Predictive PDF control in shaping of molecular weight distribution based on a new modeling algorithm

Abstract

The aims of this work are to develop an efficient modeling method for establishing dynamic output probability density function (PDF) models using measurement data and to investigate predictive control strategies for controlling the full shape of output PDF rather than the key moments. Using the rational square-root (RSR) B-spline approximation, a new modeling algorithm is proposed in which the actual weights are used instead of the pseudo weights in the weights dynamic model. This replacement can reduce computational load effectively in data-based modeling of a high-dimensional output PDF model. The use of the actual weights in modeling and control has been verified by stability analysis. A predictive PDF model is then constructed, based on which predictive control algorithms are established with the purpose to drive the output PDF towards the desired target PDF over the control process. An analytical solution is obtained for the non-constrained predictive PDF control. For the constrained predictive control, the optimal solution is achieved via solving a constrained nonlinear optimization problem. The integrated method of data-based modeling and predictive PDF control is applied to closed-loop control of molecular weight distribution (MWD) in an exemplar styrene polymerization process, through which the modeling efficiency and the merits of predictive control over standard PDF control are demonstrated and discussed.