Intelligent PID Gain Selection via Supervised Machine Learning Approach for Decoupled MIMO Control Systems
DOI:
https://doi.org/10.62411/faith.3048-3719-92Keywords:
Decoupler, Machine Learning, MIMO System, PID Controller, Supervised Classification, Transfer FunctionAbstract
In recent times, the control of engineering processes has gained attention, making it critical to protect devices from operating beyond their designed capabilities. Therefore, this study investigates the modelling and optimization of gain factors for a MIMO-based PID controller employing a machine learning classifier approach. Traditional approaches like Ziegler-Nichols and Cohen-Coon may not handle dynamic coupling between channels well, struggle with nonlinearity, and always require manual tuning, which is tediously challenging and time-consuming. Machine-learning (ML) algorithms are introduced in this study to redesign and remodel the general model (GM) in MIMO fashion. We train and test the proposed model in Anaconda3 using Python programming on synthetic and iteratively generated datasets. Four different ML classifiers, namely, Support Vector Machine (SVM), Random Forest (RF), Logistic Regression (LR), and Naïve Bayes (NB), are employed to generate confusion matrices with accuracies of 30.67%, 72%, 25.33%, and 76%, respectively, using the PM system. Furthermore, the dataset corresponding to 76% of the NB is predicted to give an optimal output, as the output of the GM serves as the initial solution of the controller, and the test numerical results are fed back into the MATLAB scripts to produce an optimized version of the GM. Comparatively speaking, the GM, with an average settling time of 238.33 s, and the PM, with an average of 93.33 s, demonstrate faster steady-state response times, smaller gain, phase margins, and better overlap of the ideal gain factors on their target open-loop gain curves, depicting excellent stability. In addition, it can be inferred that the PM is more efficient than the existing model (GM) as it yields better-desired results. As a future direction, it is suggested that more machine learning classifiers, such as XGBOOST, neural networks, and K-nearest neighbour, be incorporated into the training and testing of larger datasets for better, improved, and optimized outputs.
Downloads
References
Q. A. Mumuni, A. I. Olayiwola-Mumuni, and A. A. Youssouf, “The Advent of The Proportional Integral Derivative Controller: A Review,” J. Adv. Eng. Technol., vol. 2, no. 10, pp. 5–22, 2023, doi: 10.24412/2181-1431-2023-2-5-22.
A. Noshadi, J. Shi, W. S. Lee, P. Shi, and A. Kalam, “Optimal PID-type fuzzy logic controller for a multi-input multi-output active magnetic bearing system,” Neural Comput. Appl., vol. 27, no. 7, pp. 2031–2046, Oct. 2016, doi: 10.1007/s00521-015-1996-7.
D. W. Lee, W. J. Yoo, and S. C. Won, “An integral control for synchronization of a class of unknown non-autonomous chaotic systems,” Phys. Lett. A, vol. 374, no. 41, pp. 4231–4237, Sep. 2010, doi: 10.1016/j.physleta.2010.08.050.
A. M. Nagy Kiss, B. Marx, G. Mourot, G. Schutz, and J. Ragot, “State estimation of two-time scale multiple models. Application to wastewater treatment plant,” Control Eng. Pract., vol. 19, no. 11, pp. 1354–1362, Nov. 2011, doi: 10.1016/j.conengprac.2011.07.009.
Y. Yang, Y. Gao, J. Wu, Z. Ding, and S. Zhao, “Improving PID Controller Performance in Nonlinear Oscillatory Automatic Generation Control Systems Using a Multi-objective Marine Predator Algorithm with Enhanced Diversity,” J. Bionic Eng., vol. 21, no. 5, pp. 2497–2514, Sep. 2024, doi: 10.1007/s42235-024-00548-w.
S. Charkoutsis and M. Kara-Mohamed, “A Particle Swarm Optimization tuned nonlinear PID controller with improved performance and robustness for First Order Plus Time Delay systems,” Results Control Optim., vol. 12, p. 100289, Sep. 2023, doi: 10.1016/j.rico.2023.100289.
C. Zhao and L. Guo, “Control of Nonlinear Uncertain Systems by Extended PID,” IEEE Trans. Automat. Contr., vol. 66, no. 8, pp. 3840–3847, Aug. 2021, doi: 10.1109/TAC.2020.3030876.
A. Aboelhassan, M. Abdelgeliel, E. E. Zakzouk, and M. Galea, “Design and Implementation of Model Predictive Control Based PID Controller for Industrial Applications,” Energies, vol. 13, no. 24, p. 6594, Dec. 2020, doi: 10.3390/en13246594.
R. P. Borase, D. K. Maghade, S. Y. Sondkar, and S. N. Pawar, “A review of PID control, tuning methods and applications,” Int. J. Dyn. Control, vol. 9, no. 2, pp. 818–827, Jun. 2021, doi: 10.1007/s40435-020-00665-4.
H. Q. Naccache and G. C. Gannod, “Using Proportional-Integral-Derivative Control in Self-Healing Adaptive Content Systems,” in 2009 Congress on Services - I, Jul. 2009, pp. 797–804. doi: 10.1109/SERVICES-I.2009.105.
S. K. Pandey and V. Laxmi, “Control of twin rotor MIMO system using PID controller with derivative filter coefficient,” in 2014 IEEE Students’ Conference on Electrical, Electronics and Computer Science, Mar. 2014, pp. 1–6. doi: 10.1109/SCEECS.2014.6804451.
A. E. Konkov and Y. V. Mitrishkin, “Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions,” Mathematics, vol. 12, no. 6, p. 810, Mar. 2024, doi: 10.3390/math12060810.
S. Mate, P. Pal, A. Jaiswal, and S. Bhartiya, “Simultaneous tuning of multiple PID controllers for multivariable systems using deep reinforcement learning,” Digit. Chem. Eng., vol. 9, p. 100131, Dec. 2023, doi: 10.1016/j.dche.2023.100131.
H. Jesawada, A. Yerudkar, C. Del Vecchio, and N. Singh, “A Model-Based Reinforcement Learning Approach for PID Design,” ArXiv. Jun. 07, 2022. [Online]. Available: http://arxiv.org/abs/2206.03567
I. Carlucho, M. De Paula, and G. G. Acosta, “An adaptive deep reinforcement learning approach for MIMO PID control of mobile robots,” ISA Trans., vol. 102, pp. 280–294, Jul. 2020, doi: 10.1016/j.isatra.2020.02.017.
P. Grelewicz, T. T. Khuat, J. Czeczot, P. Nowak, T. Klopot, and B. Gabrys, “Application of Machine Learning to Performance Assessment for a class of PID-based Control Systems,” ArXiv. Jan. 08, 2021. doi: 10.1109/TSMC.2023.3244714.
L. Liu, S. Tian, D. Xue, T. Zhang, Y. Chen, and S. Zhang, “A Review of Industrial MIMO Decoupling Control,” Int. J. Control. Autom. Syst., vol. 17, no. 5, pp. 1246–1254, May 2019, doi: 10.1007/s12555-018-0367-4.
J. Li and Y. Yuan, “A Nonlinear Proportional Integral Derivative-Incorporated Stochastic Gradient Descent-based Latent Factor Model,” in 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Oct. 2020, pp. 2371–2376. doi: 10.1109/SMC42975.2020.9283344.
Y. Wang, T. Xie, and H. Wu, “Latent Tensor Factorization with Nonlinear PID Control for Missing Data Recovery in Non-Intrusive Load Monitoring,” ArXiv. 2025.
S. D. Hanwate and Y. V. Hote, “Optimal PID design for Load frequency control using QRAWCP approach,” IFAC-PapersOnLine, vol. 51, no. 4, pp. 651–656, 2018, doi: 10.1016/j.ifacol.2018.06.170.
A. P. S. Ramalakshmi and P. S. Manoharan, “Non-linear modeling and PID control of twin rotor MIMO system,” in 2012 IEEE International Conference on Advanced Communication Control and Computing Technologies (ICACCCT), Aug. 2012, pp. 366–369. doi: 10.1109/ICACCCT.2012.6320804.
M. H. Moradi, “State space representation of MIMO predictive PID controller,” in Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003., 2003, pp. 452–457. doi: 10.1109/CCA.2003.1223453.
M. H. Moradi, M. R. Katebi, and M. A. Johnson, “Robust MIMO PID tuning method,” in Proceedings of the International Conference on Control Applications, vol. 1, pp. 247–252. doi: 10.1109/CCA.2002.1040193.
A. Faruq, M. F. Nor Shah, and S. S. Abdullah, “Multi-objective Optimization of PID Controller using Pareto-based Surrogate Modeling Algorithm for MIMO Evaporator System,” Int. J. Electr. Comput. Eng., vol. 8, no. 1, p. 556, Feb. 2018, doi: 10.11591/ijece.v8i1.pp556-565.
M. Nagarajapandian, S. Kanthalakshmi, P. A. M. Devan, and K. Bingi, “Optimal iterative learning PI controller for SISO and MIMO processes with machine learning validation for performance prediction,” Sci. Rep., vol. 14, no. 1, p. 23568, Oct. 2024, doi: 10.1038/s41598-024-74813-7.
M. F. El-Khatib, F. M. H. Khater, E. Hendawi, and M. I. Abu El-Sebah, “Simplified and intelligent controllers for multi-input multi-output processes,” Eng. Appl. Artif. Intell., vol. 141, p. 109816, Feb. 2025, doi: 10.1016/j.engappai.2024.109816.
Y. S. Hagh, R. M. Asl, A. Fekih, and H. Handroos, “A Non-singular Terminal Synergetic Control Design for Servo-hydraulic Systems,” in 2020 6th International Conference on Control, Automation and Robotics (ICCAR), Apr. 2020, pp. 255–260. doi: 10.1109/ICCAR49639.2020.9108057.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Quadri Ademola Mumuni, Olatayo Moses Olaniyan, Oluwafemi Ipinnimo, Lateef Adesola Akinyemi, Ameena Idowu Olayiwola-Mumuni
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
