Temperature Control of Nonlinear Continuous Stirred Tank Reactors Using an Enhanced Nature-Inspired Optimizer and Fractional-Order Controller

The temperature regulation of nonlinear continuous stirred tank reactor (CSTR) processes remains a challenging control problem due to strong nonlinearities, time-delay effects, and sensitivity to disturbances and parameter variations. Conventional proportional–integral–derivative (PID)-based control strategies often fail to provide the robustness and precision required under such conditions, motivating the use of more flexible controller structures and advanced optimization techniques. In this study, an enhanced joint-opposition artificial lemming algorithm (JOS-ALA) is proposed for the optimal tuning of a fractional-order PID (FOPID) controller applied to CSTR temperature control. The proposed JOS-ALA incorporates a joint opposite selection mechanism into the original ALA to improve population diversity, convergence stability, and resistance to local optima stagnation. A nonlinear CSTR model is linearized around a stable operating point, and the resulting model is employed for controller design and optimization. The FOPID controller parameters are tuned by minimizing a composite cost function that simultaneously accounts for tracking accuracy, overshoot suppression, and instantaneous error behavior. The effectiveness of the proposed approach is assessed through extensive simulation studies and benchmarked against state-of-the-art and high-performance metaheuristic optimizers, including ALA, electric eel foraging optimization (EEFO), linear population size reduction success-history based adaptive differential evolution (L-SHADE), and the improved artificial electric field algorithm (iAEFA). The benchmarking set is further extended with the success rate-based adaptive differential evolution variant (L-SRTDE) to broaden the comparative evaluation. Simulation results demonstrate that the JOS-ALA-based FOPID controller consistently achieves superior performance across multiple criteria. Specifically, it attains the lowest mean cost function value of 0.1959, eliminates overshoot, and yields a normalized steady-state error of 4.7290 × 10−4. In addition, faster transient response and improved robustness under external disturbances and measurement noise are observed when compared with competing methods. Statistical reliability of the observed performance differences is additionally examined using a Wilcoxon signed-rank test conducted over 25 independent runs. The resulting p-values confirm that the improvements achieved by the proposed approach are statistically significant at the 5% level across all pairwise algorithm comparisons. These findings indicate that the proposed JOS-ALA provides an effective and reliable optimization framework for high-precision temperature control in nonlinear CSTR systems and offers strong potential for broader application in complex process control problems.