Mathematical modeling and designing an optimized fuzzy temperature controller for a vacuum box electric furnace: Numerical and experimental study

Abstract

In this article, an experimentally validated new mathematical model is developed to show a vacuum box electric furnace’s thermal behavior and predict the temperature of the desired point inside it. The model is derived by extracting the equivalent electrical circuit of the system based on heat transfer principles. To show the accuracy of the model, its behavior has been evaluated by comparing it with experimental data. Then, an optimized fuzzy controller is designed using four metaheuristic algorithms, that is, genetic algorithm, harmony search, cuckoo optimization algorithm, and water cycle algorithm. The rule-base and the membership functions are optimized by these optimization algorithms with four criteria, that is, integral of absolute error, integral of square error, integral of time absolute error, and integral of time square error. The simulation results indicate that the fuzzy controllers tuned by the integral of time square error criterion get better performance, especially in genetic and water cycle algorithms. The designed controller based on the proposed model is implemented on an experimental setup. The experimental test shows a good agreement between experimental and simulation results. The obtained results show the ability of the fuzzy controller and approve that the developed model can be used for transient performance analysis of a vacuum box electric furnace and real-time controller design.