A Modified Enzyme Action Optimizer-Based FOPID Controller for Temperature Regulation of a Nonlinear Continuous Stirred Tank Reactor

A modified Enzyme Action Optimizer (mEAO) is proposed to tune a Fractional-Order Proportional–Integral–Derivative (FOPID) controller for precise temperature regulation of a nonlinear continuous stirred tank reactor (CSTR). The nonlinear reactor model, adopted from a standard benchmark formulation widely used in CSTR control studies, is employed as the simulation reference. The tuning framework operates in a simulation-based manner, as the optimizer relies solely on the time-domain responses to evaluate a composite cost function combining overshoot, settling time, rise time, and steady-state error. Comparative simulations involving EAO, Starfish Optimization Algorithm (SFOA), Success History-based Adaptive Differential Evolution with Linear population size reduction (L-SHADE), and Particle Swarm Optimization (PSO) demonstrate that the proposed mEAO achieves the lowest cost value, the fastest convergence, and superior transient performance. Further comparisons with classical tuning methods, Rovira 2DOF-PID, Ziegler–Nichols PID, and Cohen–Coon PI, confirm improved tracking accuracy and smoother actuator behavior. Robustness analyses under varying set-points, feed-temperature disturbances, and measurement noise confirm stable temperature regulation without retuning. These findings demonstrate that the mEAO-based FOPID controller provides an efficient and reliable optimization framework for a nonlinear thermal-process control, with strong potential for future real-time and multi-reactor applications.