Gray-box modeling and control of polymer molecular weight distribution using orthogonal polynomial neural networks

A method of modeling and control on polymer molecular weight distribution (MWD) is presented in this paper. An orthogonal polynomial feedforward neural network (OPFNN) and a recurrent neural network (RNN) are combined to model the shape of MWD. In this combined neural networks, the weights of OPFNN are equivalent to moments of MWD through a linear transformation, when the polynomial used as the basis function of OPFNN satisfies some requirements. So the weights are given practical feature, and terms the neural network model a gray-box model. Then the requirements of polynomial are deduced. After modeling, an optimal control scheme is discussed on tracking the desired MWD during the polymerization process. The modeling error is added into the performance function to improve the control effect. The modeling and control method is tested on styrene polymerization reacted in CSTR, and simulation results proved the effectiveness of the method.