Ball and Beam Control: Evaluating Type-1 and Interval Type-2 Fuzzy Techniques with Root Locus Optimization

(1) Rawiphon Chotikunnan Mail (College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand, Thailand)
(2) * Phichitphon Chotikunnan Mail (College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand, Thailand)
(3) Alfian Ma'arif Mail (Universitas Ahmad Dahlan, Yogyakarta 55191, Indonesia, Indonesia)
(4) Nuntachai Thongpance Mail (College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand, Thailand)
(5) Yutthana Pititheeraphab Mail (College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand, Thailand)
(6) Anuchart Srisiriwat Mail (Department of Electrical Engineering, Pathumwan Institute of Technology, Bangkok 10330, Thailand, Thailand)
*corresponding author


This study evaluates the performance of three control systems, namely the root locus method, type-1 Mamdani fuzzy logic system (FLS), and interval type-2 Mamdani FLS, in noise-free and noisy ball and beam systems. The main contribution of this study is enabling improved design and implementation of control systems in real-world applications by offering a comprehensive understanding of each control system's performance. The methodology involves conducting four tests focusing on various input types, including a 0.8-meter step input and sine wave function, and assessing the presence of noise in the system. The performance of each control system is analyzed using parameters such as rise time, setting time, and percentage overshoot, with the interval type-2 Mamdani FLS further examined by varying footprint of uncertainty values. Results from noise-free tests reveal that the root locus method has shorter rise and setting times, but a higher percentage overshoot compared to the type-1 Mamdani FLS and type-2 Mamdani FLS. In noisy environments, the type-2 Mamdani FLS with varying Footprint of Uncertainty values outperforms the type-1 Mamdani FLS with reduced rise time, setting time, and percentage overshoot. The root locus method shows a significantly higher percentage overshoot in noisy conditions compared to the other two control systems. In conclusion, the type-2 Mamdani FLS control system demonstrates superior capability under changing conditions compared to the type-1 Mamdani FLS, with its performance varying based on footprint of uncertainty values. This study highlights the importance of selecting the appropriate control system depending on specific needs and environmental factors.


Ball and Beam; Fuzzy Logic; Interval Type-2; Root Locus



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[1] O. Bingül and A. Yıldız, "Fuzzy logic and proportional integral derivative based multi-objective optimization of active suspension system of a 4× 4 in-wheel motor driven electrical vehicle," Journal of Vibration and Control, vol. 29, no. 5-6, pp. 1366-1386, 2023,

[2] B. Khokhar, S. Dahiya, and K. S. Parmar, "A novel fractional order proportional integral derivative plus second-order derivative controller for load frequency control," International Journal of Sustainable Energy, vol. 40, no. 3, pp. 235-252, 2021,

[3] A. Ma'arif and N. R. Setiawan, "Control of DC motor using integral state feedback and comparison with PID: simulation and arduino implementation," Journal of Robotics and Control (JRC), vol. 2, no. 5, pp. 456-461, 2021,

[4] A. Rakshit, A. Konar, and A. K. Nagar, "A hybrid brain-computer interface for closed-loop position control of a robot arm," IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 5, pp. 1344-1360, 2020,

[5] H. Zhou, S. Zhang, and C. Ru, "Lateral flight control method of UAV based on small disturbance and root locus theory," 2021 33rd Chinese Control and Decision Conference (CCDC), 2021, pp. 6949-6954,

[6] C. Guo, W. Xie, and N. Pei, "Ballbeam System Analysis and Design Based on Root Locus Correction and State Space Correction," Wireless Communications and Mobile Computing, vol. 2022, 2022,

[7] S. Senthil Kumar and G. Anitha, "A novel self-tuning fuzzy logic-based PID controllers for two-axis gimbal stabilization in a missile seeker," International Journal of Aerospace Engineering, vol. 2021, pp. 1-12, 2021,

[8] A. L. Shuraiji and S. W. Shneen, "Fuzzy Logic Control and PID Controller for Brushless Permanent Magnetic Direct Current Motor: A Comparative Study," Journal of Robotics and Control (JRC), vol. 3, no. 6, pp. 762-768, 2022,.

[9] R. Kristiyono and W. Wiyono, "Autotuning fuzzy PID controller for speed control of BLDC motor," Journal of Robotics and Control (JRC), vol. 2, no. 5, pp. 400-407, 2021,

[10] H. Maghfiroh, A. Ramelan, and F. Adriyanto, "Fuzzy-pid in bldc motor speed control using matlab/simulink," Journal of Robotics and Control (JRC), vol. 3, no. 1, pp. 8-13, 2022,

[11] H. Y. Abed, A. T. Humod, and A. J. Humaidi, "Type 1 versus type 2 fuzzy logic speed controllers for brushless DC motors," International Journal of Electrical and Computer Engineering, vol. 10, no. 1, pp. 265-274, 2020,

[12] M. A. Márquez-Vera, A. Rodríguez-Romero, C. A. Márquez-Vera, and K. R. Ramos-Téllez, "Interval Type-2 Fuzzy Observers Applied in Biodegradation," International Journal of Robotics and Control Systems, vol. 1, no. 2, pp. 145-158, 2021,

[13] H. Q. T. Ngo and M. H. Nguyen, "Enhancement of the Tracking Performance for Robot Manipulator by Using the Feed-forward Scheme and Reasonable Switching Mechanism," Journal of Robotics and Control (JRC), vol. 3, no. 3, pp. 328-337, 2022,

[14] J. Hauser, S. Sastry, and P. Kokotovic, "Nonlinear control via approximate input-output linearization: The ball and beam example," IEEE Transactions on Automatic Control, vol. 37, no. 3, pp. 392-398, 1992,

[15] B. Hamed, "Application of a LabVIEW for real-time control of ball and beam system," IACSIT International Journal of Engineering and Technology, vol. 2, no. 4, pp. 401-407, 2010,

[16] M. Virseda, "Modeling and control of the ball and beam process," MSc Theses, Chalmers University of Technology, 2004,

[17] A. T. Ali, A. M. Ahmed, H. A. Almahdi, O. A. Taha, and A. Naseraldeen, "Design and implementation of ball and beam system using pid controller," MAYFEB Journal of Electrical and Computer Engineering, vol. 3, no. 1, pp. 1-4, 2017,

[18] R. Deepa, R. Velnath, E. H. Guhan, C. Moorthy, P. Gomathi, and A. Dinesh, "Stability Analysis of Ball and Beam System using PID Controller," 2021 International Conference on Advancements in Electrical, Electronics, Communication, Computing and Automation (ICAECA), 2021, pp. 1-4,

[19] I. H. Ibrahim and H. I. Ali, "Quantitative PID Controller Design using Black Hole Optimization for Ball and Beam System," Iraqi Journal of Computers, Communications, Control and Systems Engineering, vol. 21, no. 3, pp. 65-75, 2021,

[20] O. T. Altinoz and A. E. Yilmaz, "Investigation of the Optimal PID-Like Fuzzy Logic Controller for Ball and Beam System with Improved Quantum Particle Swarm Optimization," International Journal of Computational Intelligence and Applications, vol. 21, no. 04, p. 2250025, 2022,

[21] V. Srivastava and S. Srivastava, "Hybrid optimization based PID control of ball and beam system," Journal of Intelligent & Fuzzy Systems, vol. 42, no. 2, pp. 919-928, 2022,

[22] M. C. Rodrigues, F. M. U. Araújo, and A. L. Maitelli, "Neuro-fuzzy control of nonlinear systems-application in a ball and beam system," International Conference on Informatics in Control, Automation and Robotics, 2009, pp. 201-206,

[23] N. S. Abdul Aziz, N. Ishak, R. Adnan, and M. Tajjudin, "Hybrid fuzzy PID controller design for ball and beam system," Journal of Electrical and Electronic Systems Research (JEESR), vol. 15, pp. 47-51, 2019,

[24] M. K. Saleem, M. L. U. R. Shahid, A. Nouman, H. Zaki, and M. A. U. R. Tariq, "Design and implementation of adaptive neuro-fuzzy inference system for the control of an uncertain ball and beam apparatus," Mehran University Research Journal of Engineering & Technology, vol. 41, no. 2, pp. 178-184, 2022,

[25] B. Panomruttanarug and P. Chotikunnan, "Self-balancing iBOT-like wheelchair based on type-1 and interval type-2 fuzzy control," 2014 11th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), May 2014, pp. 1-6,

[26] P. Chotikunnan and B. Panomruttanarug, "The application of fuzzy logic control to balance a wheelchair," Journal of Control Engineering and Applied Informatics, vol. 18, no. 3, pp. 41-51, 2016,

[27] P. Chotikunnan, R. Chotikunnan, A. Nirapai, A. Wongkamhang, P. Imura, and M. Sangworasil, "Optimizing Membership Function Tuning for Fuzzy Control of Robotic Manipulators Using PID-Driven Data Techniques," Journal of Robotics and Control (JRC), vol. 4, no. 2, pp. 128-140, 2023,

[28] P. Chotikunnan, and Y. Pititheeraphab, " Adaptive P Control and Adaptive Fuzzy Logic Controller with Expert System Implementation for Robotic Manipulator Application," Journal of Robotics and Control (JRC), vol. 4, no. 2, pp. 217-226, 2023,

[29] A. Latif, A. Zuhri Arfianto, H. Agus Widodo, R. Rahim, and E. T. Helmy, "Motor DC PID System Regulator for Mini Conveyor Drive Based-on Matlab," Journal of Robotics and Control (JRC), vol. 1, no. 6, pp. 185-190, 2020,

[30] F. Abdullah, G. Aziz, and S. Shneen, "Simulation Model of Servo Motor by Using Matlab," Journal of Robotics and Control (JRC), vol. 3, no. 2, pp. 176-179, 2022,

[31] Z. Lin, C. Cui, and G. Wu, "Dynamic Modeling and Torque Feedforward based Optimal Fuzzy PD control of a High-Speed Parallel Manipulator," Journal of Robotics and Control (JRC), vol. 2, no. 6, pp. 527-538, 2021,

[32] K. Lee, D. Y. Im, B. Kwak, and Y. J. Ryoo, "Design of fuzzy-PID controller for path tracking of mobile robot with differential drive," International Journal of Fuzzy Logic and Intelligent Systems, vol. 18, no. 3, pp. 220-228, 2018,

[33] M. J. Mohamed and M. Y. Abbas, "Design of a Fuzzy PID Controller for Trajectory Tracking of a Mobile Robot," Engineering and Technology Journal, vol. 36, no. 1, pp. 100-110, 2018,

[34] K. Eltag, M. S. Aslamx, and R. Ullah, "Dynamic Stability enhancement using fuzzy PID control technology for power system," International Journal of Control, Automation and Systems, vol. 17, pp. 234-242, 2019,

[35] M. Rabah, A. Rohan, Y. J. Han, and S. H. Kim, "Design of fuzzy-PID controller for quadcopter trajectory-tracking," International Journal of Fuzzy Logic and Intelligent Systems, vol. 18, no. 3, pp. 204-213, 2018,

[36] X. Long, Z. He, and Z. Wang, "Online optimal control of robotic systems with single critic NN-based reinforcement learning," Complexity, vol. 2021, 2021,

[37] N. Razmjooy and M. Ramezani, "Optimal control of two-wheeled self-balancing robot with interval uncertainties using Chebyshev inclusion method," Majlesi Journal of Electrical Engineering, vol. 12, no. 1, pp. 13-21, 2018,

[38] C. L. Dembia, N. A. Bianco, A. Falisse, J. L. Hicks, and S. L. Delp, "Opensim moco: Musculoskeletal optimal control," PLOS Computational Biology, vol. 16, no. 12, p. e1008493, 2020,

[39] C. Sánchez-Sánchez and D. Izzo, "Real-time optimal control via deep neural networks: study on landing problems," Journal of Guidance, Control, and Dynamics, vol. 41, no. 5, pp. 1122-1135, 2018,

[40] B. Zhao, D. Liu, and C. Luo, "Reinforcement learning-based optimal stabilization for unknown nonlinear systems subject to inputs with uncertain constraints," IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 10, pp. 4330-4340, 2019,

[41] Y. Pan, C. A. Cheng, K. Saigol, K. Lee, X. Yan, E. A. Theodorou, and B. Boots, "Imitation learning for agile autonomous driving," The International Journal of Robotics Research, vol. 39, no. 2-3, pp. 286-302, 2020,

[42] F. Ejaz, M.T. Hamayun, S. Hussain, S. Ijaz, S. Yang, N. Shehzad, and A. Rashid, "An adaptive sliding mode actuator fault tolerant control scheme for octorotor system," International Journal of Advanced Robotic Systems, vol. 16, no. 2, 2019,

[43] J.Y. Zhai and Z.B. Song, "Adaptive sliding mode trajectory tracking control for wheeled mobile robots," International Journal of Control, vol. 92, no. 10, pp. 2255-2262, 2019,

[44] B. Jiang, H.R. Karimi, S. Yang, C. Gao, and Y. Kao, "Observer-based adaptive sliding mode control for nonlinear stochastic Markov jump systems via T–S fuzzy modeling: Applications to robot arm model," IEEE Transactions on Industrial Electronics, vol. 68, no. 1, pp. 466-477, 2020,

[45] L. Gracia, J.E. Solanes, P. Muñoz-Benavent, J.V. Miro, C. Perez-Vidal, and J. Tornero, "Adaptive sliding mode control for robotic surface treatment using force feedback," Mechatronics, vol. 52, pp. 102-118, 2018,

[46] K. Liu, H. Gao, H. Ji, and Z. Hao, "Adaptive sliding mode based disturbance attenuation tracking control for wheeled mobile robots," International Journal of Control, Automation and Systems, vol. 18, no. 5, pp. 1288-1298, 2020,

[47] T. Zhang, Y. Yu, and Y. Zou, "An adaptive sliding-mode iterative constant-force control method for robotic belt grinding based on a one-dimensional force sensor," Sensors, vol. 19, no. 7, p. 1635, 2019,


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International Journal of Robotics and Control Systems
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