Disturbance Rejection Technique on an Industrial Vacuum Furnace: The Model-Free iPID-DOB Approach

Slow non-minimum-phase (NMP) processes present significant control challenges due to inverse response behaviour, sluggish dynamics, and sensitivity to disturbances and model uncertainty. This study investigates the performance of two model-independent control strategies, namely a disturbance observer-based intelligent proportional–integral controller (iPID-DOB) and a Particle Swarm Optimization-tuned Active Disturbance Rejection Controller (ADRC-PSO), for the regulation of a slow NMP process identified from experimental open-loop data of an industrial vacuum furnace. The iPID-DOB integrates a conventional PI structure with an online disturbance observer to estimate and compensate disturbance-related effects, whereas the ADRC employs an extended state observer (ESO) optimized using Particle Swarm Optimization to estimate system states and lumped uncertainties in real time. Both controllers were evaluated under identical conditions involving multiple reference changes, actuator constraints, and repeated disturbance scenarios. Performance was assessed using steady-state error, root-mean-square error (RMSE), rise time, settling time, overshoot, integral error indices (ISE, IAE, and ITAE), control effort, disturbance-rejection capability, and recovery time. The results demonstrate that both controllers achieved stable closed-loop operation and effective disturbance attenuation across the investigated operating range. However, the iPID-DOB consistently outperformed the ADRC-PSO in all quantitative performance metrics, exhibiting faster convergence, lower tracking error, improved disturbance rejection, and reduced recovery times. Conversely, the ADRC-PSO generated a significantly smoother and more stable control action, primarily due to the optimized extended state observer, which provided accurate estimation of process states and lumped disturbances while suppressing excessive control activity. The findings indicate that the iPID-DOB offers superior tracking and robustness performance for the considered slow NMP process, whereas the ADRC-PSO provides enhanced control smoothness and operational stability. These results highlight the trade-off between aggressive disturbance-compensation strategies and observer-driven robust control, providing practical guidance for selecting suitable model-independent control architectures for challenging industrial processes.