Nonlinear active disturbance rejection control for unstable processes with time delay: A case study of a continuous stirred tank reactor

• NL-ADRC is applied to unstable time-delay processes with minimal model dependence • Lyapunov analysis establishes boundedness of NL-ADRC for unstable nonlinear systems • Robust performance is validated on multiple benchmark unstable pro-cesses • A nonlinear CSTR case study demonstrates effective disturbance rejec-tion • IMC-based frequency-domain interpretation provides robustness insight Unstable time-delay processes present considerable difficulties in controller design because of inherent nonlinear behavior, system uncertainties, and strong sensitivity to external perturbations. In this study, a nonlinear active disturbance rejection control (NL-ADRC) scheme is developed for stabilizing such unstable systems, with special focus on a continuous stirred tank reactor (CSTR) process. The proposed approach incorporates an extended state observer that reconstructs aggregated uncertainties and disturbances in real time, while a nonlinear feedback mechanism compensates their influence without relying on an accurate mathematical model of the plant. The controller performance is evaluated on several benchmark unstable processes with time delay, followed by a detailed nonlinear CSTR case study. To further interpret robustness characteristics, an internal model control (IMC)–based frequency-domain analysis is carried out using the linearized CSTR model, providing insight into the closed-loop system’s gain and phase margins. A Lyapunov-based analysis establishes uniform ultimate boundedness of the closed-loop dynamics. Simulation results demonstrate improved tracking performance, faster disturbance rejection, and enhanced robustness compared with existing control strategies. The results confirm the suitability of NL-ADRC for nonlinear and unstable industrial processes.