Nonlinear parameters estimation via Zakai filtering in deposition process control

Abstract

A stochastic evolutionary process inspired by electrodeposition is considered in single dimension. The process is fixed on one boundary and is observed-controlled on other boundary where the process in addition is influenced by the unmodelled side reactions; their effect on the boundary is considered as a random noise that disturbs the control and measurements. The process is given by a finite diffusion process model which main parameters are unknown: the diffusivity of species and thickness of the diffusion layer are unknown, also the throwing power of electrolyte is unknown and, in addition, the systematic effect of the side reactions is unknown. Even so the paper demonstrates in certain additional condition that the deposition process can be well controlled using feed-forward boundary controls adapted with the estimated parameters in the course of Zakai filtering. The consistency of estimates is exposed in simulation as well as the stabilising property of the adaptive control.