A Novel and Robust Fractional-Order Proportional-Integral-Derivative Acceleration Controller for Electric Furnace Temperature Regulation

Abstract

Electric furnaces are widely used in industrial thermal treatments because they combine high energy efficiency with precise temperature regulation. However, the nonlinear system dynamics, inherent time delays, and large thermal inertia often limit the achievable level of control performance in practice. A novel fractional-order Proportional–Integral–Derivative–Acceleration (PIαDA) controller is presented in this work, with its parameters tuned via a Modified Flower Pollination Algorithm (MFPA) to address the aforementioned limitations. The tuning procedure is formulated to explicitly improve transient response characteristics while enhancing robustness, thereby supporting reliable operation under varying operating conditions.​ Controller performance is assessed through comprehensive simulation studies that include reference tracking, step changes in the temperature setpoint, external disturbance rejection, and tracking under noisy reference signals. Compared with MFPA-tuned benchmark controllers (i.e., the MFPA-optimized PIDA and the conventional PID), the proposed MFPA-optimized PIαDA  controller achieves higher tracking accuracy, shorter rise and settling times, reduced overshoot, and improved robustness against disturbances and measurement noise. Overall, these findings indicate that combining fractional-order control structures with advanced metaheuristic optimization can substantially enhance temperature regulation performance in industrial electric furnace applications.