Real-Time Moving Horizon State and Parameter Estimation for SMB Processes

Advances in numerical algorithms have rendered the application of advanced process control schemes feasible for complex chemical processes that are described by high-order first-principles models. Applying real-time iteration schemes reduces the CPU requirement such that rigorous models can be applied that enable a precise forecast of the system behaviour. In this paper, a moving horizon state and parameter estimation scheme for chromatographic simulated moving bed SMB processes is presented. The simultaneous state and parameter estimation is based on a high-order nonlinear SMB model which incorporates rigorous models of the chromatographic columns and the discrete shifting of the inlet and outlet ports. The estimation is performed using sparse measurement information: the concentrations of the components are only measured at the two outlet ports (which are periodically switched) and at one fixed location between two columns. The goal is to reconstruct the full state of the system, i.e. the concentration profiles along all columns, and to identify model parameters reliably. The state estimation scheme assumes a deterministic model within the prediction horizon, state noise is only present in the state and in the parameters prior to and at the beginning of the horizon. The scheme can be applied online. The advantage of this estimation scheme is that it is applicable to all process scenarios encountered during the real operation of an SMB plant, e. g. start up, transition periods, varying flows and switching times, since no model simplification nor a state reduction scheme are applied. Numerical simulations (start up of the SMP process) of a validated model for a separation problem with nonlinear isotherms of the Langmuir type demonstrate the efficiency of the algorithm.