Analytical predictor

Several control techniques have been developed to compensate for large dead-times in processes and have recently been reviewed by Gopalratnam, et al. (4). Among the most effective of these techniques and the one which appears to be most readily applicable to continuous emulsion polymerization is the analytical predictor method of dead-time compensation (DTC) originally proposed by Moore ( 5). The analytical predictor has been demonstrated by Doss and Moore (6) for a stirred tank heating system and by Meyer, et al. (7) for distillation column control in the only experimental applications presently in the literature. Implementation of the analytical predictor method to monomer conversion control in a train of continuous emulsion polymerization reactors is the subject of this paper. 

The analytical predictor, as well as the other dead-time compensation techniques, requires a mathematical model of the process for implementation. The block diagram of the analytical predictor control strategy, applied to the problem of conversion control in an emulsion polymerization, is illustrated in Figure 2(a). In this application, the current measured values of monomer conversion and initiator feed rate are input into the mathematical model which then calculates the value of conversion T units of time in the future assuming no changes in initiator flow or reactor conditions occur during this time. 

The objective of this paper is to illustrate, by simulation of the vinyl acetate system, the utility of the analytical predictor algorithm for dead-time compensation to regulatory control of continuous emulsion polymerization in a series of CSTR s utilizing initiator flow rate as the manipulated variable. 

The feedback value used in the calculation of error is the measured conversion for the standard feedback loop, while it is the predicted value of future conversion for the analytical predictor algorithm, the predicted value being obtained from the model of Kiparissides. 

The utility of the analytical predictor method of dead-time compensation to control of conversion in a train of continuous emulsion polymerizers has been demonstrated by simulation of the vinyl acetate system. The simulated results clearly show the extreme difficulty of controlling the conversion in systems which are operated at Msoap-starvedM conditions. The analytical predictor was shown, however, to provide significantly improved control of conversion, in presence of either setpoint or load changes, as compared to standard feedback systems in operating regions that promote continuous particle formation. These simulations suggest the analytical predictor technique to be the preferred method of control when it is desired that only one variable (preferably initiator feed rate) be manipulated. 

To improve the performance of time-delay systems, special control algorithms have been developed to provide time-delay compensation. The Smith predictor technique is the best-known algorithm a related method is called the analytical predictor. Various investigators have... 

D APC ASTEEM BC CAM3 Three-dimensional The analytical predictor of condensation The adaptive step time-split explicit Euler method Black carbon The community atmospheric model v. 3 ... 

Ghosh, A. A., Daemon, J. J. K. (1983). A new analytical predictor of ground vibrations induced by blasting, Volume TV (Rep. to the offiee of surface mining). 

Another control strategy for treating both disturbances and set-point changes is the analytical predictor, which utilizes a prediction of the process behavior in the future based on the process and disturbance transfer functions, G and G. In the context of Eq. 16-23, if Gc included a term (a perfect prediction 0 units of time ahead), then the time delay would effectively be eliminated from the characteristic equation. However, this is an idealized view, and further details are given in Chapter 17. 

The IMC block diagram in Fig. 12.5 can be expanded to include a block A in the feedback path as well as a disturbance transfer function G. The block A can be used to predict the effect of the disturbance on the error signal to the controller, and it can also provide time-delay compensation. This two-degree-of-freedom controller (see Chapter 12) is known as an analytical predictor (Doss and Moore, 1982 Wellons and Edgar, 1987). 

Doss, J. E., and C. F. Moore, The Discrete Analytical Predictor—A Generalized Dead-Time Compensation Technique, ISA Trans., 20 (4), 77 (1982). 

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