization of a Real Inverted Pendulum. Industrial Electronics, IEEE Transactions on, 53, 631-639. https://doi.org/10.1109/TIE.2006.870667
  • Okubanjo, A. A., & Oyetola, O. K. (2019). Dynamic Mathematical Modeling and Control Algorithms Design of an Inverted Pendulum System (IPS). Turkish Journal of Engineering, 1-10. https://doi.org/10.31127/tuje.435028
  • Önen, Ü., Çakan, A., & İLhan, İ. (t.y.). Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. 16.
  • Prasad, L., Tyagi, B., & Gupta, H. (2014). Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input. International Journal of Automation and Computing, 11, 661-670. https://doi.org/10.1007/s11633-014-0818-1
  • Razzaghi, K., & Jalali, A. A. (2012). A New Approach on Stabilization Control of an Inverted Pendulum, Using PID Controller. Advanced Materials Research, 4674-4680. https://doi.org/10.4028/www.scientific.net/AMR.403-408.4674
  • Shehu, M., Ahmad, M. R., Shehu, A., & Alhassan, A. (2015). LQR, Double-PID and Pole Placement Stabilization and Tracking Control of Single Link Inverted Pendulum. 2015 IEEE International Conference on Control System, Computing and Engineering (ICCSCE), 218-223. https://doi.org/10.1109/ICCSCE.2015.7482187
  • Wang, J.-J. (2011). Simulation Studies of Inverted Pendulum Based on PID Controllers. Simulation Modelling Practice and Theory, 19(1), 440-449. https://doi.org/10.1016/j.simpat.2010.08.003
  • Yeung, K. S., & Chen, Y. P. (1990). Sliding Mode Controller Design of a Single-Link Flexible Manipulator Under Gravity. International Journal of Control, 52(1), 101-117. https://doi.org/10.1080/00207179008953526
There are 19 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Mehmet Tayyip Özdemir 0000-0002-4290-0045

Muhammet Mevlüt Karaca 0000-0001-9644-3663

Ali Tahir Karaşahin 0000-0002-7440-1312

Publication Date November 30, 2020
Published in Issue Year 2020 Ejosat Special Issue 2020 (ISMSIT)

Cite

APA Özdemir, M. T., Karaca, M. M., & Karaşahin, A. T. (2020). Ters Sarkaç Sistemi İçin LQR Kontrolcü Tasarımında Genetik Algoritma Optimizasyonu. Avrupa Bilim Ve Teknoloji Dergisi163-171. https://doi.org/10.31590/ejosat.820337