Dead time compensator

Dead-Time Compensation. Dead time within a control loop can greatiy iacrease the difficulty of close control usiag a PID controller. Consider a classical feedback control loop (Fig. 18a) where the process has a dead time of If the setpoiat is suddenly iacreased at time t, the controller immediately senses the deviation and adjusts its output. However, because of the dead time ia the loop, the coatroUer does aot begia to see the impact of that change ia its feedback sigaal, that is, a reductioa ia the deviatioa from setpoiat, uatil the time t +. Because the deviatioa does aot change uatil... 

Fig. 18. Dead-time compensation (a) classical feedback and (b) Smith dead-time compensator. SP = setpoint C = controlled variable and (+) and (—)...

The Smith dead-time compensator is designed to aUow the controUer to be tuned as tightly as it would be if there were no dead time, without the concern for cycling and stabUity. Therefore, the controUer can exert more reactive control. The dead-time compensator utilizes a two-part model of the process, ie, Gp, which models the portion of the process without dead time, and exp — sTp,pj ), which models the dead time. As seen from Figure 18b, the feedback signal is composed of the sum of the model (without dead time) and the error in the overaU model Gpj exp — sTppj )), ie, C —. Using... 

Now, if td > 0, it is possible for the feedforward controller to incorporate dead time compensation. 

Now the error E also includes the feedback information from the dead time compensator ... 

Since few things are exact in this world, we most likely have errors in the estimation of the process and the dead time. So we only have partial dead time compensation and we must be conservative in picking controller gains based on the characteristic polynomial 1 + GCG = 0. 

Fig. 7.60. As Fig. 7.59 but with dead time compensation included in the controller... 

The signal X can be introduced by means of an internal feedback loop within the controller (Fig. 7.60) which constitutes the dead time compensator GDTC(s) such that ... 

Fig. 7.61. Schematic representation of the effect of the dead time compensation shown in Fig. 7.60. Dead time now effectively outside the control loop...

A Simulation Study on the Use of a Dead-Time Compensation Algorithm for Closed-Loop Conversion Control of Continuous Emulsion Polymerization Reactors... 

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. 

Closed-loop response to process disturbances and step changes in setpoint is simulated with the model of Kiparissides extended to predict the behavior of downstream reactors. Additionally, a self-optimizing control loop is simulated for conversion control of downstream reactors when the first reactor of the train is operating under closed-loop control with dead-time compensation. 

These controllability" criteria are used to judge the performance of the various control systems described above in Table III. As seen in Table III, dead-time compensation markedly improves system performance at the high emulsifier concentration. 

These simulated results for the high emulsifier concentration operating condition demonstrate the utility of dead-time compensation to the control of conversion from the first reactor in a train. With implementation of this degree of control on the first reactor, control schemes for downstream reactors can be simplified as discussed in the next section. 

SFB = standard feedback control DTC = dead-time compensation... 

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. 

Special considerations, such as dead time compensation, can be discussed under the three areas. 

This design may yield controllers which are quite sensitive to model errors and require high order derivative action. If the dead time in P(s) is the same as the dead time in G(s), the controller contains dead time compensation, as in the Smith predictor. Bristol (42) has extended this idea to apply to multivariable systems, although he treats the controller in a more general form, allowing a pre-compensation block before G(s) and a postcompensation block after G(s) in the direct path between r(s) and y(s). 

A related approach which has been used successfully in industrial applications occurs in discrete-time control. Both Dahlin (43) and Higham (44) have developed a digital control algorithm which in essence specifies the closed loop response to be first order plus dead time. The effective time constant of the closed loop response is a tuning parameter. If z-transforms are used in place of s-transforms in equation (11), we arrive at a digital feedback controller which includes dead time compensation. This dead time predictor, however, is sensitive to errors in the assumed dead time. Note that in the digital approach the closed loop response is explicitly specified, which removes some of the uncertainties occurring in the traditional root locus technique. 

As shown in the above works, an optimal feedback/feedforward controller can be derived as an analytical function of the numerator and denominator polynomials of Gp(B) and Gn(B). No iteration or integration is required to generate the feedback law, as a consequence of the one step ahead criterion. Shinnar and Palmor (52) have also clearly demonstrated how dead time compensation (discrete time Smith predictor) arises naturally out of the minimum variance controller. These minimum variance techniques can also be extended to multi-variable systems, as shown by MacGregor (51). 

Quantitative models and numerical computations are and will continue to be central in the implementation of model-predictive feedback controllers. Unfortunately, numerical computations alone are weak or not robust in answering questions such as the following How well is a control system running Are the disturbances normal Why is derivative action not needed in a loop What loops need dead time compensation, and should it be increased or reduced Have the stability margins of certain loops changed and, if so, how should the controllers be automatically retuned ... 

In some situations where one or more of the latex properties are measured either directly or indirectly through their correlation with surrogate variables and where extreme nonlinearities such as the periodic generation of polymer particles does not occur, one can use much simpler modehng and control techniques. Linear transfer function-type models can he identified directly from the plant reactor data. Conventional control devices such as PID controllers or PID controllers with dead-time compensation can then be designed. If process data is also used to identify... 

Geiger counters can be designed to electronically compensate for counts lost due to dead time. However, many are not. It is important to know whether a particular Geiger counter is dead time compensated, so that if not, its drawback can be kept in mind. 

All. Ash, K. C., and Piepmeier, E. H., Double-beam photon-counting photometer with dead-time compensation. Anal. Chem. 43, 26-34 (1971). 

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