Electrodeposition process boundary concentration control based on motion planning and Zakai filtering: Control simulation for unstirred/stirred electrolytes

摘要

Electrodeposition process control problem is formulated and solved as a boundary control problem based on unknown parameter model set for a diffusion process controlled by a nonlinear reaction on the boundary. First, the concentration changes in the diffusion layer is feed-forward planned due to the set reference concentration on the cathode boundary and then adapted to a real process according to the certainty equivalent principle based on the measured current densities that compensates for the model uncertainties. In industry, the concentration of species is unobserved except the mass flux on the boundary is measured and controlled as the cathodic current. The diffusivity and apparent transfer coefficient of the deposition reaction are considered as unknown parameters; they are evaluated online along with the concentration on the boundary. The Zakai filtering method is applied for parameters estimation. This article demonstrates through simulation a relatively good convergence of the Zakai estimates to the exact parameters and convergence of the boundary concentration to the set references for tracking.