A Novel Weighted Composite-Objective-Based Evolutionary Framework for PID-Based Temperature Control of Nonlinear CSTR Systems

Error minimization alone is insufficient for industrial process control. This article develops a weighted composite-objective evolutionary optimization scheme for regulating the temperature of a nonlinear, jacket-equipped continuous stirred-tank reactor (CSTR) using a PID controller. Such reactors exhibit strong nonlinearity and pronounced parameter sensitivity. However, conventional PID tuning rarely delivers satisfactory dynamics together with low control effort. To address this issue, the authors employ several metaheuristic optimizers to determine the PID gains, namely Teaching–Learning-Based Optimization (TLBO), the Whale Optimization Algorithm (WOA), African Vulture Optimization (AVO), the Imperialist Competitive Algorithm (ICA), and Henry Gas Solubility Optimization (HGSO). The existing formulations do not provide a cost criterion that weighs the tracking error together with the effort demanded by the actuator. It is challenging to improve the transient behavior and at the same time keep the actuator demand low. The authors treat both terms simultaneously, and transient behavior improves while limiting the control effort. The newly formulated criterion is benchmarked against the classical indices, namely the integral of squared error (ISE), the integral of time error (ITE), and the integral of time-weighted absolute error (ITAE). The gains in rise time, settling time, overshoot suppression, and disturbance handling are verified and presented. The proposed formulation incorporates both tracking error and control effort into a single weighted composite objective. Five metaheuristic optimization algorithms, namely TLBO, ICA, WOA, AVO, and HGSO, are considered, while ISE, ITE, and ITAE are used as conventional benchmark objectives. The controllers are evaluated using directly executed simulations under a common nonlinear CSTR configuration, with emphasis on transient response, steady-state tracking, and actuator usage.