Research On The Application Of Grey System Theory Into The Batch Dyeing Process

China is a large producer of dyeing goods, and Batch dyeing is the principal means of dyeing production in China. Modeling of the dye-uptake process and controlling of the dye-bath temperature are the key factors to raise the level of batch dyeing automation. However, the mechanism of batch dyeing is very complex, and affected by many factors, so the traditional modeling and temperature control methods have the disadvantages such as the complexity of the modeling process, the poor interoperability of the model and the low precision of temperature control, etc. In this paper the grey system theory, which has features with little data and high accuracy, is applied into the batch dyeing for establishing the dye-uptake rate model and the dye-bath temperature prediction control system. Based on these, the dyeing results can be predicted and the control precision of the temperature can be improved so as to be helpful to improve the quality of dye products and the right-first-time rate of dyeing. As a result, the purpose of saving energy and improving benefit can be achieved.As for the modeling, two dye-uptake rate models are established for the disperse dyestuff and the direct dyestuff respectively. Firstly, the grey Verhulst model is used to describe the effects of temperature on the polyester fabric. It can be integrated with the Nernst isotherm model and the Arrhenius equation to establish the dye-uptake rate model of the disperse dyestuff of blue RSE to dye the polyester fabric based on the reaction rate equation. It is a single-factor (temperature) model. Here, the using of the grey Verhulst model is the most important for the precision of the dye-uptake rate model. Next, the two modeling methods based on the grey model GM(1,1) and the GM(1,1) model combined with the GM(0,N) model are used to establish the model of dyeing equilibrium percentage for the direct fast red F3B dyestuff to dye the cotton fabric. This is the most important step to establish the dye-uptake rate model. Then, with the dyeing equilibrium percentage model, the dye-uptake rate model is established based on the adsorption rate equation, which includes three factors (temperature, electrolyte, and pH). These two dye-uptake rate models both have enough accuracy to predicate the results of dyeing. Moreover, as the use of the grey system theory, these models have the following advantages: its parameters are easily to determine, and its calculation amount is small, and it can also be used for the same type of dyestuff only with changing the parameters'value.As for temperature control, the GNNM(1,1) model, which combines the grey model GM(1,1) and the BP neural network, is adopted to predict the temperature value of dye-bath. The strategies of multi-step prediction, rolling optimization and weighted feedback are used to build the PID control system based on GNNM(1,1) prediction. The simulation results of this sytem with three kinds of input signals are significantly better than the unit feedback PID control system.