A New PDF Modelling Algorithm and Predictive Controller Design*

Output distribution control is required in many industrial processes mainly for the purpose of improving product qualities. Different from the traditional mean and variance control of stochastic processes, the probability density function (PDF) control provides a comprehensive solution to deal with outputs with general distributions. Various models based on B-splines have been developed to approximate the output PDF required for closed-loop control, among them the rational square-root (RSR) B-spline model can guarantee the nonnegativeness and the integration constraint of a PDF. In this paper, the relationship between the so-called actual weights and pseudo weights of the RSR B-spline PDF model is investigated so as explore a simplified modelling algorithm for the very complex nonlinear PDF modelling problem. Based on the proposed modelling algorithm, a predictive PDF control strategy has been established and applied to an exemplar system of closed-loop molecular weight distribution (MWD) control in a polymerisation process. The merit of predictive control over conventional PDF control is clearly demonstrated through the simulation study.