Data-Driven Linear Quadratic Gaussian using LightGBM Algorithm for Batch Distillation Column

The batch distillation column plant inherently is highly nonlinear system due to its adherence to physical principles, with only a single sensor designated for measuring the output. Based on these conditions, a traditional control approach that can be employed is Linear Quadratic Gaussian (LQG). However, conventional LQG methods have certain constraints. To address these limitations, this research presents a novel data-driven LQG approach using the Light Gradient-Boosting Machine (LightGBM) algorithm for batch distillation column systems. The LightGBM algorithm is used to replace the roles of both the Linear Quadratic Regulator (LQR) controller and Kalman Filter. The dataset sample sizes for training range from 1,000 to 1,000,000. From the simulation, For each LightGBM regressor model produced, one for LQR controller gain and another for Kalman gain, performance metrics such as R-squared, Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) are utilized to assess the training process. The results show that larger sample sizes lead to better LightGBM regressor models. The outcomes suggest that both LightGBM models, created to substitute for the functions of LQR controller gain and Kalman gain, demonstrate the ability to precisely forecast output values using the provided input variables.