Multi-loop active disturbance rejection control for shell-and-tube heat exchanger: Decoupled design and optimization

• A decoupled multi-channel ADRC framework. • A Shell-and-tube heat exchanger thermal control. • A distributed-parameter model linearized for multi-channel controller design. • A bandwidth-extended GA tuning method for interpretable optimization. • Robustness and scalability up to quadruple channels. Shell-and-tube heat exchanger plays a fundamental role in the energy industry, whose temperature control faces persistent challenges due to inherent nonlinear dynamics, multi-variable coupling, and external disturbances. To this end, this study proposes a multi-loop Active Disturbance Rejection Control (ADRC) framework. A distributed-parameter model based on partial differential equations (PDEs) is constructed to capture spatially-varying thermal–hydraulic dynamics. The PDEs model is discretized and locally linearized to reflect the dynamics and interactions. Based on this model, a decoupled multi-loop ADRC system is designed, with independent Extended State Observers (ESOs) to estimate and compensate for total disturbances. A tuning approach extended from the conventional bandwidth method is proposed to guide initial controller design. Subsequently, a multi-objective Genetic Algorithm (GA) is employed to optimize controller parameters through Pareto-optimal trade-offs between settling time and robustness. The simulation results demonstrate three key advances: (1) The linearization-discretization-based tuning method enables accurate control despite nonlinear effects; (2) The ESO structure achieves fast convergence under simultaneous flow and temperature perturbations; (3) The GA-optimized parameters maintain robustness against ± 25 % model parameter variations. These results provide a complete guidance from physics-based modeling to computationally efficient control for precision thermal control.