Abstract
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.
Highlights
Polymers are continuously substituting traditional materials along with low cost and good processability
The following assumptions are made: (i) only ethylene glycol (EG) exists in the vapor phase; (ii) mass transfer resistance on the gas side is negligible; (iii) the concentration of vinyl end groups in the feed is equal to the concentration of carboxyl end groups; (iv) the mass transfer parameter does not change over time in each reactor
This work presents an application of a nonlinear state observer for monitoring degree of polymerization (DP) in a series of Polyethylene terephthalate (PET) polycondensation reactors
Summary
Polymers are continuously substituting traditional materials (e.g., glass, woods and metals) along with low cost and good processability. An alternative approach for estimation in polymerization processes is state observer design [19,20,21,22,23,24,25,26]. A significant amount of work has been done in the monitoring and control of free radical polymerization reactors, very few state estimation studies are available for polycondensation reactors. The nonlinear observer design method of exact linearization with eigenvalue assignment [30,31] is applied to a series of three continuous polycondensation reactors. The objective is to estimate unmeasured concentrations, as well as the degree of polymerization in the PET finishing stage from continuous hydroxyl measurement and sampled acidimetric titration, where different sampling rates and time delays are considered.
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