A Stochastic Model for Electrodeposition Process with Simple Boundary Control

Electrodeposition is a complex partially observed mass-transfer process driven by surface reactions without exact model. In this paper these uncertainties are described by a finite number of Wiener processes in a stochastic model that represents a finite diffusion layer. The model is solved as a mixed boundary problem with the Dirichlet data on one end (bulk solution) and Neumann data on the other end (cathode surface). The concentration of relevant species in the domain interior is controlled by the flux on the boundary (electric current) that can be measured with a limited accuracy. Although the concentration of species on the boundary cannot be observed and must be estimated but for shortening of the paper assumed here to be attainable for observations with certain accuracy (sensor error). The total flux of the main reaction and side reaction is controlled by the current density on the cathode surface. The disturbing effect of the side reactions is modelled as a noise. A relatively effective control is demonstrated in process of simulation with realistic uncertainties for a copper deposition process, but the direct controls use here without filtering create a large variation of mass-flux on the boundary.