Design and Performance Evaluation of a Novel FOPID Control Strategy for Electric Furnace Temperature Regulation using HHO Algorithm
Keywords:
PIᵅD controller, Temperature Control, Harris Hawks Optimization (HHO), Transient and Frequency Stability Analysis, Electric FurnaceAbstract
This study introduces the development and implementation of an advanced Proportional-Integral-Derivative (PID) control strategy, termed the Proportional Fractionalized Integral Derivative (PD) controller, aimed at enhancing transient dynamics, frequency response, and robustness in the regulation of electric furnace temperature. A key feature of the proposed controller design is the incorporation of the Harris Hawks Optimization (HHO) algorithm, employed to optimally tune the controller parameters. The selection of HHO is justified by its superior global search capability, fast convergence, and effectiveness in avoiding local minima, making it well-suited for addressing the complex, nonlinear characteristics of electric furnace systems. The suggested PD controller is used for the first time in electric furnace applications, providing a novel enhancement to traditional PID controllers by incorporating a fractional-order element. The controller’s efficacy is evaluated through stringent simulations encompassing step reference alterations, load disturbances, and continuous random setpoints. Compared to classical PID, PID Acceleration (PIDA), and Real PID with second-order derivative (RPIDD²) controllers, the proposed PD controller exhibits superior performance, achieving the fastest rise time (1.65 s), shortest settling time (3.43 s), and lowest overshoot (0.12%). It also provides the best robustness trade-off, with high gain and phase margins, the largest bandwidth, and the lowest error indices. Frequency-domain analysis further confirms its enhanced disturbance rejection and stability, underscoring the suitability of the proposed controller and HHO for accurate, reliable, and energy-efficient temperature regulation in nonlinear industrial systems.References
[1] J. W. Li, C. F. Yan and J. Liu, Design of temperature control system based on fuzzy PID, Advanced Materials Research, 418, 2012, 1756-1759.
[2] T. Sheng, H. Luo and M. Wu, Design and simulation of a multi-channel biomass hot air furnace with an intelligent temperature control system, Agriculture, 14(3), 2024, 419.
[3] E. Grassi and K. Tsakalis, PID controller tuning by frequency loop-shaping: Application to diffusion furnace temperature control, IEEE Transactions on Control Systems Technology, 8(5), 2000, 842-847.
[4] D. Ajorloo, M. Nazari, N. Sepehry and A. Mohammadzadeh, Mathematical modeling and designing an optimized fuzzy temperature controller for a vacuum box electric furnace: Numerical and experimental study, Transactions of the Institute of Measurement and Control, 45(7), 2023, 1193-1212.
[5] N. Pringsakul and D. Puangdownreong, MOFPA-based PIDA controller design optimization for electric furnace temperature control system, International Journal of Innovative Computing, Information and Control, 16(6), 2020, 1863-1876.
[6] L. Liu, D. Xue and S. Zhang, General type industrial temperature system control based on fuzzy fractional-order PID controller, Complex & Intelligent Systems, 9(3), 2023, 2585-2597.
[7] K. Rsetam, M. Al-Rawi and Z. Cao, Robust adaptive active disturbance rejection control of an electric furnace using additional continuous sliding mode component, ISA Transactions, 130, 2022, 152-162.
[8] G. C. Goodwin, R. H. Middleton, M. M. Seron and B. Campos, Application of nonlinear model predictive control to an industrial induction heating furnace, Annual Reviews in Control, 37(2), 2013, 271-277.
[9] R. Valarmathi, P. R. Theerthagiri, S. Rakeshkumar and V. Gomathi, Design of genetic algorithm based internal model controller for a heat exchanger, Proceedings of the International Conference on Computation of Power, Energy, Information and Communication (ICCPEIC), Chennai, India, 2018, 489-495.
[10] A. Jayachitra and R. Vinodha, Genetic algorithm based PID controller tuning approach for continuous stirred tank reactor, Advances in Artificial Intelligence, 2014(1), 2014, 791230.
[11] V. Sinlapakun and W. Assawinchaichote, Optimized PID controller design for electric furnace temperature systems with Nelder-Mead algorithm, Proceedings of the 12th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), Hua Hin, Thailand, 2015, 1-4.
[12] W. Jiang and X. Jiang, Design of an intelligent temperature control system based on the fuzzy self-tuning PID, Procedia Engineering, 43, 2012, 307-311.
[13] R. Zhang, Q. Zou, Z. Cao and F. Gao, Design of fractional order modeling based extended non-minimal state space MPC for temperature in an industrial electric heating furnace, Journal of Process Control, 56, 2017, 13-22.
[14] H. Liang, Z. K. Sang, Y. Z. Wu, Y. H. Zhang and R. Zhao, High precision temperature control performance of a PID neural network-controlled heater under complex outdoor conditions, Applied Thermal Engineering, 195, 2021, 117234.
[15] M. M. Hussein, S. Alkhalaf, T. H. Mohamed, D. S. Osheba, M. Ahmed, A. Hemeida and A. M. Hassan, Modern temperature control of electric furnace in industrial applications based on modified optimization technique, Energies, 15(22), 2022, 8474.
[16] S. A. Alzakari, D. Izci, S. Ekinci, A. A. Alhussan and F. A. Hashim, A new control scheme for temperature adjustment of electric furnaces using a novel modified electric eel foraging optimizer, AIMS Mathematics, 9(5), 2024, 13410-13438.
[17] I. Chew, F. Wong, A. Bono, J. Nandong and K. Wong, Genetic algorithm optimization analysis for temperature control system using cascade control loop model, International Journal of Computing and Digital Systems, 9(1), 2020, 119-128.
[18] V. D. Phan, X. H. Nguyen, V. N. Dinh, T. S. Dang, V. C. Le, S. P. Ho, H. C. Ta, D. T. Duong and T. A. Mai, Development of an adaptive fuzzy-neural controller for temperature control in a brick tunnel kiln, Electronics, 13(2), 2024, 342.
[19] A. Idir, Y. Bensafia, K. Khettab and L. Canale, Performance improvement of aircraft pitch angle control using a new reduced order fractionalized PID controller, Asian Journal of Control, 25(4), 2023, 2588-2603.
[20] A. Idir, Y. Bensafia and L. Canale, Influence of approximation methods on the design of the novel low-order fractionalized PID controller for aircraft system, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 46(2), 2024, 98.
[21] A. Idir, H. Akroum, S. A. Tadjer and L. Canale, A comparative study of integer order PID, fractionalized order PID and fractional order PID controllers on a class of stable system, Proceedings of the IEEE International Conference on Environment and Electrical Engineering and Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe), Madrid, Spain, 2023, 1-6.
[22] S. Guedida, B. Tabbache, K. Nounou and A. Idir, Reduced-order fractionalized controller for disturbance compensation based on direct torque control of DSIM with less harmonic, Electrica, 24(2), 2024, 450-462.
[23] Z. Ousaadi, H. Akroum and A. Idir, Robustness enhancement of fractionalized order proportional integral controller for speed control of indirect field-oriented control induction motor, Przegląd Elektrotechniczny, 2024(3), 2024, 166-171.
[24] M. M. Gani, M. S. Islam and M. A. Ullah, Optimal PID tuning for controlling the temperature of electric furnace by genetic algorithm, SN Applied Sciences, 1, 2019, 880.
[25] Y. Bensafia, K. Khettab and A. Idir, A novel fractionalized PID controller using the sub-optimal approximation of FOTF, Algerian Journal of Signals and Systems, 7(1), 2022, 21-26.
[26] A. A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja and H. Chen, Harris hawks optimization: Algorithm and applications, Future Generation Computer Systems, 97, 2019, 849-872.
[27] Y. Bensafia, K. Khettab and A. Idir, An improved robust fractionalized PID controller for a class of fractional-order systems with measurement noise, International Journal of Intelligent Engineering and Systems, 11(2), 2018, 200-207.
[28] A. Oustaloup, F. Levron, B. Mathieu and F. M. Nanot, Frequency-band complex noninteger differentiator: Characterization and synthesis, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(1), 2000, 25-39.
[29] D. Xue and Y. Chen, Sub-optimum H₂ rational approximations to fractional order linear systems, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE), Long Beach, USA, 2005, 1527-1536.
[30] W. Zhao, L. Wang, Z. Zhang, H. Fan, J. Zhang, S. Mirjalili, N. Khodadadi and Q. Cao, Electric eel foraging optimization: A new bio-inspired optimizer for engineering applications, Expert Systems with Applications, 238, 2024, 122200.
[31] S. Mirjalili and A. Lewis, The whale optimization algorithm, Advances in Engineering Software, 95, 2016, 51-67.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Abdelhakim Idir, Hamza Akroum, Mokhtar Nesri, Sifelislam Guedida, Laurent Canale
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:Authors hold and retain copyright, and grant the journal right of first publication, with the work after publication simultaneously licensed under a Creative Commons Attribution 4.0 License CC BY that permits any use, reproduction and distribution of the work and article without further permission provided that the original work is properly cited.
Authors are permitted and encouraged to post their work online in institutional repositories, website and other social media before and after publication, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
