Abstract: The combined orthogonal polynomial neural network has been used to model the molecular weight distribution(MWD)of polymers,therefore MWD is decomposed into a function of its moments.In this paper,tracking of a desired MWD is realized through choosing moment vector as directive control goal.In order to obtain the control solution for the non-affine nonlinear multivariate system,a model architecture utilizing an improved nonlinear autoregressive orthogonal polynomial neural network is proposed,and the linear relationship between the model outputs and current control strategy U(k)is realized.Taking the higher-dimensional controlled variable into consideration,the paper shows the equivalent of independent variables in moment vector and parameters of distribution function,thus the criterion of moment vector dimensionality reduction are proposed to transforming the higher-dimensional output control problem into low-dimensional.Based on the improved neural network model,the output feedback control method is used for the moment control of MWD,and then the tracking of desired MWD is realized.The control method is tested on styrene polymerization reacted in CSTR,and simulation results proved the effectiveness of the method.This paper proposed a new solution for modeling and control of nonlinear multivariate system.

Key words: molecular weight distribution of polymer, combined orthogonal polynomial neural networks, moments, output feedback method, nonlinear multivariate system

摘要： 利用正交多项式组合神经网络对聚合反应分子量分布(MWD)进行建模,MWD被解构为若干矩值组成的矩向量函数,由此二元MWD控制问题可被转换为一元分布矩控制问题。以矩向量为直接被控对象,通过对矩的控制实现MWD的跟踪。为便于求解这类非仿射非线性多变量系统的控制策略,提出了改进型非线性自回归正交多项式网络结构,建立模型输出与U(k)之间的线性映射关系;针对高维被控矩向量,证明了矩向量中独立变量与分布函数参变量间的数量对等关系,给出了矩向量降维准则,将高维输出控制转化为低维问题。基于改进的神经网络模型,利用输出反馈方法对MWD矩向量进行控制,实现了对MWD的形状跟踪,仿真实验证明了方法的有效性。所提出的方法为非线性多变量系统的建模控制问题提供了新思路。

关键词: 聚合物分子量分布, 正交多项式组合神经网络, 矩, 输出反馈, 非线性多变量系统