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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 20 C. KIPARISSIDES et al. ten minutes. This indicates that the latter model exhibits a more linear behaviour than the former one. The DMC and ESTR presented in this study addressed an important problem of polymer quality control in a batch polymerization reactor operating under strong diffusional limitations of propagation and termination rate constants. Good results were obtained for both negative and positive disturbances in the total initial initiator concentration. Both controllers were proven to be robust and had desirable convergence and stability properties. Finally, the present study provides a fairly detailed framework for dealing with the application of long-range predictive control to polymerization reactors. NOMENCLATURE 3 x 3 state matrix in the linear model bias parameter 3 x 1 control matrix in the linear model 3 x I disturbance matrix in the linear model error prediction vector initiator efficiency 3 x 3 state matrix in the discrete model 3 x 1 control matrix in the discrete model 3 x 1 disturbance matrix in the discrete model initiator concentration, mol/L =k;/k,, Llmol-s initiator dissociation rate constant, s-' transfer to monomer rate constant, L/mol-s propagation rate constant, L/mol-s transfer to solvent rate constant, L/mol-s =k, + ktd, L/mol-s termination by combination rate constant, L/mol-s termination by disproportionation rate constant, Llmol-s time horizon monomer concentration, mol/L number-average molecular weight weight-average molecular weight molecular weight of monomer weighting matrix for state variables weighting matrix for control variables

Downloaded By: [HEAL-Link Consortium] At: 12:27 29 July 2008 Greek Letters POLYMERIZATION REACTOR CONTROL solvent concentration, mol/L time, s temperature, "K control vector disturbance vector monomer conversion process output state vector a; I3 parameters in prediction model E fractional volume change 4 noise sequence A,, A,, A, zeroth, first and second moment of live polymer distribution p,, p,, p2 zeroth, first and second moment of dead polymer distribution r sampling interval Subscripts 0 S denotes initial condition denotes the desired condition Superscripts s denotes the desired condition REFERENCES Astrom, K.J., and Wittenmark, B., Computer Controlled System, Prentice Hall, Englewood Cliffs, NJ, (1984). Astrom, K.J., Borisson, U., Ljung, L., and Wittenmark, B., "Theory and Application of Adaptive Regulators", Automatics, W, 457 (1977). Balhoff, R.A., and Lau, H.K., "A Transfer Function Form of Dynamic Matrix Control and Its Relationship With Some Classical Controllers", AIChE Meeting, (1985). Balke, S.T., "The Free-Radical Polymerization of Methyl Methacrylate to High Conversion", Ph.D. Thesis, McMaster University, Ontario. Canada, (1972). Cutler, C.R., and Ramaker, B.L., "Dynamic Matrix Control-A Computer Control Algorithm", Proceed., JACC, WP5-B, San Francisco, (1980). Economou, C.G., Morari, M., and Palsson, B.O., "Internal Model Control 5. Extension to Nonlinear Systems. I&EC Proc. Des. Dev., 25, 403 (1986). Farber, J.N., and Ydstie. B.E., "Adaptive Compensation for Large Disturbances in a Continuous Polymerization Reactor". l&EC Fundam., 25, 350 (1986). Fortesque, T.R., Kershenbaun, L.S., and Ydstie, B.E., "lmplementation of Self-Tuning Regulators With Variable Forgetting Factors", Auromatica, 17, 831 (1981). Franklin, G.F., and Powell, J.D., Digital Control of Dynamic System, Addison-Wesley, Menlo Park, CA, (1981).

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