  We present a formulation for both implicit and explicit dual model predictive
control for a steel recycling process. The process consists in the production
of new steel by choosing a combination of several different steel scraps with
unknown pollutant content. The pollutant content can only be measured after a
scrap combination is molten, allowing for inference on the pollutants in the
different scrap heaps. The production cost should be minimized while ensuring
high quality of the product through constraining the maximum amount of
pollutant. The dual control formulation allows to achieve the optimal
explore-exploit trade-off between uncertainty reduction and cost minimization
for the examined problem. Specifically, the dual effect is obtained by
considering the dependence of the future pollutant uncertainties on the scrap
selection in the predictions. The implicit formulation promotes uncertainty
reduction indirectly via the impact of active constraints on the objective,
while the explicit formulation adds a heuristic cost on uncertainty to
encourage active exploration. We compare the formulations by numerical
simulations of a simplified but representative industrial steel recycling
process. The results demonstrate the superiority of the two dual formulations
with respect to a robustified but non-dual formulation.
