Comparison of Stochastic Steepest Gradient Descent and Extended Kalman Filter as ARMA-FNN Learning Algorithms for Data-Driven System Identification of Batch Distillation Column

A process that is almost always present in the chemical industry is distillation. The plant used in this study is a batch-type distillation column system located in the ITB Honeywell Control Systems Laboratory, capable of separating binary mixtures of ethanol and water. To apply the control scheme effectively, the plant’s dynamics model is required. However, the challenge lies in the fact that the distillation column plant is a highly nonlinear and multivariable system based on its physical laws, with a limited number of sensors available to collect all states information, where only 1 state, which is also an output, can be measured. As a result, this research performs data-driven system identification through black-box modeling based on experimental input-output data using a neural network to generate a linear model. This research employs a discrete-time ARMA-FNN linear model for online identification of the distillation column system, with a focus on comparing learning algorithms for weight updating in the FNN. Specifically, a comparison is made between the stochastic Steepest Gradient Descent (SGD) algorithm and the Extended Kalman Filter (EKF) algorithm. Both algorithms are suitable for comparison because they both operate in an instance-by-instance mode and can be employed for online system identification. Based on the results presented in TABLE II, it can be observed that the best Mean Squared Error (MSE) is achieved by entry number 2, utilizing the EKF algorithm, with a value of 5,5418e-05. Furthermore, as shown in TABLE II, entry number 3 demonstrates that the EKF algorithm can converge the fastest, approximately by the $6^{\mathrm{t}\mathrm{h}}$ instance. This achievement comes with a trade-off, as the resulting MSE slightly deteriorates.