Predictive two-loop fractional-order control law for industry-oriented integrating type chemical processes and reactors

Integrating processes with time delays is commonly found in many industrial systems, especially in chemical, thermal, and fluid-level applications. These processes pose significant control challenges due to their inherent tendency toward instability and their delayed response to input changes. For such processes, 1-degree-of-freedom (1-DOF) controllers have limitations: either they are capable of providing good set-point tracking or disturbance rejection, but not both. This paper presents a Smith-predictor-based effective two-loop fractional-order control law for such processes. Here, a fractional-order PD controller is employed in the inner loop to provide stability and robustness, while an outer loop controller is designed to control the entire inner loop, thereby achieving a desirable closed-loop response. A set-point filter is also employed in the framework to minimize overshoot in set-point tracking, which may be caused by a sudden change in the set point. The controllers are tuned using stability margin and maximum sensitivity (Ms) criteria, and analytical solutions for the same are derived. The proposed control law is evaluated through theoretical analysis and simulations on various chemical process models, including a heat exchanger, a distillation column, a continuous stirred-tank reactor (CSTR), and a boiler steam drum. In addition, robust stability analysis confirms stable performance even under parametric uncertainties. Finally, a performance comparison is presented based on different error indices.