System Identification of a Non-Uniformly Sampled Multi-Rate System in Aluminium Electrolysis Cells

Standard system identication algorithms are usually designed to generate mathematical models with equidistant sampling instants, that are equal for both input variables and output variables. Unfortunately, real industrial data sets are often disrupted by missing samples, variations of sampling rates in the dierent variables (also known as multi-rate systems), and intermittent measurements. In industries with varying events based maintenance or manual operational measures, intermittent measurements are performed leading to uneven sampling rates. Such is the case with aluminium smelters, where in addition the materials fed into the cell create even more irregularity in sampling. Both measurements and feeding are mostly manually controlled. A simplied simulation of the metal level in an aluminium electrolysis cell is performed based on mass balance considerations. System identication methods based on Prediction Error Methods (PEM) such as Ordinary Least Squares (OLS), and the sub-space method combined Deterministic and Stochastic system identication and Realization (DSR), and its variants are applied to the model of a single electrolysis cell as found in the aluminium smelters. Aliasing phenomena due to large sampling intervals can be crucial in avoiding unsuitable models, but with knowledge about the system dynamics, it is easier to optimize the sampling performance, and hence achieve successful models. The results based on the simulation studies of molten aluminium height in the cells using the various algorithms give results which tally well with the synthetic data sets used. System identication on a smaller data set from a real plant is also implemented in this work. Finally, some concrete suggestions are made for using these models in the smelters.