A Novel Fuzzy Identification Approach for Nonlinear Industrial Systems: Eliminating Singularity for Enhanced Control
DOI:
https://doi.org/10.18196/jrc.v6i1.24241Keywords:
Fuzzy Identificationl, PDC Control, Takagi - Sugeno, Nonlinear Systems, Industrial Control, Aeropendulum.Abstract
The control of nonlinear systems poses significant challenges due to their inherent complexities, limiting the effectiveness of traditional control strategies. This paper presents an improved fuzzy identification and control method for nonlinear industrial systems, using Takagi-Sugeno fuzzy inference to model nonlinear dynamics as an interpolation of multiple linear subsystems. A key improvement of this approach lies in the accurate identification of the nonlinear model, which leads to fewer control system failures. The research contribution is the development of a control strategy that enhances system reliability while simplifying implementation. The method involves minimizing a cost function that optimizes the system’s output error, refining the fuzzy identification process for dynamic adaptation to varying operating conditions. The strategy also enables the design of linear controllers for each subsystem and applies Parallel Distributed Compensation (PDC) to regulate the overall nonlinear system. This approach is validated through experimental testing on an aero-pendulum system. The results show that the PDCbased control scheme not only ensures high performance across a wide operational range but also significantly reduces identification errors compared to traditional methods. Given its improved accuracy, reduced complexity, and adaptability, this approach holds significant potential for practical application in industrial environments, where robust and efficient control of nonlinear systems is crucial for operational success.References
A. Ma’arif et al., “Sliding Mode Control Design for Magnetic Levitation System,” Journal of Robotics and Control, vol. 3, no. 6, pp. 848–853, 2022, doi: 10.18196/jrc.v3i6.12389.
M. Maaruf, A. Babangida, H. A. Almusawi, and P. S. Tamas, “Neural Network-based Finite-time Control of Nonlinear Systems with Unknown Dead-zones: Application to Quadrotors,” Journal of Robotics and Control, vol. 3, no. 6, pp. 735–742, 2022, doi: 10.18196/jrc.v3i6.15355.
A. Ma’arif, M. A. M. Vera, M. S. Mahmoud, S. Ladaci, A. C¸ akan, and J. Nino Parada, “Backstepping Sliding Mode Control for Inverted Pendulum ˜ System with Disturbance and Parameter Uncertainty,” Journal of Robotics and Control, vol. 3, no. 1, pp. 86–92, 2021, doi: 10.18196/jrc.v3i1.12739.
N. H. Nguyen, T. X. Vu, and H. V. Nguyen, “Tracking Control for Affine Time-Varying Nonlinear Systems with Bounds,” Journal of Robotics and Control, vol. 5, no. 4, pp. 1137–1148, 2024, doi: 10.18196/jrc.v5i4.22077.
O. Y. Ismael, M. Almaged, and A. I. Abdulla, “Nonlinear Model Predictive Control-based Collision Avoidance for Mobile Robot,” Journal of Robotics and Control, vol. 5, no. 1, pp. 142–151, 2024, doi: 10.18196/jrc.v5i1.20615.
T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” in IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-15, no. 1, pp. 116-132, 1985, doi: 10.1109/TSMC.1985.6313399.
Satriya Ramahdika Utama, Ahmad Firdausi, and Galang Persada Hakim, “Control and Monitoring Automatic Floodgate based on NodeMCU and IoT with Fuzzy Logic Testing,” Journal of Robotics and Control, vol. 3, no. 1, pp. 14-17, 2022, doi: 10.18196/jrc.v3i1.11199.
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, vol. 4, no. 2, pp. 217-226, 2023, doi: 10.18196/jrc.v4i2.17757.
M. Almaged, A. Mahmood, and Y. H. S. Alnema, “Design of an Integral Fuzzy Logic Controller for a Variable-Speed Wind Turbine Model,” Journal of Robotics and Control, vol. 4, no. 6, pp. 762-768, 2023.
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, vol. 3, no. 6, pp. 762-768, 2022, doi: 10.18196/jrc.v3i6.15974.
F. Furizal, S. Sunardi, and A. Yudhana, “Temperature and Humidity Control System with Air Conditioner Based on Fuzzy Logic and Internet of Things,” Journal of Robotics and Control, vol. 4, no. 3, pp. 308-322, 2023, doi: 10.18196/jrc.v4i3.18327.
I. R. F. Arif, A. Firdausi, and G. P. N. Hakim, “Nebulizer Operational Time Control Based on Drug Volume and Droplet Size Using Fuzzy Sugeno Method,” Journal of Robotics and Control, vol. 2, no. 2, pp. 94-97, 2021, doi: 10.18196/jrc.2259.
I. Zaway, R. J. Khlif, B. Maalej, and N. Derbel, “A Robust Fuzzy Fractional Order PID Design Based on Multi-Objective Optimization for Rehabilitation Device Control,” Journal of Robotics and Control, vol. 4, no. 3, pp. 388–402, 2023, doi: 10.18196/jrc.v4i3.18411.
M. Sugeno and G. T. Kang, “Structure identification of fuzzy model,” Fuzzy Sets and Systems, vol. 28, no. 1, pp. 15-33, 1988, doi: 10.1016/0165-0114(88)90113-3.
T. A. Johansen and B. A. Foss, “Identification of non-linear system structure and parameters using regime decomposition,” Automatica, vol. 31, no. 2, pp. 321-326, 1995, doi: 10.1016/0005-1098(94)00096-2.
R. Babuska and H. B. Verbruggen, “Neuro-fuzzy methods for nonlinear system identification,” Annual Reviews in Control, vol. 27, no. 1, pp. 73-85, 2011, doi: 10.1016/S1367-5788(03)00009-9.
M. Gong et al., “Deep Fuzzy Variable C-Means Clustering Incorporated With Curriculum Learning,” in IEEE Transactions on Fuzzy Systems, vol. 31, no. 12, pp. 4321-4335, 2023, doi: 10.1109/TFUZZ.2023.3283046.
D. Sun, Q. Liao and H. Ren, “Type-2 Fuzzy Modeling and Control for Bilateral Teleoperation System With Dynamic Uncertainties and TimeVarying Delays,” in IEEE Transactions on Industrial Electronics, vol. 65, no. 1, pp. 447-459, 2018, doi: 10.1109/TIE.2017.2719604.
G. Chen, T. Pham, and H. Yang, “A fuzzy model identification method for nonlinear dynamic systems,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 3, pp. 525-538, 2016.
X. Li and Y. Zhao, “Adaptive fuzzy control of nonlinear systems with unknown control directions,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 2, pp. 288-299, 2017.
M. S. Karis et al., “Analysis of ANN and Fuzzy Logic Dynamic Modelling to Control the Wrist Exoskeleton,” Journal of Robotics and Control, vol. 4, no. 4, pp. 572–583, 2023, doi: 10.18196/jrc.v4i4.19299.
Z. Zeng and W. Chen, “A data-driven fuzzy modeling approach for complex industrial processes,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 4, pp. 778-792, 2019.
B. M. Al-Hadithi, A. Jimenez, and F. Mat ´ ´ıa, “A new approach to fuzzy estimation of Takagi–Sugeno model and its applications to optimal control for nonlinear systems,” Applied Soft Computing, vol. 12, no. 2, pp. 280- 290, 2012, doi: 10.1016/j.asoc.2011.08.044.
S. Coupland and R. I. John, “A fast geometric method for the generation of type-2 fuzzy membership functions,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 6, pp. 1331-1338, 2011.
T. Q. Ngo, T. H. Tran, T. T. H. Le, and B. M. Lam, “An Application of Modified T2FHC Algorithm in Two-Link Robot Controller,” Journal of Robotics and Control, vol. 4, no. 4, pp. 509–520, 2023, doi: 10.18196/jrc.v4i4.18943.
J. M. Mendel and R. I. B. John, “Type-2 fuzzy sets made simple,” in IEEE Transactions on Fuzzy Systems, vol. 10, no. 2, pp. 117-127, 2002, doi: 10.1109/91.995115.
O. Castillo, P. Melin, J. Kacprzyk and W. Pedrycz, “Type-2 Fuzzy Logic: Theory and Applications,” 2007 IEEE International Conference on Granular Computing, pp. 145-145, 2007, doi: 10.1109/GrC.2007.118.
D. Wu and W. W. Tan, “A simplified type-2 fuzzy controller for realtime control,” ISA Transactions, vol. 45, no. 4, pp. 503-516, 2006, doi: 10.1016/S0019-0578(07)60228-6.
Qilian Liang and J. M. Mendel, “Interval type-2 fuzzy logic systems: theory and design,” in IEEE Transactions on Fuzzy Systems, vol. 8, no. 5, pp. 535-550, 2000, doi: 10.1109/91.873577.
M. A. Abdelghany, A. O. Elnady, and S. O. Ibrahim, “Optimum PID Controller with Fuzzy Self-Tuning for DC Servo Motor,” Journal of Robotics and Control, vol. 4, no. 4, pp. 500–508, 2023, doi: 10.18196/jrc.v4i4.18676.
Z. Wang, D. W. C. Ho, and H. K. Lam, “Fuzzy-model-based control of nonlinear systems: an LMI approach,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 3, pp. 611-623, 2010.
K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, Wiley-Interscience, 2001, doi: 10.1002/0471224596.
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, vol. 2, no. 6, pp. 527-538, 2021, doi: 10.18196/jrc.26133.
P. Chotikunnan et al., “Optimizing Membership Function Tuning for Fuzzy Control of Robotic Manipulators Using PID-Driven Data Techniques,” Journal of Robotics and Control, vol. 4, no. 2, pp. 128-140, 2023, doi: 10.18196/jrc.v4i2.18108.
E. Marliana, A. Wahjudi, L. Nurahmi, I. M. L. Batan, and G. Wei, “Optimizing the Tuning of Fuzzy-PID Controllers for Motion Control of Friction Stir Welding Robots,” Journal of Robotics and Control, vol. 5, no. 4, pp. 1002–1017, 2024, doi: 10.18196/jrc.v5i4.21697.
J. Sonawane, M. Patil, and G. K. Birajdar, “Enhancement of Underwater Video through Adaptive Fuzzy Weight Evaluation,” Journal of Robotics and Control, vol. 5, no. 2, pp. 500–508, 2024, doi: 10.18196/jrc.v5i2.20496.
L. -X. Wang and J. M. Mendel, “Generating fuzzy rules by learning from examples,” in IEEE Transactions on Systems, Man, and Cybernetics, vol. 22, no. 6, pp. 1414-1427, 1992, doi: 10.1109/21.199466.
M. Alzubi, M. Almseidin, S. Kovacs, J. Al-Sawwa, and M. Alkasassbeh, “EI-FRI: Extended Incircle Fuzzy Rule Interpolation for Multidimensional Antecedents, Multiple Fuzzy Rules, and Extrapolation Using Total Weight Measurement and Shift Ratio,” Journal of Robotics and Control, vol. 5, no. 1, pp. 217–227, 2024, doi: 10.18196/jrc.v5i1.20515.
M. M. Hassan, A. Khosravi, and S. Nahavandi, “A parallel distributed fuzzy controller for nonlinear systems with dead zone,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 4, pp. 816-828, 2014.
D. Xue, C. Zhao, and J. Cao, “Parallel distributed fuzzy control of nonlinear systems with time-varying delays,” IEEE Transactions on Cybernetics, vol. 45, no. 7, pp. 1360-1371, 2015.
H. Zheng, Y. Zou and S. Li, “Distributed Fuzzy Model Predictive Control of Nonlinear Systems: An Interval Predictor Approach,” 2024 14th Asian Control Conference (ASCC), pp. 01-06, 2024.
J. Zhang, C. Gao, and X. Xie, “Distributed fuzzy control for a class of nonlinear large-scale systems,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 4, pp. 969-979, 2017.
Q. Liu, J. Yang, and L. He, “Distributed fuzzy control of nonlinear largescale systems with unknown interconnections,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 1, pp. 164-176, 2018.
X. Yan, Y. Wang, and D. Zhou, “Distributed fuzzy adaptive control of nonlinear large-scale systems with actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 3, pp. 532-544, 2019.
N. Rafiuddin and Y. U. Khan, “Nonlinear Controller Design for Mechatronic Aeropendulum,” International Journal of Dynamics and Control, vol. 11, pp. 1662–1670, 2023, doi: 10.1007/s40435-022-01080-7.
A. Kharola, “Design of a Hybrid Adaptive Neuro Fuzzy Inference System (ANFIS) Controller for Position and Angle control of Inverted Pendulum (IP) Systems,” International Jurnal of Fuzzy System Application, vol. 5, no. 1, 2016, doi: 10.4018/IJFSA.2016010102.
E. R. Lucena, S. O. D. Luiz, and A. M. N. Lima, “Modeling, Parameter Estimation, and Control of an Aero-pendulum,” Simposio Brasileiro de ´ Automac¸ao Inteligente ˜, vol. 1, no. 1, 2021, doi: 10.20906/sbai.v1i1.2837.
A. G. O. Mutambara, Design and Analysis of Control Systems: Driving the Fourth Industrial Revolution, CRC Press, pp. 1–794, 2024.
H. R. M. Silva, I. T. M. Ramos, R. Cardim, E. Assunc¸ao, and M. C. ˜ M. Teixeira, “Identification and Switched Control of an Aeropendulum System,” Congresso Brasileiro de Automatica (CBA) ´ , vol. 2, no. 1, 2020, doi: 10.48011/asba.v2i1.1429.
R. R. Galvan´ et al., “Hunting Search Algorithm-Based Adaptive Fuzzy Tracking Controller for an Aero-Pendulum,” Technologies, vol. 12, no. 5, 2024, doi: 10.3390/technologies12050063.
G. Escobar, L. Fridman, A. Levant, Control of a Spherical Pendulum: Design and Experimental Validation, IEEE Transactions on Control Systems Technology, 2005.
Mohammed Al-Tuwairqi, “Optimal Fuzzy-PID Controller Design for Aero Pendulum Using Metaheuristic Algorithms,” 2023 6th International Conference on Signal Processing and Information Security (ICSPIS), pp. 1-5, 2023.
Mojtaba Ahmadieh Khanesar, Okyay Kaynak, and Erdal Kayacan, “Adaptive Network Sliding-Mode Fuzzy Logic Control Systems,” in SlidingMode Fuzzy Controllers, pp. 179–202, 2021, doi: 10.1007/978-3-030- 69182-0 7.
M. Chen, Y. Li, J. Zhao, Sliding Mode Control of an Aeropendulum Using Nonlinear Observer, IEEE Transactions on Industrial Electronics, 2015.
H. Aslan, S. K. Kollimalla, A. K. Samantara, and H. Mishra, “A Novel Hybrid Controller for Enhancing Power Quality in PV Integrated Smart Grid,” in IEEE Transactions on Industrial Electronics, vol. 70, no. 8, pp. 7914-7924, 2023, doi: 10.1109/TIE.2023.3241459.
A. P. Rodrigues, A. Mukherjee, B. Marques, and A. K. Saha, “A Comprehensive Review of Open-Source Platforms for the Industrial Internet of Things,” in IEEE Access, vol. 11, pp. 14439-14458, 2023, doi: 10.1109/ACCESS.2023.3245085.
S. Chatterjee, B. K. Roy, and S. Kar, “A Novel Frequency-Domain Fuzzy Adaptive Proportional-Integral Controller for Frequency Regulation of an Isolated Microgrid,” IEEE Transactions on Industry Applications, vol. 56, no. 2, pp. 2022-2030, 2020, doi: 10.1109/TIA.2019.2947736.
D. Li, Y. Zhang, D. Wu, and X. Du, “A Blockchain-Based Security Architecture for Edge Computing: A Case Study of Smart Grid,” IEEE Internet of Things Journal, vol. 10, no. 6, pp. 5064-5077, 2023, doi: 10.1109/JIOT.2023.3233923.
N. S. Sabar, T. Zhang, T. Bao, and A. Keedwell, “A Comprehensive Review on Adaptive Dynamic Optimization Approaches in Evolutionary Algorithms for Real-World Optimisation Problems,” in IEEE Access, vol. 8, pp. 95801-95825, 2020, doi: 10.1109/ACCESS.2020.2994224.
W. Yang, F. Xiang, H. Zhang, and H. Gao, “Adaptive Dynamic Programming-Based Optimal Control for Nonlinear Systems: Methods and Applications,” IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 9, pp. 4949-4963, 2023, doi: 10.1109/TNNLS.2023.3260825.
R. Morell-Gimenez, J. Armesto, R. J. Saltarelli, G. J. Garc ´ ´ıa, D. Biel, and F. Blanes, “Event-based control system for a DC–DC buck converter based on a FPGA,” IEEE Transactions on Industrial Informatics, vol. 17, no. 6, pp. 3960-3968, 2021, doi: 10.1109/TII.2020.3047384.
H. Alaskar, A. Gasparyan, and M. M. H. Mokhtar, “Digital twin conceptual model development for smart asset management of off-grid renewable energy assets,” in IEEE Access, vol. 9, pp. 85741-85755, 2021, doi: 10.1109/ACCESS.2021.3087831.
J. Armesto, R. J. Saltarelli, R. Morell-Gimenez, G. J. Garc´ıa, D. Biel, and F. Blanes, “Event-Based Control System for a DC–DC Buck Converter Based on a FPGA,” IEEE Transactions on Industrial Informatics, vol. 17, no. 6, pp. 3960-3968, 2021, doi: 10.1109/TII.2020.3047384.
K. J. B. K. Mahapatra, J. Patra, and D. P. Mishra, “Implementation of Hybrid Model Predictive Control Strategy for Grid Integration of Solar PV System,” IEEE Transactions on Sustainable Energy, vol. 10, no. 2, pp. 931-941, 2019, doi: 10.1109/TSTE.2018.2867512.
M. Darweesh, R. Muresan, and T. N. Anderson, “Solar Forecasting Using Machine Learning Techniques: A Review,” in IEEE Access, vol. 8, pp. 70167-70180, 2020, doi: 10.1109/ACCESS.2020.2986782.
T. Immanuel, S. A. Daniel, M. M. Krishna, B. Eswara, and T. Arunkumar, “Multi-Objective Power Scheduling in Renewable Energy System for Blockchain-Based Industrial Applications,” IEEE Transactions on Industrial Informatics, vol. 19, no. 4, pp. 4450-4457, 2023, doi: 10.1109/TII.2022.3224215.
A. Al-Shamma, M. Abusharkh, and K. N. Salama, “Deep Reinforcement Learning for Demand Response Management in Smart Grids: A Survey,” in IEEE Access, vol. 11, pp. 25295-25312, 2023, doi: 10.1109/ACCESS.2023.3251544.
W. Pedrycz, “Why triangular membership functions?” Fuzzy Sets and Systems, vol. 64, no. 1, pp. 21-30, 1994, doi: 10.1016/0165-0114(94)90003-5.
X. Zhou, X. Chen, and W. Yan, “A Gaussian membership function based approach to fuzzy modeling and control,” Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 25-37, 2017.
H. A. Hagras, “A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots,” in IEEE Transactions on Fuzzy Systems, vol. 12, no. 4, pp. 524-539, 2004, doi: 10.1109/TFUZZ.2004.832538.
Y. Luo, W. Zhu, J. Cao and L. Rutkowski, “Event-Triggered FiniteTime Guaranteed Cost H-Infinity Consensus for Nonlinear Uncertain Multi-Agent Systems,” in IEEE Transactions on Network Science and Engineering, vol. 9, no. 3, pp. 1527-1539, 2022, doi: 10.1109/TNSE.2022.3147254.
Vladimir Damic, Marek Stryczek, and Adam Czaban, “Analysis of hydraulic linear actuator operation in the high-frequency oscillatory motion regime,” International Journal of Applied Mechanics and Engineering, vol. 26, no. 4, pp. 158-169, 2021, doi: 10.2478/ijame-2021-0046.
A. Levant, I. Yaesh, D. Alciatore, Nonlinear H∞ Control of an Aeropendulum, IEEE Transactions on Control Systems Technology, 2000.
R. Ortega, M. Asyali, J. Loraud, Adaptive Control of an Aeropendulum with Guaranteed Stability Margins, Automatica, 2007.
S. Jiang, Y. Guo, X. Wang, Fuzzy Logic Control of an Aeropendulum, Journal of Intelligent and Fuzzy Systems, 2003.
B. S. D. Vasconcellos, M. D. S. Pinheiro, F. M. U. D. Araujo, and A. G. D. ´ C. Junior, “Controlador Adaptativo MRAC em um Pendulo Amortecido ˆ Baseado em Modelos Matematicos Determin ´ ´ısticos,” Revista Principia, vol. 1, no. 1, 2021, doi: 10.18265/1517-0306a2021id4149.
O. Saleem, M. Rizwan, A. A. Zeb, A. H. Ali, and M. A. Saleem, “Online Adaptive PID Tracking Control of an Aero-Pendulum Using PSO-Scaled Fuzzy Gain Adjustment Mechanism,” Soft Computing, vol. 24, pp. 10629–10643, 2020, doi: 10.1007/s00500-019-04568-1.
H. Khalil, M. Asyali, Robust Adaptive Control of an Aeropendulum with Uncertain Parameters, International Journal of Adaptive Control and Signal Processing, 2012.
K. Zhang, X. Chen, L. Liu, Optimal Control of an Aeropendulum Using Model Predictive Control, Control Engineering Practice, 2018.
Downloads
Additional Files
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
This journal is based on the work at https://journal.umy.ac.id/index.php/jrc under license from Creative Commons Attribution-ShareAlike 4.0 International License. You are free to:
- Share – copy and redistribute the material in any medium or format.
- Adapt – remix, transform, and build upon the material for any purpose, even comercially.
The licensor cannot revoke these freedoms as long as you follow the license terms, which include the following:
- Attribution. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- ShareAlike. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
• Creative Commons Attribution-ShareAlike (CC BY-SA)
JRC is licensed under an International License
