A Fuzzy Cascaded FOPI-FOPD Controller Optimized by TLBO for Nonlinear Temperature Control in CSTH Systems

Precise temperature regulation in nonlinear and highly dynamic systems—such as the Continuous Stirred-Tank Heater (CSTH)—poses significant control challenges due to internal nonlinearities, time-varying dynamics, and external disturbances. Traditional linear controllers often fall short in addressing these issues effectively. To overcome these limitations, this paper proposes a novel Fuzzy Logic Control (FLC) strategy tailored for CSTH temperature regulation. The proposed controller features a hybrid structure that combines a Fuzzy Fractional-Order Proportional-Integral (FOPI) controller cascaded with a Fractional-Order Proportional-Derivative (FOPD) compensator, forming a Fuzzy FOPI-FOPD control scheme. This configuration harnesses the strengths of fuzzy logic for handling uncertainty and nonlinearity. To optimize the controller's parameters, various metaheuristic algorithms are employed, with a primary focus on the Teaching-Learning-Based Optimization (TLBO) technique. The Integral Time Absolute Error (ITAE) is used as the performance index to implememt the optimization process, ensuring effective minimization of tracking error over time. Extensive simulation studies are conducted under different operating conditions, including setpoint variations and external disturbances, to validate the effectiveness of the proposed method. Comparative analysis reveals that the Fuzzy FOPI-FOPD controller outperforms conventional control strategies in terms of transient response, steady-state accuracy, and robustness. Specifically, the controller exhibits reduced overshoot, faster settling time, and improved disturbance rejection. These results highlight the controller's potential for practical deployment in industrial thermal processes. Overall, the proposed optimization-based fuzzy fractional-order control framework offers a highly effective and flexible solution for complex nonlinear process control applications.