Design of Fractional-Order Sliding Mode Controller for an Unstable Three-State Model Jacketed CSTR

Abstract

Control of a jacketed continuous stirred tank reactor (CSTR) is challenging due to nonlinear dynamics, complexity, and rapid reactor dynamics under imperfect mixing in the jacket. Current controller designs mainly focus on the two-state model, neglecting the potential of three-state models in scenarios with nonperfect mixing and fast reactor dynamics. This study proposes a sliding mode controller (SMC) design scheme based on the transfer function model using a newly developed jellyfish optimisation algorithm. Further, a fractional-order sliding mode control (FO-SMC) strategy is proposed, which integrates modifications to the SMC to mitigate chattering, enhance control robustness, and provide better disturbance rejection capability. PID and fractional-order PID (FOPID) controllers were also designed for comparative analysis. The simulation results demonstrated that FO-SMC outperformed other designed controllers, shown by a 37.14% reduction in settling time, 10.69% reduction in integral absolute error (IAE), and 19.06% reduction in time-weighted absolute error (ITAE) compared to SMC and various other improved performance indicators. Parameter variation and noise analysis highlighted the ability of the controller to maintain stability and performance under dynamic conditions.