Optimal control problems arising in the zinc sulphate electrolyte purification process

Before zinc electrolysis, zinc powder is added to the zinc sulphate electrolyte solution to facilitate the removal of harmful metallic ions. This purification process can be modeled by a time delay differential equation. Since some of the parameters in this model are unknown, zinc powder is normally added excessively. We use an optimization technique to estimate the unknown parameters from experimental data. Then, we formulate an optimal control problem to minimize the amount of zinc powder added. We solve this optimal control problem numerically by using the control parametrization method. The results indicate that the amount of zinc powder added can be decreased, on average, by approximately 7%.