Application of AFFDE-RBF-PID-PI Cascade Control in Heating Furnace Temperature Control System

Yue-Ting  Liu; Yan  Zhang

doi:10.6180/jase.202407_27(7).0008

Application of AFFDE-RBF-PID-PI Cascade Control in Heating Furnace Temperature Control System

Computer Science and Information Engineering

Yue-Ting LiuThis email address is being protected from spambots. You need JavaScript enabled to view it. and Yan Zhang

School of Media Engineering, Lanzhou University of Arts and Science, Lanzhou 730000, China

Received: May 31, 2023
Accepted: July 12, 2023
Publication Date: November 5, 2023

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202407_27(7).0008

Given the large hysteresis in the material outlet temperature of the heating furnace, a differential evolution algorithm with adaptive adjustment factors (AAFDE)-radial basis function (RBF)-proportional integral derivative (PID)-PI cascade is proposed. First, we introduce an adaptive mutation factor into the differential evolution (DE) algorithm and define the individual merit coefficient to incorporate a self-adaptive crossover probability factor. Second, the initial parameters of RBF are optimized by the AFFDE algorithm, and RBF neural network model is established. Then, we obtain gradient information by RBF online identification. Finally, we perform online adjustments to the three parameters of PID based on the gradient information. The three parameters are applied to the adjustment of the main controller, while the sub-controller employs PI control. Experimental results show that the anti-disturbance performance of the AFFDE-RBF-PID-PI cascade control outperforms the improved differential evolution (IDE)-RBF-PID-PI cascade control, generalized opposition-based differential evolution (GODE)-RBF-PID-PI cascade control, and MCOBDE-RBF-PID-PI cascade control respectively by 16%, 11%, and 7%, with the response speed improving by 18%, 12%, and 9%, and the stability improving by 19%, 13%, and 8%. These results show that AFFDE-RBF-PID-PI cascade control exhibits enhanced anti-disturbance performance, faster response speed, improved stability, and superior control effect.

Keywords: adaptive adjustment factor; differential evolution algorithm; radial basis function neural network; cascade control; heating furnace system

[1] Y. Zhang, (2016) “Research on Temperature Control System of Aging Oven Based on Fuzzy PID Theory" Changchun: Jilin University:
[2] Z. Xu, (2020) “Research and application of control method of electric heating furnace temperature system" Hangzhou: Hangzhou Dianzi University:
[3] H. Jing, (2017) “Research on temperature control algorithm of rotary furnace" Tianjin: Tiangong University:
[4] W. Tu, Y. Yang, B. Du, J. Zheng, and S. Zhai, (2019) “Towards a real-time production of immersive spatial audio of high individuality with an RBF neural network" Journal of Parallel and Distributed Computing 131: 120–129. DOI: 10.1016/j.jpdc.2019.04.020.
[5] L. L. Sonfack, G. Kenné, and A. M. Fombu, (2018) “A new static synchronous series compensator control strategy based on rbf neuro-sliding mode technique for power flow control and dc voltage regulation" Electric Power Components and Systems 46(4): 456–471. DOI: 10.1080/15325008.2018.1445795.
[6] Y. Xie, J. Yu, S. Xie, T. Huang, and W. Gui, (2019) “On-line prediction of ferrous ion concentration in goethite process based on self-adjusting structure RBF neural network" Neural Networks 116: 1–10. DOI: 10.1016/j.neunet.2019.03.007.
[7] S. Feng, (2021) “Research on differential evolution algorithm based on opposition-based learning strategy" Beijing University of Posts and Telecommunications:
[8] Y. Yuan, (2021) “Research on Differential Evolution Algorithm to Solve Constrained Optimization Problems" XIDIAN University:
[9] H.-l. Sun, (2020) “Research on improvement and application of differential evolution algorithm" Harbin Institute of Technology:
[10] L. Wei and W. Yagang, (2018) “Closed loop identification and PID parameter setting of cascade control system [J]" Control Engineering 25(01): 11–8. DOI: 10.14107/j.cnki.kzgc.160551.
[11] W. Yu, H. Liang, and Y. Luo, (2021) “An Improved Differential Evolution Algorithm for Fractional Order System Identification" Journal of System Simulation 33(1157-1166): DOI: 10.16182/j.issn1004731x.joss.20-0853.
[12] J. Li, J. Zou, B. Li, and J. Liu, (2018) “A differential evolution algorithm using multi-neighborhood strategy and neighborhood centroid opposition based learning" Journal of Wuhan University of Science and Technology 41(232-240):