{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T18:53:12Z","timestamp":1762195992419,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T00:00:00Z","timestamp":1762128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Traditional heat diffusion systems are typically regulated using Proportional\u2013Integral\u2013Derivative (PID) controllers. PID controllers still remain the backbone of numerous industrial control applications due to their simplicity, robustness, and efficiency. However, traditional tuning methods\u2014such as Ziegler\u2013Nichols or Cohen\u2013Coon\u2014often exhibit limitations when applied to systems with nonlinear dynamics, time-varying behaviors, or parametric uncertainties. To address these challenges, Fuzzy Logic Controllers (FLC) have emerged as a promising hybrid strategy, by translating quantitative and imprecise linguistic inputs into quantitative control actions, thereby enabling more adaptive and precise regulation. This is achieved through the integration of fuzzy inference mechanisms that dynamically adjust PID gains in response to changing system conditions. This study proposes a fuzzy logic control strategy for a heat diffusion system and conducts a comparative analysis against conventional PID control. The methodology encompasses system modeling, design of the fuzzy inference system, and simulation studies. To improve transient response and address time delays, additional features such as Anti-Windup compensation and a Smith Predictor are integrated into the control scheme. The final validation step involves the introduction of simulated environmental disturbances, including abrupt temperature drops, to evaluate the controller\u2019s robustness. Simulation results demonstrate that the proposed FLC provides superior dynamic performance compared to the conventional PID controller, achieving approximately 5\u20137% faster rise time and 8\u201310% lower settling time. The incorporation of an anti-windup mechanism did not yield significant benefits in this application. In contrast, the integration of a Smith Predictor further reduced oscillatory behavior and substantially improved disturbance rejection, tracking accuracy, and adaptability under simulated thermal variations. These results underscore the effectiveness of the FLC in handling systems with time delays and nonlinearities, reinforcing its role as a robust and adaptable control strategy for thermal processes with complex dynamics.<\/jats:p>","DOI":"10.3390\/a18110694","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T18:21:46Z","timestamp":1762194106000},"page":"694","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Robust Control of Heat Diffusion Systems with Time Delay Using Fuzzy Logic and Model-Based Compensation"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-0746-9719","authenticated-orcid":false,"given":"Rui S.","family":"Mendes","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering\u2014Polytechnic of Porto (ISEP\/IPP), 4249-015 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7545-5822","authenticated-orcid":false,"given":"Isabel S.","family":"Jesus","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering\u2014Polytechnic of Porto (ISEP\/IPP), 4249-015 Porto, Portugal"},{"name":"GECAD\u2014Research Group on Intelligent Engineering and Computing for Advanced Innovation and Development, Institute of Engineering\u2014Polytechnic of Porto (ISEP\/IPP), 4249-015 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,3]]},"reference":[{"key":"ref_1","unstructured":"Ogata, K. (2022). Modern Control Engineering, Prentice Hall."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1102","DOI":"10.35378\/gujs.873380","article-title":"Temperature Waves Phase Optimal Time Lag in the Refrigerated Warehouse Thermal Insulation","volume":"35","author":"Myronchuk","year":"2022","journal-title":"Gazi Univ. J. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109981","DOI":"10.1016\/j.automatica.2021.109981","article-title":"Optimal state-delay control in nonlinear dynamic systems","volume":"135","author":"Liu","year":"2022","journal-title":"Autom. J."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Jensen, C.M., Frederiksen, M.C., Kalles\u00f8e, C.S., Jensen, J.N., Andersen, L.H., and Izadi-Zamanabadi, R. (2023). HAVOK Model Predictive Control for Time-Delay Systems with Applications to District Heating, Elsevier. IFAC-Papers OnLine.","DOI":"10.1016\/j.ifacol.2023.10.1187"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Vivek, R., Abdelfattah, W.M., and Elsayed, E.M. (2025). Analysis of Delay-Type Integro-Differential Systems Described by the \u03a6-Hilfer Fractional Derivative. Axioms J., 14.","DOI":"10.3390\/axioms14080629"},{"key":"ref_6","first-page":"796","article-title":"Model Predictive Control for the Operation of Building Cooling Systems","volume":"20","author":"Ma","year":"2009","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_7","unstructured":"Wang, L. (2003). Model Predictive Control System Design and Implementation Using MATLAB, Springer."},{"key":"ref_8","first-page":"012102","article-title":"Computation of Time Delay for Delayed Network Controlled Temperature Control System","volume":"2070","author":"Venkatachalam","year":"2021","journal-title":"J. Phys."},{"key":"ref_9","first-page":"4486756","article-title":"Stability Results of Thermal Control System with Time-Dependent Delays and Perturbations of Nonlinearity","volume":"2022","author":"Gemechu","year":"2022","journal-title":"J. Adv. Mater. Sci. Eng."},{"key":"ref_10","unstructured":"Seborg, D.E., Edgar, T.F., Mellichamp, D.A., and Doyle, F.J. (2010). Process Dynamics and Control, Wiley. [3rd ed.]."},{"key":"ref_11","unstructured":"\u00c5str\u00f6m, K.J., and H\u00e4gglund, T. (1995). PID Controllers, International Society for Measurement and Control."},{"key":"ref_12","unstructured":"Marlin, T.E. (2015). Process Control: Designing Processes and Control Systems for Dynamic Performance, McGraw-Hill. [2nd ed.]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1109\/91.493904","article-title":"Fuzzy Logic = Computing with Words","volume":"4","author":"Zadeh","year":"1996","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_14","unstructured":"Deshpande, P.B., and Ash, R.H. (1981). Elements of Computer Process Control, with Advanced Control Applications, Instrument Society of America."},{"key":"ref_15","unstructured":"Gerald, C.F., and Wheatley, P.O. (2003). Applied Numerical Analysis, Pearson College Div. [7th ed.]."},{"key":"ref_16","unstructured":"Incropera, F.P., and DeWitt, D.P. (1996). Fundamentals of Heat and Mass Transfer, John Wiley & Sons. [4th ed.]."},{"key":"ref_17","unstructured":"Cengel, Y.A. (2022). Heat Transfer: A Practical Approach, McGraw Hill. [2nd ed.]. Available online: https:\/\/pt.scribd.com\/doc\/76358132\/Heat-Transfer-Yunus-a-Cengel-2nd-Edition."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1029\/1998RG900006","article-title":"Fourier\u2019s Heat Conduction Equation: History, Influence, and Connections","volume":"37","author":"Narasimhan","year":"1999","journal-title":"Rev. Geophys."},{"key":"ref_19","unstructured":"Lienhard, J.H. (2020). A Heat Transfer Textbook, Phlogiston Press. [5th ed.]. Available online: http:\/\/ahtt.mit.edu."},{"key":"ref_20","unstructured":"Nise, N.S. (2011). Control Systems Engineering, Wiley. [6th ed.]."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zimmermann, H.-J. (2001). Fuzzy Set Theory and Its Applications, Springer.","DOI":"10.1007\/978-94-010-0646-0"},{"key":"ref_22","unstructured":"Passino, K.M., and Yurkovich, S. (1998). Fuzzy Control, Addison-Wesley."},{"key":"ref_23","unstructured":"Castillo, O., and Melin, P. (2025, May 13). A Classification of Fuzzy Controllers. Available online: https:\/\/www.researchgate.net\/figure\/A-classification-of-fuzzy-controllers_fig1_255567860."},{"key":"ref_24","unstructured":"Kova\u010di\u0107, Z., and Bogdan, S. (2006). Fuzzy Controller Design Theory and Applications, Taylor & Francis."},{"key":"ref_25","unstructured":"Widrow, B. (2014). Intelligent Control Nazmul Siddique: A Hybrid Approach Based on Fuzzy Logic, Neural Networks and Genetic Algorithms, Springer. Available online: http:\/\/www.springer.com\/series\/7092."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Machado, J.A.T., P\u00e1tkai, B., and Rudas, I.J. (2009). On the Fractional Order Control of Heat Systems. Intelligent Engineering Systems and Computational Cybernetics, Springer.","DOI":"10.1007\/978-1-4020-8678-6"},{"key":"ref_27","unstructured":"The MathWorks, Inc. (2023). Fuzzy Logic Toolbox User\u2019s Guide, MathWorks. Available online: https:\/\/www.mathworks.com\/products\/fuzzy-logic.html."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Cirstea, M.N., Dinu, A., Khor, J.G., and Mc Cormick, M. (2002). Neural and Fuzzy Logic Control of Drives and Power Systems, Springer.","DOI":"10.1016\/B978-075065558-3\/50003-9"},{"key":"ref_29","unstructured":"MathWorks (2025). PID Tuner\u2014Tune PID Controllers, The MathWorks, Inc.. Available online: https:\/\/www.mathworks.com\/help\/control\/ref\/pidtuner-app.html."},{"key":"ref_30","unstructured":"Dorf, R.C., and Bishop, R.H. (2016). Modern Control Systems, Pearson. [13th ed.]."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1016\/j.engappai.2011.10.004","article-title":"A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices","volume":"25","author":"Das","year":"2012","journal-title":"Eng. Appl. Artif. Intell. J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"21","DOI":"10.24018\/ejece.2024.8.4.639","article-title":"Robust Fuzzy-PID Technique for the Automatic Generation Control of Interconnected Power System with Integrated Renewable Energy","volume":"8","author":"Othman","year":"2024","journal-title":"Eur. J. Electr. Eng. Comput. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"\u0130\u00e7mez, Y., and Can, M.S. (2023). Smith Predictor Controller Design Using the Direct Synthesis Method for Unstable Second-Order and Time-Delay Systems. Processes, 11.","DOI":"10.3390\/pr11030941"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/11\/694\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T18:32:58Z","timestamp":1762194778000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/11\/694"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,3]]},"references-count":33,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["a18110694"],"URL":"https:\/\/doi.org\/10.3390\/a18110694","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,3]]}}}