Application of Genetic Algorithm in Optimizing LQR Control for Ball and Beam

Nguyen-Dang-Khoa Tran1*, Minh-Quan Nguyen2, Tuan-Kiet Le2, Duy-Khanh Bui2, Thanh-Vinh Le2, Thi-Ngoc-Thi Vo2, Thi-Toi Nguyen2, Ngo-Quoc-Bao Pham2

1 Ton Duc Thang University (TDTU)
19Đ, Nguyen Huu Tho, district 7, Ho Chi Minh city, Vietnam
2 Ho Chi Minh city University of Technology and Education (HCMUTE)
Vo Van Ngan, Thu Duc city, Ho Chi Minh city, Vietnam
* Corresponding author. E-mail: dangkhoa.tran195@gmail.com

Robotica & Management, Vol. 28, No. 2, pp. 48-54
DOI: https://doi.org/10.24193/rm.2023.2.9

Abstract: In this paper, we apply genetic algorithm (GA) to optimize LQR controller – a linear control algorithm which stability is guaranteed by mathematics. This searching algorithm proves its ability in finding better control parameters through generations. Our model is ball and beam (B&B) – a classical single input – multi output (SIMO) system. This system is balanced around equilibrium point in simulation.

Keywords: ball and beam, genetic algorithm, LQR control.

Full text

References

[1] Shixuan, Y. et al.: “Research on Solving Nonlinear Problem of Ball and Beam System by Introducing Detail-Reward Function”, Symmetry, 2022.

[2] Ali A.T. et al: “Design and Implementation of Ball and Beam System Using PID Controller”, Automatic Control and Information Sciences, pp. 1-4, 2017.

[3] Gergely B. et al: “Establishing metrics and control laws for the learning process: ball and beam balancing”, Biological Cybernetics, pp. 114, 2020.

[4] Le A.T. Tran N.D.K: “Applying a Genetic Algorithm to optimize Linear Quadratic Regulator for Ball and Beam system”, The 7th International Conference on Advanced Engineering – Theory and Applications, Ton Duc Thang University,  2022.

[5] Liqing G., Yongxin L: “Design of BP neural network controller for ball-beam system”, IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), 2016.

[6] Muhammad I. et al.: “Sliding mode control design for stabilization of underactuated mechanical systems”, Advances in Mechanical Engineering, 2019.

[7] Nguyen X.C. et al.: “Building Quasi-Time-Optimal Control Laws For Ball And Beam System”, 3rd International Conference on Recent Advances in Signal Processing, Telecommunications & Computing (SigTelCom), 2019.

[8] Nguyen X.C. et al.: “The design of a quasi-time optimal cascade controller for ball and beam system”, IOP Conference Series: Materials Science and Engineering, pp. 1029, 2021.

[9] Valluru S.K. et al.: “Prototype design and analysis of controllers for one dimensional ball and beam system”, IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), 2016.

[10] Wang Q. et al.: “Evolving a neural controller for a ball-and-beam system”, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826), 2004.