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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 6 Comparison of LQC, DMC and ESTR control policies for the same disturbance AI = -0.025 mol/L. to positive and negative changes in the total initiator concentration. This can be seen by comparing the results of Figures 3 and 6 obtained for a positive and negative step change in the initial initiator concentration, respectively. In what follows the effects of associated tuning parameters on the performance of DMC and ESTR controllers are examined. In all subsequent simulations it is assumed that a positive step change in the initial initiator concentration (A1 = 0.025 mol/L) is introduced to the system. Figure 7 depicts the effect of prediction horizon, M, on the control action E 4 0 L - 0 l- a -1 c -2 U - m 5 KlO Tim, min FIGURE 7 Effect of prediction horizon parameter, M, on the calculated DMC control action.

Downloaded By: [HEAL-Link Consortium] At: 12:27 29 July 2008 POLYMERIZATION REACTOR CONTROL 17 calculated by DMC. It is apparent that as the parameter M increases the controller's ability to respond quickly decreases. It should be pointed out that the large value of q,, in the weighting matrix Q is due to the fact that the two state variables x and p, are of considerably different magnitude (x = 1, po;= Figure 8 depicts the effect of the control horizon, L, on the calculated control action. It can be seen that as the value of L increases the controller responds faster at the expense of a more oscillatory response. However, no significant difference in the controller's behaviour is observed as the value of L changes from two to three. It is interesting to notice that the unit step response coefficients, a;., for the two discrete convolution models relating the state variables x and p, to the polymerization temperature were obtained from the linearized process model by considering an one-degree step change in the temperature at time t = 0. Despite the highly nonlinear dynamics of the process, simulation results showed that adaptation of unit step response coefficients was not necessary. This clearly demonstrates the controller's robustness and ability to accommodate large process modeling errors. Figure 9 illustrates the effects of the control horizon, L, and asymptotic memory length, Z, on the performance of ESTR. In all cases, the ESTR controller was able to move the controlled variables closer to their corresponding desired values. The order of A and B polynomials for both models in Eqs. (48) and (49) was chosen to be equal to one. Sampling times of 1 to 5 minutes were tried. However, a sampling time of one minute gave the best results. It was found that the selection of the parameter L was the most critical one in our simulation studies. As the value of L increased from one to two the controller's performance was markedly improved. The effect of L on the calculated control action is shown in Figures 9a, b, c. It can be seen that a long control horizon gives a slower response, but leads to more robust control. Notice that a long time horizon FIGURE 8 EBect of control horizon parameter, L, on the calculated DMC control action.

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