A model-based supersaturation estimator (inferential or soft-sensor) for industrial sugar crystallization process

Abstract

The degree of supersaturation of the mother liquor is a key factor in improving the monitoring and control of the final stage of industrial sugar crystallization. However, the difficulty of obtaining online supersaturation measurements is one of the challenges associated with monitoring and controlling sugar crystallization. There is no direct method or single instrument for measuring supersaturation. It can only be calculated or inferred from other measurements. In the literature, estimators of mother liquor supersaturation are reported, typically focused on the first stage of crystallization. The SeedMaster series transmitters are the sole industrial instruments that provide online supersaturation information by calculating it from external measurements. The purpose of this study is to design a first-principles model-based soft-sensor as a practical alternative to obtain real-time information about supersaturation in the last stage of sugar crystallization. The proposed estimator relies on two models: a supersaturation model and a second simplified model of the last stage of crystallization. The parameters of both models were estimated based on real industrial data. The estimation is performed in three steps: 1. An Unscented Kalman Filter estimates the states of the crystallization model and their variance. 2. The estimated supersaturation value is obtained by substituting the estimated states into the supersaturation model. 3. The estimator's bias, and variance are calculated to establish error bounds. The main characteristics of the obtained estimator are: practical unbiasedness, nearly minimum variance and robustness. The performance and behavior of the supersaturation estimator are contrasted using real data from an industrial crystallization plant (Urbano Noris factory, Holguín, Cuba). Regardless of its initial conditions, the estimator converges to the three standard deviation error band in less than three minutes. The exact time may vary depending on how much the estimator's initial conditions deviate from those of the process. After this time (Reach Time), the estimates remain within the calculated error limits of three standard deviations. The maximum absolute errors obtained were less than 0.019 units, corresponding to a maximum relative error of less than 1.5%. These values are favorable since they are well below critical values (0.125 units of absolute error). Moreover, the error bands are much smaller than the operating zone width (approximately 0.25 units), which is a necessary condition for any supersaturation estimator to be useful. Finally, it should be noted that the errors have been reduced compared to the values reported in previous research focused on the sugar industry using other techniques.