Nonlinear Multivariable Control of a Dividing Wall Column Using a Different-Factor Full-Form Model-Free Adaptive Controller

Abstract

A dividing wall column (DWC), characterized by multivariable control, strong nonlinearity, and highly coupled systems, shows effective distillation capacity with a significant reduction in energy consumption and capital cost. Although multivariable control strategies for DWCs have attracted certain attention from both academia and industry, relatively little work has focused on data-driven multivariable controllers for such a complex system that is not easy to model. In this work, a novel different-factor full-form model-free adaptive controller (DF-FFMFAC) is first proposed for DWCs aiming to solve the problem of simultaneous control of the liquid level, column pressure, and temperature channels with quite different characteristics between them, which may be a challenging task for the prototype FFMFAC. Taking such complex dynamics into account, a parameter selection technique for the DF-FFMFAC based on neural networks is also developed, where gradient descent for the neural network is improved by the full-form dynamic linearization technique utilized in the DF-FFMFAC. Furthermore, the stability of the parameter tuning process is guaranteed by Lyapunov theory. The present work makes a noteworthy contribution to the multivariable control of DWCs in a purely online data-driven way without any offline training procedure and mathematical information. In terms of the separation of an ethanol–n-propanol–n-butanol DWC, the controller is cosimulated in MATLAB/SIMULINK and Aspen Plus Dynamics and tested against a series of feed flow rate and feed composition disturbances. As a result, the proposed method achieves encouraging control performance with smaller oscillations and faster responses compared with model predictive control and proportional–integral–derivative controllers, proving to be a promising data-driven method for the multivariable control of DWCs. Finally, the efficacy of the proposed scheme for the practical control of DWCs in the presence of measurement noise has also been demonstrated by adding white noise to the simulation.