The validity of an online state estimator for a semi-batch
IntroductionCopolymer has a variety of better properties than homopolymer, because two monomers having different characteristics are used to compose the structure of a polymer chain. However, the use of two monomers brings about a greater complexity and requires several factors to be determined for the production of copolymers with desired end-user properties. Hence, a great deal of research interest has been focused on the development of the operation technique for the control of these factors.Copolymer composition is one of the most important factors that affect the properties of copolymer. It is well known that copolymer composition drift occurs in a batch or semibatch free radical copolymerization reactor due to the different reactivities of two monomers. Choi and Butala (1989) proposed open-loop control policies for both molecular weight and copolymer composition by using an inverse feedback control method. On the other hand, Kozub and MacGregor (1992a) applied the optimal instantaneous property Correspondence concerning this article should be addressed to H.-K. Rhee. condition in such a way that the instantaneous polymer being produced at every instant of time might have the desired properties. This method, which has been used by many researchers in recent years (Saldivar and Ray, 1997; Sayer et al., 20001, suffers from several features such as the existence of disturbances appearing in most chemical reactors, or mismatches between the real system and the model used for the calculation of optimal trajectory.To overcome these difficulties, offline measurements or online measurements with time delay were used to update the optimal trajectory. A midcourse correction policy was employed by Yabuki and MacGregor (1997), who used online measurement of the reactor temperature and offline measurements of the residual monomer concentration by gas chromatography and the volume average particle sue by dynamic light scattering in order to make the midcourse adjustment. Gattu and Zafiriou (1999) used the temperature as the primary measurement and the average molecular weights and conversion as the secondary measurements.As reported by Congalidis and Richards (1998), polymerization reactors lack the online measurements of polymer properties and this has been the major obstacle in the appli-1013 AIChE Journal cation of control strategies to industrial reactors. To make an estimation for the state of a polymerization reactor, Dimitratos et al. (1989Dimitratos et al. ( , 1991 implemented the conventional extended Kalman filter (EKF) to the semicontinuous emulsion copolymerization reactor and developed a filter with parameter adaptation and noise adaptation algorithms. Kozub and MacGregor (1992b) augmented the EKF with a second EKF to improve the convergence, whereas Kazantzis et al. (2000) designed the model based nonlinear observer for process monitoring.Recently, the development of online measurement devices such as a densitometer, a calorimeter, and a viscomet...