Electrodeposition Process Filtering and Boundary Control

Electrodeposition process filtering and boundary control problem is solved in this paper based on a stochastic model that depends on a finite number of Wiener processes. The problem is solved as a boundary observation-control problem based on a finite diffusion model with uncertainties in the domain interior and on the boundaries. A mixed boundary problem is considered in an interval with the Dirichlet data on one end (bulk solution) and Neumann data on the other end (cathode surface). Since the concentration of oxidizing species is unattainable for observations the flux on the boundary is measured with a sensor noise. The total flux of the main reaction and side reactions is controlled by the electric current measurements on the cathode while the disturbing effect of the side reactions is considered as a noise. The concentration of species is stabilised at the desired level near to the cathode surface with a relatively simple feedback control. The concentration on the boundary and in the domain is estimated as a conditionally Gaussian process in the course of filtering. The estimated conditional mean of concentration is solved from a stochastic PDE in dependence on the covariance kernel. A relatively good quality of estimation and control is demonstrated in process of simulation in the realistic conditions for a copper deposition process.