Modelowanie koncentracji części stałych w nadawie do flotacji węgla kamiennego

In Polish control and monitoring solutions of coal flotation process usually only flow rate and solids concentration (from the feed parameters) are measured on-line. From the coal flotation control’s point of view these values should be regarded as disturbances since they are subject to random disturbances of the time-varying feed. Random variations of the solids concentration in the feed can significantly affect both quantitative and qualitative parameters of coal flotation products. From this point of view a description of measuring solids concentration in the feed in the form of a mathematical model comes into particular importance. This article presents the results of the model identification of feed solids concentration sent to the coal flotation process as disturbance. Measurement data that are necessary to determine the empirical model of solids concentration in the feed are obtained from the recording carried out in the three successive periods of the industrial plant operation of one of the polish mines. Solids concentration measurement has been performed by using a radiometric densitometer. The first series of measurement data was used to determine the model of solids concentration in the feed and the other two were used to validate the calculated model. Time series of solids concentration in the feed were described by the ARMA model of the form (1) and the model parameter estimation was made by a two-stage least squares method. The results of identification as well as the performed verification of the calculated model determined the validity of an adoption of ARMA model of the third order with parameters (9). Parameters of this ARMA model were determined on the basis of model error time-series described by a fourth order model (Table 1). The calculated model of feed solids concentration for the coal flotation as disturbance was used to develop a predictive model that allows the one-step prediction of solids concentration values in the feed with the prediction horizon equal to the sampling period. It was found that one-step prediction based on the determined predictor equation (13) gives the results that coincide with the recorded values of the solids concentration in the feed.