Real Time Swinging Up and Stabilizing a Double Inverted Pendulum Using PID-LQR

Shala, Erjon; Bajrami, Xhevahir; Likaj, Rame; Pajaziti, Arbnor

doi:10.2478/scjme-2023-0013

Abstract

This study describes a method for swinging up and stabilizing a double inverted pendulum (DIP) in real-time utilizing a PID-LQR combined control system. Firstly, a dynamic model of the double inverted pendulum system is made up and the equations of motion are constructed. The pendulum then is moved from its unstable position to a stable one using a PID-LQR controller. A comparison of the PID-LQR controller’s output and suggestions for improving system stability is presented and is suggested combined control system.

References

[1] Li, Wende, Hui Ding, and Kai Cheng “An investigation on the design and performance assessment of double-PID and LQR controllers for the inverted pendulum”, Proceedings of 2012 UKACC international conference on control. IEEE, 2012.
Search in Google Scholar Back to article
[2] Abhijeet, L., Khubalkar S. W., Junghare, A. S. Modeling and control of fractional order PID controller fed rotary inverted pendulum.”, 2018 International Conference on Power, Instrumentation, Control and Computing (PICC). IEEE, 2018.
Search in Google Scholar Back to article
[3] Elkinany, B., Mohammed, A., Krafes, S., Chalh, Z. “Backstepping controller design with a quadratic error for a double inverted pendulum”, International Journal of Modelling, Identification and Control 34 (1), pp. 33 – 40, 2020.
Search in Google Scholar Back to article
[4] Kavirayani, S. “Novel Fuzzy Preview Control With Granular Computing for Underactuated Systems: Underactuated System Case Studies”, In Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures, pp. 352 – 368, IGI Global. 2020.
Search in Google Scholar Back to article
[5] Hazem, Z. B., Bingül, Z. “A Study of Stabilization and Swing-up Linear Control for a Single Link Rotary Pendulum”, In 2022 International Conference on Theoretical and Applied Computer Science and Engineering (ICTASCE), pp. 60 – 65, IEEE, 2022,
Search in Google Scholar Back to article
[6] Yadav, S. K., Sharma, S., & Singh, N. “Optimal control of double inverted pendulum using LQR controller”, International Journal of Advanced Research in Computer Science and Software Engineering 2(2), 2012.
Search in Google Scholar Back to article
[7] Quanser, Available online: https://www.quanser.com/products/rotary-inverted-pendulum (accessed on 10 May 2022).
Search in Google Scholar Back to article
[8] Guo, X., Zhang, G., Tian, R., Periodic solution of a non-smooth double pendulum with unilateral rigid constrain. Symmetry 11(7), 886, 2019.
Search in Google Scholar Back to article
[9] Bajrami, X., Pajaziti, A., Likaj, R., Shala, A., Berisha, R., Bruqi, M. “Control theory application for swing up and stabilisation of rotating inverted pendulum”, Symmetry 13(8), 1491, 2021.
Search in Google Scholar Back to article
[10] Maki K., H., Ayankoso, S. A. “Modeling and Control of a Double Inverted Pendulum using LQR with Parameter Optimization through GA and PSO”, 21st International Conference on Research and Education in Mechatronics (REM), IEEE, 2020.
Search in Google Scholar Back to article
[11] Bajrami, X., Shala A., Hoxha G., Likaj, R. “Dynamic Modelling and Analyzing of a Walking of Humanoid Robot”, Strojnícky časopis – Journal of Mechanical Engineering 68 (3), pp. 59 – 76, 2018. DOI: 10.2478/scjme-2018-0027
Search in Google Scholar Back to article
[12] Likaj R., Shala, A. “Optimisation and Control of Vehicle Suspension Using Linear Quadratic Gaussian Control”, Strojnícky časopis – Journal of Mechanical Engineering 68 (1), pp. 61 – 68. 2018. DOI: 10.2478/scjme-2018-0006
Search in Google Scholar Back to article
[13] Šlesar, P., Jančo, R. “The Calculation of the Contact Force and the Contact Width of Shaft Seals”, Strojnícky časopis – Journal of Mechanical Engineering 69(1), pp. 123 – 130, 2019. DOI: 10.2478/scjme-2019-0010
Search in Google Scholar Back to article

Real Time Swinging Up and Stabilizing a Double Inverted Pendulum Using PID-LQR

Abstract

Paradigm

My account