Efficient control strategy for electric furnace temperature regulation using quadratic interpolation optimization

Electric furnaces play an important role in many industrial processes where precise temperature control is essential to ensure production efficiency and product quality. Traditional proportional-integral-derivative (PID) controllers and their modified versions are commonly used to maintain temperature stability by reacting quickly to deviations. In this study, the real PID plus second-order derivative (RPIDD²) controller is introduced for the first time for industrial temperature control applications, which is a novel alternative that has not yet been investigated in the literature. To ensure optimal performance, the parameters of the RPIDD² controller are optimized using metaheuristic algorithms, including the flood optimization algorithm (FLA), reptile search algorithm (RSA), particle swarm optimization (PSO) and differential evolution (DE). A new approach is proposed which combines the quadratic interpolation optimization (QIO) algorithm with the RPIDD² controller, taking advantage of the fast convergence, low computational cost and high accuracy of QIO. Comparative analyses between QIO-RPIDD², FLA-RPIDD², RSA-RPIDD², PSO-RPIDD² and DE-RPIDD² controller are performed by evaluating performance metrics such as transient and frequency response. The results show that QIO-RPIDD² achieves superior performance, adapts quickly to different reference temperatures and performs excellently on key performance indicators. These results make the proposed QIO-RPIDD² controller a promising solution for industrial temperature control and contribute to more efficient and adaptive optimization techniques.