The grey system theory, with the characteristics of fewer modeling data and higher accuracy, was employed to model the batch dyeing process for the purpose of accurate online control. The GM（1, 1） and GM （0, N） models of the grey system theory were discussed for their feasibilities of modding for batch dyeing process. The combination of direct dyestuff Fast Red F3B on cotton was chosen as a representative of the common dyeing method for describing the modeling process. Firstly, the GM（ 1, 1 ） model and the GM（1, 1） combined with GM（0, N） model were employed to model the equilibrium percentage of dyeing uptake rate. Secondly, an integrated dyeing uptake rate model with three factors （ temperature, salt concentration, and pH） was established based on the adsorption rate equation. Experimental results show that this model has higher accuracy and beetler generalization ability, which can predict the results of batch dyeing process. Due to the application of grey system theory, the model has a lot of advantages, such as being easy to determine the parameter value and small amount of calculation. So it can also be suitable for the same type of combination of dyestuff-fahric by changing the parameters value only.
The batch dyeing process is a typical nonlinear process with time-delay,where precise controlling of temperature plays a vital role on the dyeing quality.Because the accuracy and robustness of the commonly used proportion integration differentiation(PID) algorithm had been limited,a novel method was developed to precisely control the heating and cooling stages for batch dyeing process based on predictive sliding mode control(SMC) algorithm.Firstly,a special predictive sliding mode model was constructed according to the principle of generalized predictive control(GPC);secondly,an appropriate reference trajectory for SMC was designed based on the improved approaching law;finally,the predictive sliding mode model and the Diophantine equation were used to predict the output and then the optimized control law was derived using the generalized predictive law.This method combined GPC and the SMC with their respective advantages,so it could be applied to time-delay process,making the control system more robust.Simulation experiments show that this algorithm can well track the temperature variation for the batch dyeing process.
