Comparative Study of Takagi-Sugeno-Kang and Madani Algorithms in Type-1 and Interval Type-2 Fuzzy Control for Self-Balancing Wheelchairs

(1) Manutsawee Kiew-ong-art Mail (Rangsit University, Thailand)
(2) * Phichitphon Chotikunnan Mail (Rangsit University, Thailand)
(3) Anantasak Wongkamhang Mail (Rangsit University, Thailand)
(4) Rawiphon Chotikunnan Mail (Rangsit University, Thailand)
(5) Anuchit Nirapai Mail (Rangsit University, Thailand)
(6) Pariwat Imura Mail (Rangsit University, Thailand)
(7) Manas Sangworasil Mail (Rangsit University, Thailand)
(8) Nuntachai Thongpance Mail (Rangsit University, Thailand)
(9) Anuchart Srisiriwat Mail (Pathumwan Institute of Technology, Thailand)
*corresponding author


This study examines the effectiveness of four different fuzzy logic controllers in self-balancing wheelchairs. The controllers under consideration are Type-1 Takagi-Sugeno-Kang (TSK) FLC, Interval Type-2 TSK FLC, Type-1 Mamdani FLC, and Interval Type-2 Mamdani FLC. A MATLAB-based simulation environment serves for the evaluation, focusing on key performance indicators like percentage overshoot, rise time, settling time, and displacement. Two testing methodologies were designed to simulate both ideal conditions and real-world hardware limitations. The simulations reveal distinct advantages for each controller type. For example, Type-1 TSK excels in minimizing overshoot but requires higher force. Interval Type-2 TSK shows the quickest settling times but needs the most force. Type-1 Mamdani has the fastest rise time with the lowest force requirement but experiences a higher percentage of overshoot. Interval Type-2 Mamdani offers balanced performance across all metrics. When a 2.7 N control input cap is imposed, Type-2 controllers prove notably more efficient in minimizing overshoot. These results offer valuable insights for future design and real-world application of self-balancing wheelchairs. Further studies are recommended for the empirical testing and refinement of these controllers, especially since the initial findings were limited to four-wheeled self-balancing robotic wheelchairs.


Fuzzy Logic; Interval Type-2; Self-Balancing; Wheelchairs



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[1] V. B. V. Nghia, T. Van Thien, N. N. Son, and M. T. Long, "Adaptive neural sliding mode control for two wheel self balancing robot," International Journal of Dynamics and Control, vol. 10, no. 3, pp. 771–784, 2022,

[2] A. Mehrvarz, M. J. Khodaei, W. Clark, and N. Jalili, "A new dynamic model of a two-wheeled two-flexible-beam inverted pendulum robot," in ASME International Mechanical Engineering Congress and Exposition, vol. 84553, p. V07BT07A044, 2020,

[3] G. M. Moatimid, A. T. El-Sayed, and H. F. Salman, "Dynamical analysis of an inverted pendulum with positive position feedback controller approximate uniform solution," Scientific Reports, vol. 13, no. 1, p. 8849, 2023,

[4] M. Magdy, A. El Marhomy, and M. A. Attia, "Modeling of inverted pendulum system with gravitational search algorithm optimized controller," Ain Shams Engineering Journal, vol. 10, no. 1, pp. 129-149, 2019,

[5] M. Rabah, A. Rohan, and S. H. Kim, "Comparison of position control of a gyroscopic inverted pendulum using PID, fuzzy logic and fuzzy PID controllers," International Journal of Fuzzy Logic and Intelligent Systems, vol. 18, no. 2, pp. 103–110, 2018,

[6] D. Tran, N. Hoang, N. Loc, Q. Truong, and N. Nha, "A Fuzzy LQR PID Control for a Two-Legged Wheel Robot with Uncertainties and Variant Height," Journal of Robotics and Control (JRC), vol. 4, no. 5, pp. 612–620, 2023,

[7] I. Chawla and A. Singla, "Real-Time Stabilization Control of a Rotary Inverted Pendulum Using LQR-Based Sliding Mode Controller," Arab J Sci Eng, vol. 46, pp. 2589-2596, 2021,

[8] S. J. Chacko and R. J. Abraham, "On LQR controller design for an inverted pendulum stabilization," International Journal of Dynamics and Control, vol. 11, no. 4, pp. 1584–1592, 2023,

[9] B. Bekkar and K. Ferkous, "Design of Online Fuzzy Tuning LQR Controller Applied to Rotary Single Inverted Pendulum: Experimental Validation," Arabian Journal for Science and Engineering, vol. 48, no. 5, pp. 6957-6972, 2023,

[10] K. Ashwani and N. Yadnyesh, "Control Optimization of Triple-Stage Inverted Pendulum Using PID-Based ANFIS Controllers," in Advances in Systems Engineering: Select Proceedings of NSC 2019, pp. 501-514, Singapore: Springer, 2021,

[11] M. A. R. Shafei, D. K. Ibrahim, and M. Bahaa, "Application of PSO tuned fuzzy logic controller for LFC of two-area power system with redox flow battery and PV solar park," Ain Shams Engineering Journal, vol. 13, no. 5, p. 101710, 2022,

[12] A. Ansarian and M. J. Mahmoodabadi, "Multi-objective optimal design of a fuzzy adaptive robust fractional-order PID controller for a nonlinear unmanned flying system," Aerospace Science and Technology, vol. 141, p. 108541, 2023,

[13] M. F. Masrom, N. M. A Ghani, and M. O. Tokhi, "Particle swarm optimization and spiral dynamic algorithm-based interval type-2 fuzzy logic control of triple-link inverted pendulum system: A comparative assessment," Journal of Low Frequency Noise, Vibration and Active Control, vol. 40, no. 1, pp. 367-382, 2021,

[14] A. A. bin Abdul Razak, A. N. K. bin Nasir, N. M. A. Ghani, S. Mohammad, M. F. M. Jusof, and N. A. M. Rizal, "Hybrid genetic manta ray foraging optimization and its application to interval type 2 fuzzy logic control of an inverted pendulum system," in IOP Conference Series: Materials Science and Engineering, vol. 917, no. 1, p. 012082, 2020,

[15] J. Shi, "Structure Analysis of General Type-2 Fuzzy Controller and Its Application," International Journal of Fuzzy System Applications (IJFSA), vol. 12, no. 1, pp. 1–20, 2023,

[16] I. Gandarilla, J. Montoya-Cháirez, V. Santibáñez, C. Aguilar-Avelar, and J. Moreno-Valenzuela, "Trajectory tracking control of a self-balancing robot via adaptive neural networks," Engineering Science and Technology, an International Journal, vol. 35, p. 101259, 2022,

[17] D. M. Nguyen, N. Van-Tiem, and T. T. Nguyen, "A neural network combined with sliding mode controller for the two-wheel self-balancing robot," IAES International Journal of Artificial Intelligence, vol. 10, no. 3, p. 592, 2021,

[18] I. A. Hashim, E. H. Karam, and N. S. Abdul-Jaleel, "Design and Implementation of a Two Stage Controller for Ball and Beam System Using FPGA," Engineering and Technology Journal, vol. 36, no. 4, pp. 381-390, 2018,

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

[22] 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,

[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] X. Huang, A. L. Ralescu, H. Gao, and H. Huang, "A survey on the application of fuzzy systems for underactuated systems," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 233, no. 3, pp. 217-244, 2019,

[25] 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,

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

[27] 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,

[28] R. Chotikunnan, P. Chotikunnan, A. Ma'arif, N. Thongpance, Y. Pititheeraphab, and A. Srisiriwat, "Ball and Beam Control: Evaluating Type-1 and Interval Type-2 Fuzzy Techniques with Root Locus Optimization," International Journal of Robotics and Control Systems, vol. 3, no. 2, pp. 286–303, 2023,

[29] G. Vailland et al., “VR based Power Wheelchair Simulator: Usability Evaluation through a Clinically Validated Task with Regular Users,” 2021 IEEE Virtual Reality and 3D User Interfaces (VR), pp. 420-427, 2021,

[30] 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,

[31] 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,

[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] 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,

[34] 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,

[35] 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,

[36] 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,

[37] 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,

[38] 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,

[39] 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,

[40] 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,

[41] 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,

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

[43] 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,

[44] 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,

[45] 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,

[46] N. Singh, A. K. Sharma, M. Tiwari, M. Jasiński, Z. Leonowicz, S. Rusek, and R. Gono, "Robust Control of SEDCM by Fuzzy-PSO," Electronics, vol. 12, no. 2, pp. 335, 2023,

[47] Ö. 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," J. Vibration and Control, vol. 29, no. 5-6, pp. 1366-1386, Mar. 2023,

[48] D. Saputra, A. Ma'arif, H. Maghfiroh, P. Chotikunnan, and S. Rahmadhia, "Design and Application of PLC-based Speed Control for DC Motor Using PID with Identification System and MATLAB Tuner," Int. J. Robotics and Control Systems, vol. 3, no. 2, pp. 233-244, 2023,

[49] H. Huang, H. Xu, F. Chen, C. Zhang, and A. Mohammadzadeh, "An Applied Type-3 Fuzzy Logic System: Practical Matlab Simulink and M-Files for Robotic, Control, and Modeling Applications," Symmetry, vol. 15, no. 2, pp. 475, 2023,


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