Quadratic interpolation optimization-based 2DoF-PID controller design for highly nonlinear continuous stirred-tank heater process

Temperature control in continuous stirred tank heater (CSTH) systems is essential for ensuring energy efficiency, safety, and product quality in industrial processes. However, the nonlinear dynamics and external disturbances make conventional proportional-integral-derivative (PID) control inadequate for reliable operation. This study presents a novel two-degrees-of-freedom PID (2DoF-PID) controller optimized using the quadratic interpolation optimization (QIO) algorithm to enhance CSTH temperature regulation. The QIO-based approach allows independent tuning for setpoint tracking and disturbance rejection, overcoming the limitations of classical PID controllers. Extensive nonlinear time-domain simulations, reference tracking, and disturbance rejection tests demonstrate the superior performance of the proposed controller in terms of reduced overshoot, faster settling time, and minimal steady-state error. Furthermore, comparative evaluations with traditional tuning methods (Murrill and Rovira) and several state-of-the-art metaheuristic optimizers (DE, PSO, FLA, MGO) validate the effectiveness and robustness of the QIO-optimized strategy. This work introduces a pioneering application of the QIO algorithm in industrial temperature control, offering a scalable and cost-efficient solution for complex nonlinear systems.