Dead times

Increasing the size of equipment in the steps which limit the batch cycle time to reduce the dead time for those steps which are not limiting. 

In batch process optimization, one of the principal objectives is to improve equipment utilization through reduction in dead time. This requires both structural and parameter optimization, with many options available. 

The chromatogram in Problem 4 was obtained on a 2-m column with a column dead time of 50 s. How long a column is needed to achieve a resolution of 1.5 What height of a theoretical plate is needed to achieve a resolution of 1.5 without increasing the length of the column ... 

The curve (a) traces the outline of the peak obtained directly from the number of events recorded (Figure 31.5). The second curve (b) traces the outline of the peak obtained after correcting for coincidental events (dead time, shown by the shaded area). The centroids of peaks a and b are shown, and it can be seen that they occur at the same m/z value. Thus the deadtime correction alters only the abundances and not the m/z values of the ions. 

This problem is known as dead time. To offset this effect, an algorithm is used to adjust the actual number of events into a true number of events. Since the numbers of ions represent ion abundances, the correction adjusts only abundances of ions before a mass spectrum is printed. 

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... 

Distance-Velocity Lag (Dead-Time Element) The dead-time element, commonly called a distance-velocity lag, is often encountered in process systems. For example, if a temperature-measuring element is located downstream from a heat exchanger, a time delay occurs before the heated fluid leaving the exchanger arrives at the temperature measurement point. If some element of a system produces a dead-time of 0 time units, then an input to that unit,/(t), will be reproduced at the output a.s f t — 0). The transfer function for a pure dead-time element is shown in Fig. 8-17, and the transient response of the element is shown in Fig. 8-18. 

Higher-order systems can be approximated by a first or second-order plus dead-time system for control system design. 

The controller gain is inversely proportional to the process gain for constant dead time and time constant. 

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. 

Dead time. Probably the best example of a measurement device that exhibits pure dead time is the chromatograph, because the analysis is not available for some time after a sample is injected. Additional dead time results from the transportation lag within the sample... 

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