H∞-Extended Kalman filter for the aluminium smelting process with boundness analysis of the estimation error matrix

Abstract

Alumina concentration monitoring is crucial for control of the aluminium smelting process to optimise process efficiency and product quality. Due to the harsh environment in the smelting cells, alumina concentration cannot be directly measured online, but rather estimated in real time using Kalman filters. However, accurate smelting cell models are not readily available, and cell events such as anode effects and anode setting can introduce additional uncertain disturbances into the process. In this paper, an $H_{\infty }$-extended Kalman filter (HEKF) is developed for the aluminium smelting process to improve the robustness of alumina concentration estimation with the presence of the above uncertainties. Furthermore, a detailed analysis of the estimation error matrix of the HEKF is developed, which can be used to determine the upper and lower bounds of the error matrix. These bounds provide a theoretical guarantee for the filter’s performance in managing uncertainties in the aluminium smelting process. The effectiveness of the proposed HEKF is demonstrated through experimental studies using an industrial aluminium smelting cell under different cell operations.