Dead time compensation

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... 

Time-Delay Compensation Time delays are a common occurrence in the process industries because of the presence of recycle loops, fluid-flow distance lags, and dead time in composition measurements resulting from use of chromatographic analysis. The presence of a time delay in a process severely hmits the performance of a conventional PID control system, reducing the stability margin of the closed-loop control system. Consequently, the controller gain must be reduced below that which could be used for a process without delay. Thus, the response of the closed-loop system will be sluggish compared to that of the system with no time delay. 

This is the steady state compensator. The lead-lag element with lead time constant xFLD and lag time constant XpLG is the dynamic compensator. Any dead time in the transfer functions in (10-7) is omitted in this implementation. 

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. 

In this illustration, we do not have to detune the SISO controller settings. The interaction does not appear to be severely detrimental mainly because we have used the conservative ITAE settings. It would not be the case if we had tried Cohen-Coon relations. The decouplers also do not appear to be particularly effective. They reduce the oscillation, but also slow down the system response. The main reason is that the lead-lag compensators do not factor in the dead times in all the transfer functions. 

The presence of significant amounts of dead time in a control loop can cause severe degradation of the control action due to the additional phase lag that it contributes (see Example 7.7). One method for compensating for the effects of dead time in the control loop has been suggested by SMITH<30>. This consists of the insertion of an additional element which is often termed the Smith predictor as it attempts to predict the delayed effect that the manipulated variable will have upon the process output. 

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 ... 

This means that the Smith compensator has moved the effect of the dead time outside the closed-loop as in the equivalent schematic representation in Fig. 7.61. 

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. 

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