Conference article

Industrially produced fertilizers are of key importance to produce enough food for a growing global population. On-going work on granulation in fertilizer production utilizes a population balance for finding the particle size distribution of the product. The model is intended for control design in order to dampen or remove production oscillation. This paper studies efficiency of model implementation in addition to the possibility to automate the computation of a linear approximation of the model for control synthesis. In the implementation, the current tailor-made MATLAB solver for the model was cloned in computer language Julia. The implementations in both languages were rewritten in a form that allows for use of the standard differential equation solvers of the respective languages. Results indicate that by changing from the tailor-made solvers to using the built-insolvers leads to a speed increase in the order of 6 times. Furthermore, results indicate that the Julia implementations are ca. 5 times faster than the MATLAB implementations. Overall, the fastest Julia implementation was 36 times faster than the current MATLAB implementation. The MATLAB execution can be speed up by using MATLAB Coder to convert the code to efficient C-code which is then used to generate a DLL. DLLs can be executed virtually without overhead from Julia. By measuring the execution time for the C-code/DLL vs. a similar implementation in pure Julia, the pure Julia code is ca. 12% faster than the compiled C code. The automatic linearization of the model is shown to be relatively straightforward. The linear approximation is very good for an input perturbation of 10%, and relatively good for an input perturbation of 50%. This indicates that it may be possible to use a linear model approximation for control design.

linear regression, nonlinear regression, thermal model, machine learning, surrogate model, hybrid model