Data-Driven Multiobjective Predictive Optimal Control of Refining Process with Non-Gaussian Stochastic Distribution Dynamics

The fiber length and the Canadian standard freeness (CSF) are two key indices in measuring pulp quality of the refining process with non-Gaussian stochastic distribution dynamics. Among them, it is defective to use the conventional 1-D average fiber length (AFL) as a pulp quality index because the AFL is insufficient to describe the 2-D probability density function (pdf) shaping of fiber length distribution (FLD) with non-Gaussian types. In this article, a data-driven multiobjective predictive optimal control method is proposed to control the 2-D pdf shaping of FLD and the 1-D CSF, simultaneously. First, a radial basis function neural network (RBF-NN) based stochastic distribution model is developed to approximate the 2-D pdf shaping of FLD, and the parameters of RBF basis functions are updated by an iterative learning rule. Then, taking the developed pulp quality models, including the 2-D pdf model of FLD and the model of 1-D CSF as two predictors, a multiobjective predictive controller is designed by solving the nonlinear programming problems with constraints. Then, the stability of the resulted closed-loop system is also analyzed. Ultimately, the industrial experiments demonstrate the effectiveness of the proposed method.