State Observer Design for Monitoring the Degree of Polymerization in a Series of Melt Polycondensation Reactors

A nonlinear reduced-order state observer is applied to estimate the degree of polymerization in a series of polycondensation reactors. The finishing stage of polyethylene terephthalate synthesis is considered in this work. This process has a special structure of lower block triangular form, which is properly utilized to facilitate the calculation of the state-dependent gain in the observer design. There are two possible on-line measurements in each reactor. One is continuous, and the other is slow-sampled with dead time. For the slow-sampled titration measurement, inter-sample behavior is estimated from an inter-sample output predictor, which is essential in providing continuous corrections on the observer. Dead time compensation is carried out in the same spirit as the Smith predictor to reduce the effect of delay in the measurement outputs. By integrating the continuous-time reduced-order observer, the inter-sample predictor and the dead time compensator together, the degree of polymerization is accurately estimated in all reactors. The observer performance is demonstrated by numerical simulations. In addition, a pre-filtering technique is used in the presence of sensor noise