Modelling of PID and LQR Controller for Stability and Position Control in Double Inverted Pendulum System

Abstract

Nowadays, stability of the inverted pendulum system is an up-to-date topic in which researchers working on control systems compare control theories and methods. The inverse pendulum systems are unstable and nonlinear systems in terms of controllability. Due to the complexity of the structure and the difficulty of the control process, many advanced control theories can be applied on these systems to improving the performance of the controllers. In this study, PID and LQR controller methods were applied on a double inverted pendulum modeled in MATLAB environment and their controller performances were compared. The results via experimental studies were evaluated on the applicability of PID and LQR control methods.

Keywords

• Double inverted pendulum
• PID controller
• LQR controller
• Control systems

Çift Ters Sarkaç Sisteminin Kontrolü için PID ve LQR Kontrolcü Tasarımlarının Modellenmesi

Öz

Günümüzde, ters sarkaç sisteminde denge sağlama özellikle kontrol sistemleri üzerine çalışma yapan araştırmacıların kontrol teori ve yöntemlerini kıyasladıkları güncel bir konudur. Ters sarkaç sistemi kontrol edilebilirlik açısından kararsız ve doğrusal olmayan sistemler arasında yer almaktadır. Yapısının karmaşıklığı ve kontrollerinin zorluğu nedeniyle birçok ileri düzey kontrol teorisi bu sistemler üzerinde uygulanarak kontrolcülerin performansları üzerinde değerlendirme yapılabilmektedir. Bu çalışmada, PID ve LQR kontrolcü yöntemleri MATLAB ortamında matematiksel olarak modellenen bir çift eklemli ters sarkaç üzerinde uygulanmış ve kontrolcü performansları karşılaştırılmıştır. PID ve LQR kontrol yöntemlerinin uygulanabilirliği üzerinde elde edilen sonuçlar değerlendirilmiştir.

Anahtar Kelimeler

• Çift eklemli ters sarkaç
• PID kontrolcü
• LQR kontrolcü
• kontrol sistemleri

Kaynakça

1. Arbo, M. H., Raijmakers, P. A., & Mladenov, V. M. (2014). Applications of neural networks for control of a double inverted pendulum. 12th Symposium on Neural Network Applications in Electrical Engineering (NEUREL), 89–92.
2. Åström, K. J., Hägglund, T., & Astrom, K. J. (2006). Advanced PID control (Vol. 461). ISA-The Instrumentation, Systems, and Automation Society Research Triangle~�.
3. Çeven, S., & Bayır, R. (2016). Implementation of Fuzzy Logic Based Speed Control of Brushless Direct Current Motors via Industrial PC. International Journal of Intelligent Systems and Applications in Engineering, 146–152.
4. Chang, W.-D., & Shih, S.-P. (2010). PID controller design of nonlinear systems using an improved particle swarm optimization approach. Communications in Nonlinear Science and Numerical Simulation, 15(11), 3632–3639.
5. Ding, C. J., Ping, D., Zhang, M. L., & Zhang, Y. F. (2009). Double inverted pendulum system control strategy based on fuzzy genetic algorithm. Proceedings of the 2009 IEEE International Conference on Automation and Logistics, ICAL 2009, 2007, 1318–1323. doi: 10.1109/ICAL.2009.5262779
6. Nejadfard, A., Yazdanpanah, M. J., & Hassanzadeh, I. (2013). Friction compensation of double inverted pendulum on a cart using locally linear neuro-fuzzy model. Neural Computing and Applications, 22(2), 337–347.
7. Önen, Ü., Çakan, A., & İLhan, İ. (2019). Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. Turkish Journal of Electrical Engineering and Computer Sciences, 27(3), 1938–1953. doi: 10.3906/elk-1808-51
8. Priyadarshi, P. (2013). Optimal Controller Design for Inverted Pendulum System: An Experimental Study.

9. Purnawan, H., Purwanto, E. B., & others. (2017). Design of linear quadratic regulator (LQR) control system for flight stability of LSU-05. Journal of Physics: Conference Series, 890(1), 12056.
10. Sheng, Q., Qing, Z., Gao, X. Z., & Shuanghe, Y. (2008). ANFIS controller for double inverted pendulum. IEEE International Conference on Industrial Informatics (INDIN), 475–480. doi: 10.1109/INDIN.2008.4618147
11. Sun, Z., Wang, N., & Bi, Y. (2015). Type-1/type-2 fuzzy logic systems optimization with RNA genetic algorithm for double inverted pendulum. Applied Mathematical Modelling, 39(1), 70–85.
12. Tinkir, M., Kalyoncu, M., Onen, U., & Botsali, F. M. (2010). PID and interval type-2 fuzzy logic control of double inverted pendulum system. 2010 The 2nd International Conference on Computer and Automation Engineering (ICCAE), 1, 117–121.
13. Wu, J., Liu, C., & Deng, Y. (2008). Variable Structure Control for Stabilizing Double Inverted Pendulum. 2008 International Conference on Intelligent Computation Technology and Automation (ICICTA), 1, 741–744.
14. Zhang, S., Zhang, Z., Jin, K., & Yang, C. (2012). Fuzzy control of double inverted pendulum by using state varieties fusion function. Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012, 2696–2699. doi: 10.1109/CCDC.2012.6244428
15. Zheng, Y., Zhong, P., & Yue, Q. (2016). Double Inverted Pendulum Based on LQG Optimal Control. Icacie, 83–87. doi: 10.2991/icacie-16.2016.20