Research On Molecular Weight Distribution Modeling And Control Based Moments

For decades, the increasing demand for production of polymers with prespecified properties and compressed cost has placed great emphasis on the development of accurate modeling and robust control of polymerization. A polymer product is composed of macromolecules with different molecular, thus the micromolecular architectures strongly influence the properties and applications of the polymer. Unfortunately, it is a more complex issue than conventional chemical systems due to the highly nonlinear dynamics, poor reliability, as well as the presence of long measurement delays. However, there are still many published papers focused on polymerization. Our primary contents of this research are the general modeling method and control strategy of MWD based on moments. Using intelligent neural network model, the partial online control of MWD is realized. The main achievements are obtained as follows:Firstly, a combined gray box neural network model is developed to track the shape of MWD. The linear relationship between weight vector of network and moment vector of MWD is testified using orthogonal polynomial meeting specific constraints as the basis function of neural networks. The equivalence between parameters of network and modeling object is realized, based that a new solution for prediction and control of MWD can be provided.A combined neural network structure comprises of two networks is developed for the binary distribution object. One is orthogonal polynomial feed forward neural network (OPNN) used for determining the dynamic relationship between different chain lengths of polymer molecules and MWD at every sample time. The other is nonlinear autoregressive with external input neural network (NARXNN), which is used to get the model of input variables and MWD in the reaction process. To set the weights of OPNN, a weight direct determination method is advanced. The derived result shows that the weights of OPNN have a certain linear relationship with moments of MWD using specific orthogonal polynomial meeting certain constraint as basis function. Thus, compared with values gained from data fitting, the weights of OPNN become several statistic parameters of MWD. Moreover, the orthogonal polynomial requirement is deduced. Two kinds of orthogonal polynomials (discrete orthogonal polynomial and Legendre polynomial), meeting requirement, are used as the basis function to model MWD. Then two conversion matrixes between weights of OPNN and moments of MWD are deduced. The weights of network have a clear physical meaning, thus this neural network model has a gray-box property. The number of hidden layer nodes in OPNN has a relationship with the order of moments used in neural network, so it has a physical meaning too. Consequently, there is a physical basis on the determination of structure of OPNN. Simulation experiments can testify the feasibility of the modeling of MWD based on OPNN, and the modeling abilities of two kinds of basis function neural networks are compared too.Secondly, a kind of SNARX-OPNN with affine nonlinear expression is advanced for dynamic modeling of MWD. The SNARX-OPNN has a more rapid learning speed, global approximation and is convenient for control strategy design.For the dynamic tracking of MWD, two changes on NARXNN are improved. A kind of single hidden layer orthogonal polynomial neural network is advanced as the feed forward network of NARXNN firstly. Instead of general sigmoid function, the orthogonal polynomial series are used as the basis function of feed forward network of NARXNN, and the constant mapping of input layer is realized. Hence, the learning burden is decreased which can improve the learning speed of network. Next, taking the linear mapping ability of lower order polynomial into accounts, the nonlinear links between input variables and output are cut off for the convenience of control. Then an affine nonlinear mathematical expression is gotten without changing the whole structure of networks which is beneficial for control strategy design. The gained neural network structure is called SNARX-OPNN.Thirdly, a solution for the shape control of MWD based on limited moments is proposed, at the same time, the dimensionality reduction criteria of controlled moments is deduced.The tracking question of shape of MWD is proved that can be constrained into the control of several moments which is the weights of neural network model. Taking the higher-dimensional moment vector into consideration, the thesis proves the equivalent of independent variables in moment vector and parameters of distribution function, thus the criterion of moment vector dimensionality reduction is proposed to transforming the higher-dimensional output control problem into low-dimensional. Thus the theoretical basis is improved for the practice on polymer production and the fine control of MWD can be realized.Fourthly, focusing on the polymerization system using moments as the direct control objects, H∞control algorithm is designed for the tracking of MWD. The robustness of system is improved.Based on the gray box model, the optimal control method and output feedback control method are used in which moments as direct object. The control effects of these two methods are contrasted. Due to the presence of uncertain disturbance and model mismatch faced by the closed loop system based on the neural network model, an H∞algorithm is designed to get a robust control system. The scalar differential equations gained from SNARX-OPNN is converted into discrete state equation and the constrained least squares algorithm is used for the requirement of controller design. The optimal control sequence is deduced through linear inequality method. Simulation experiment approves that the asymptotic stability of control system is guaranteed with the existence of uncertain disturbance, and the tracking of given distribution can be realized too.The modeling and control method are tested on styrene polymerization reacted in CSTR, and simulation results proved the effectiveness and advantage of the method. A new research field for modeling and control of MWD is provided, through which new solution can be offered.