A stochastic model for electrodeposition process with applications in filtering and boundary control

摘要

Electrodeposition is a complex partially observed mass-transfer process driven by several surface reactions without exact model. In this article, the process uncertainties are described by a finite number of Wiener processes in a stochastic model applied in the filtering and control problems. These problems are 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 on an interval with the Dirichlet data on one end (bulk solution) and Neumann data on the other end (cathode surface). The concentration of oxidising species in the domain interior is unattainable for observations but the flux on the boundary (electric current) can be measured with a limited accuracy (sensor error). The total flux for the main and side reactions is controlled by the current density on the cathode surface. The disturbing effect of the side reactions is modelled 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 partial differential equation in dependence on the covariance kernel. A relatively good quality of estimation and control is demonstrated in the process of simulation in the realistic conditions for a copper deposition process.