A Dual-Loop Modified Active Disturbance Rejection Control Scheme for a High-Purity Distillation Column

High-purity distillation columns typically give rise to multi-variable, strongly coupled nonlinear systems with substantial time delay and significant inertia. The control performance of high-purity distillation columns crucially influences the purity of the final product. Taking into account the process of a high-purity distillation column, this article puts forward a dual-loop modified active disturbance rejection control (MADRC) scheme to improve the control of product purity. During the stable operation of the distillation process, the structures of two control loops are, respectively, approximated by two linear transfer function models via open-loop experiments. Subsequently, the compensation part of the MADRC scheme is designed, respectively, for each approximate model. Furthermore, this paper employs singular perturbation theory to prove the stability of MADRC. The performance of the dual-loop MADRC scheme (MADRC) is compared with that of a proportional–integral–derivative (PID) control scheme, a cascade PID control scheme (CPID), and a regular ADRC scheme (ADRC). The simulations demonstrate that the dual-loop MADRC scheme is capable of efficiently tracking the reference value and exhibits optimal disturbance rejection capabilities. Additionally, the superiority of the dual-loop MADRC scheme is validated through Monte Carlo trials.