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.

I. Introduction

In The pulp and paper industries, the aim of the refining process, as shown in Fig. 1, is to extract fibers with specific physical properties from plant raw materials by employing mechanical or chemical ways, and to provide raw materials for the subsequent papermaking processes [1]. As one of the core equipment during the refining process operation, the refiner is composed of a stator disc, a rotor disc, an electrohydraulic servo device, a main motor, and other components. When the treated wood chips and the dilution water are injected into the refining area directly, employing the electric hydraulic serve system to adjust the disc gap between the stator disc and the rotor disc in real time. When the rotor disc is driven by the motor, the pretreated wood chips in the refiner are ultimately broken down into single fibers under the actions of the mechanical friction, shear, tear, cutting, and other effects. After that, the pulp is to achieve slurry separation by a cyclone separator, and eventually obtaining the required pulp for the papermaking processes [2], [3].