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control of molecular weight in a batch polymerization reactor using ...

control of molecular weight in a batch polymerization reactor using ...

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Downloaded By: [HEAL-Link Consortium] At: 12:27 29 July 2008 C. KIPARISSIDES et al. Time, min FIGURE 3 Comparison of LQC, DMC and ESTR control policies for the same disturbance A1 = 0.025 mol/L. the DMC is very similar to that of LQC. On the other hand, the ESTR control action initially shows an oscillatory response which, subsequently, levels off and approaches the final value obtained by the LQC and DMC controllers. The observed initial large deviation in the calculated control action by ESTR is typical of the adaptive nature of the parameter estimation algorithm. The main difference between ESTR and (LQC, DMC) controllers is that the latter presuppose complete knowledge of the process dynamics and kinetic parameters which are not always known. On the other hand, the ESTR does not require any prior information on the model parameters since an initial estimate of the parameter vector, go= 0, can be assumed. It should be pointed out that the calculated control action for both LQC and DMC was based on a five-minutes sampling interval which is the expected sampling time for the measurement of molecular weight averages using an on-line size exclusion chromatograph (SEC). However, it was found out that a sampling time of the order of one minute was necessary for the ESTR controller to obtain a satisfactory closed-loop performance. This problem has been addressed by Ponnuswamy et al. (1986) who showed that an indirect continuous measurement of molecular weight averages in a MMA batch reactor was possible by using an experimental correlation between the molecular weight and monomer conversion, the viscosity of the reaction mixture and polymerization temperature. Alternatively, one can use an on-line state estimator to calculate the number-average molecular weight from on-line measurements on temperature, monomer conversion and viscosity. The overall performance of the state estimator can be further improved by including infrequent off-line (or on-line) measurements of molecular weight using a SEC (Ray 1985, Schuler and Papadopoulou, 1986). Figures 4,5 and 6 depict the performance of the controlled and uncontrolled polymerization process for the case of a negative step change (AI =

Downloaded By: [HEAL-Link Consortium] At: 12:27 29 July 2008 POLYMERIZATION REACTOR CONTROL Time. min FIGURE 4 Desired, uncontrolled and controlled monomer conversion responses for a negative disturbance A1 = -0.025 mol/L in the initial initiator concentration. -0.025 mol/L) in the initial initiator concentration. As with the previous case, the operation under feedback control (LQC, DMC, ESTR) results in a significant reduction of the effects of initiator disturbance on the output process variables. This is accomplished by increasing the polymerization temperature from its nominal value (T = 65°C) to a new temperature of about 70°C. Alike the results of Figures 1 and 2, the calculated control policy (Figure 6) cannot completely eliminate the observed offsets in the two controlled variables, Figures 4 and 5. Finally, it is important to point out the highly unsymmetric response of the system uncontrolled ESTR desired Time. min FIGURE 5 Desired, uncontrolled and controlled number-average molecular weight responses for A1 = -0.025 mol/L.

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