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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 2 C. KIPARISSIDES et al. and pressure. There are several valid reasons for the lack of progress in closed-loop control of polymer quality: (i) Polymerization reactions are highly nonlinear processes with time-varying parameters. (ii) The formulation of a meaningful objective function is not always easy, especially in terms of the end-use properties of polymer products. (iii) Molecular properties such as number-average, weight-average molecular weight and copolymer composition often react in opposite directions to manipulations of the control variables (e.g. temperature, initiator concentration). (iv) On-line measurements of molecular properties are usually the weakest link in any polymerization closed-loop control study. Presence of long measurement delays as well as poor reliability are two common problems associated with on-line characterization of polymer quality. In spite of the difficulties yet to be overcome, recent advances in modeling and on-line measurements (MacGregor et al., 1983) as well as the availability of new robust long-range predictive control methods have largely increased the scope for on-line control of polymer quality in polymerization reactors. In recent years, two powerful long-range predictive control design methods have been proposed based on either a parametric or a nonparametric process representation. The former method uses a linear discrete-time (ARMA) model to approximate the process dynamics. To better cope with the problem of controlling nonlinear time-varying processes, an extended self-tuning regulator (ESTR) has been proposed (Lee and Lee, 1983; Ydstie et al., 1985). The new adaptive predictive controller includes a variable forgetting factor and a longrange control criterion to improve its robustness and adaptivity in a nonlinear time-varying environment. The nonparametric control approach uses a discrete convolution model to represent the process dynamics. Model Algorithmic Control (MAC) (Richalet et al., 1978) and Dynamic Matrix Control (DMC) (Cutler and Ramaker, 1980) both utilise a discrete convolution model and the concept of a long-range predictor to calculate the control policy in order to follow a prescribed reference trajectory. Both techniques have attracted wide attention and a number of papers have been published dealing with the robustness, stability and application of DMC and ESTR controllers (Martin, 1981; Garcia and Morari, 1982; Marchetti el al., 1983; Garcia, 1984;' Maurath et al., 1985; Garcia and Morari, 1985; Economou et al., 1986; Farber and Ydstie, 1986). Compared to the successful application of DMC and ESTR methods to other chemical processes (distillation, reactors, etc.) there is only a limited number of studies on the control of polymerization reactors. Garcia (1984) described the development of a DMC controller to regulate the polymerization temperature in a synthetic rubber semibatch reactor. Houston and Schork (1986) developed an on-line linear time-series model of a polymerization reactor to calculate the optimal control strategy that maximizes a predetermined objective functional expression in terms of the molecular weight averages. Farber

Downloaded By: [HEAL-Link Consortium] At: 12:27 29 July 2008 POLYMERIZATION REACTOR CONTROL 3 and Ydstie (1986) applied an extended horizon adaptive controller to regulate the temperature in a polymerization reactor. Takamatsu et al. (1986) proposed an adaptive-inferential control scheme to control molecular weight in a continuous polymerization reactor. Kiparissides et al. (1987) described the application of DMC and ESTR to a solution MMA batch polymerization reactor. Finally Takamatsu et al. (1987) proposed a new adaptive control strategy in terms of reaction temperature and initiator concentration in order to get a final polymer product which has a desired molecular weight distribution in a free-radical batch polystyrene reactor. It is evident that relatively little has been reported on the control of molecular weight in bulk polymerization reactors using long-range predictive control methods. Furthermore, it appears that there are no results published on the control of molecular weight in batch polymerization reactors operating under strong diffusional limitations of propagation and termination rate constants. The objective of the present study is to show that DMC and ESTR controllers can be efficiently used to control the molecular weight and monomer conversion in a batch MMA reactor and minimize the effects of process disturbances. Moreover, the aim of this work is to examine the similarities, differences and main operating features of the two design control strategies (DMC, ESTR) in comparison with the performance of the more traditional linear quadratic controller (LQC). DEVELOPMENT OF THE I'OLYMERIZATION REACTOR MODEL The free radical polymerization of MMA in a batch reactor can be modeled in terms of a set of nonlinear differential equations of the following form: where I, M denote the initiator and monomer concentration, respectively, A,, A,, A, and po, p1 and p, are the corresponding zeroth, first and second moment of the growing radicals and dead polymer distributions. S is the solvent concentration, E is the fractional volume change at conversion 100% and x is the monomer conversion defined as x = (V,M, - VM)/V,M, (10)

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