Modelling and state observation of Simulated Moving Bed processes based on an explicit functional wave form description

This paper proposes a method for the on-line determination of the concentration profiles in a Simulated Moving Bed (SMB) process in terms of discrete measurement values. A direct solution of this state observation problem is very complex because the physical SMB model exhibits the infinite state dimension of distributed-parameter systems with switching initial conditions and cyclic boundary conditions. This paper proposes a solution that is based on a parametric model describing the wave fronts of the concentration profiles of SMB processes. The parametric model is derived for SMB processes which are a good approximation of the TMB. The model parameters determine the form, the movement and the position of the wave fronts. If the parameters are interpreted as a model state, a three-dimensional linear state-space model describing the properties of the profiles is obtained whose state can be determined by a Luenberger observer. An application study shows the simplicity of the observation scheme and the correctness of the results under practical circumstances like the existence of model uncertainties.