# High-performance temperature regulation of nonlinear CSTRs via a hybrid stellar oscillation optimizer and differential evolution-based PID-F control

## TL;DR

A new hybrid optimization method improves temperature control in chemical reactors by combining two algorithms.

## Contribution

A novel hybrid stellar oscillation optimizer and differential evolution method is proposed for PID-F controller tuning.

## Key findings

- The hybrid method achieves the lowest mean objective value with minimal variance compared to other optimizers.
- Time-domain results show reduced rise and settling times with minimal overshoot.
- Integral performance indices confirm improved steady-state precision.

## Abstract

This study introduces a hybrid stellar oscillation optimizer with differential evolution (hSOO-DE) for high-performance tuning of PID controllers with derivative filtering (PID-F) in nonlinear temperature regulation of continuous stirred tank reactors (CSTRs). The hybrid approach combines the global exploration capability of the stellar oscillation optimizer (SOO) with the local exploitation strength of differential evolution, ensuring a well-balanced search between diversification and intensification during parameter optimization. The proposed algorithm was applied to a benchmark nonlinear CSTR model and comprehensively compared with state-of-the-art metaheuristic optimizers SOO, birds of prey-based optimization (BPBO), covariance matrix adaptation evolution strategy (CMA-ES) and differential evolution (DE) as well as classical tuning techniques including Ziegler-Nichols, Tyreus-Luyben, and Simulink Tuner. The optimization objective jointly minimizes overshoot and integral absolute error to enhance transient and steady-state control quality. Statistical analyses, including boxplot evaluations and Mann-Whitney U-tests, demonstrate that hSOO-DE achieves the lowest mean objective value with minimal variance compared to recent optimizers. Time-domain results confirm superior transient performance, reflected in reduced rise and settling times and minimal overshoot, while integral performance indices verify improved steady-state precision. Validation against conventional PID-F tuning methods further highlights the robustness and reliability of the proposed design. The findings demonstrate that embedding DE within the oscillatory structure of the SOO yields a robust and efficient framework for PID-F controller tuning in nonlinear chemical reactor systems.