A Novel 2-DOF PIDA control strategy with GCRA-based parameter optimization for electric furnace temperature control

Accurate and energy-efficient temperature regulation in electric furnace systems remains a challenging control problem due to nonlinear dynamics, significant thermal inertia, and inevitable time delays. Conventional proportional-integral-derivative (PID) and PID-acceleration (PIDA) controllers, though widely used, often exhibit degraded performance under such conditions, particularly when implemented in a single-degree-of-freedom. To address these limitations, this study proposes, for the first time, a two-degree-of-freedom (2-DOF) PIDA controller tailored for electric furnace temperature control. The controller structure allows independent tuning of set-point tracking and disturbance rejection by introducing separate feedforward paths in the proportional and derivative channels while maintaining integral and acceleration actions on the error signal. To optimize the controller parameters, the recently developed greater cane rat algorithm (GCRA) is employed for the first time in this context. A novel adaptive objective function (combining normalized overshoot, normalized settling time, and cumulative tracking error) guides the tuning process to achieve a balanced improvement in both transient and steady-state performance. The proposed GCRA-based 2-DOF PIDA controller is evaluated through extensive simulations and compared against state-of-the-art metaheuristic tuning approaches, including polar fox optimization (PFA), hiking optimization (HOA), success-history based adaptive differential evolution with linear population size reduction (L-SHADE), and particle swarm optimization (PSO), as well as several benchmark furnace control methods. Results demonstrate that the proposed method consistently achieves faster settling times, reduced overshoot, and near-zero steady-state error, while maintaining robustness under external disturbances and measurement noise. For instance, in the nominal case, the method yields an overshoot of 1.8382% and a settling time of 3.4542 s, outperforming PFA, HOA, L-SHADE, and PSO. Robustness tests under load disturbances and measurement noise confirm stable operation with minimal performance degradation, achieving less than 2.5% overshoot and under 4 s settling time across all evaluated scenarios. These findings highlight the potential of the GCRA-based 2-DOF PIDA controller as a high-precision and energy-efficient solution for temperature regulation in industrial time-delay systems.