This paper concerns nonlinear state estimation in a continuous polymerization reactor where free-radical solution polymerization of methyl methacrylate takes place. Initiator and solvent concentrations and the leading moments of the molecular weight distribution of the polymer are estimated in three measurement cases. For one of the measurement cases, the global convergence of the nonlinear observer is proved. The convergence of the nonlinear observers is shown by numerical simulations, for different values of observer gains, for different observer initial conditions, and in the presence of a measurable disturbance. Furthermore, in each case, the implementation and performance of the nonlinear observer are compared with those of a deterministic extended Kalman filter.

Nonlinear State Estimation in a Polymerization Reactor

This paper concerns nun-linear state estimation in a batch polymerization reactor where suspension polymerizationof methyl methacrylate takes place. A kinetic model proposed in tree literature is selected and its validity has been verified through an experimental set-up . Based on this model monomer conversion and average molecular weights of the polymer are estimated using only one output measurement (reactor temperature) . The perlormance of the estimator, which has the structure of en extended Kalman filter, is examined through simulation and experimental studies in the presence of different levels of parameter uncertainties . The effects of addingfictitious noise' and parameter state' to the estimation algorithm are also investigated . To find the best fictitious state, the main parameters of polymerization model are divided into three groups . The parametric study of the MMA polymerization model indicates that, when the source of parameter uncertainty is unknown, the best selection of parameter state is the initial mass of monomer.

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State Estimation in a Batch Suspension Polymerization Reactor

The analysis of a parameter identification algorithm which was derived from the continuous time Kalman filter

A Kalman filter type of extension to a deterministic gradient technique for parameter estimation

The relationship between a continuous-time identification algorithm based on the deterministic filter and least-squares methods

It is shown that the optimality of the Kalman filter prevents its application to estimate the state of deterministic; systems but that if the gain is slightly modified a deterministic filter is possible. Such a filter is subsequently used to explain some of the difficulties encountered in Kalman filter computations, from which it transpires that much Kalman filtering is essentially an application of a deterministic filter to stochastic problems. To reduce the order of the algorithm the concept of observer robustness is incorporated into the subsequent development of the deterministic filter. Exactly equivalent discrete- and continuous-time algorithms are derived and used for a new treatment of the problem of obtaining estimates of the state variables of a stochastic system when the measurements are free of noise.

M. W. A. Smith

Papers

A study of the Kalman filter as a state estimator of deterministic and stochastic systems