Dead-time element

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. 

If the input into the deadtime element is and the output of the dead time element is then and are related by... 

Distance-Velocity Lag (Dead-Time Element) The dead-time or time-delay element, commonly called a distance-velocity lag, is often encountered in process systems. For example, if a temperaturemeasuring element is located downstream from a heat exchanger, a time delay occurs before the heated fluid leaving the exchanger... 

Problem III. 56 implies that a dead-time element is basically a distributed system, described by a partial differential equation. Suppose that the tube of Problem III. 56 (Figure PIII.6) is approximated by a series of N identical well-stirred tanks (Figure PHI.7). 

The response of a dead-time element to any signal whatever will be the signal delayed by that amount of time. Dead time is measured as shown in Fig. 1.3. 

Because there are no dynamic elements in the proportional controller, the entire 180 phase shift will take place in the dead-time element. This determines the natural period ... 

Notice that the period is twice that for proportional control, because only 90 of phase shift was allowed to take place in the dead-time element. 

To keep testing to a minimum, all available knowledge of the process must be employed. The volume of vessels and flow rates are always available, from which time constants may be calculated. The length and diameter of piping runs can serve to locate dead-time elements. By identifying all the known or knowable elements in this way, any tests will be of more value in defining the unknown elements which make up the balance of the loop. 

It has been pointed out that dynamic compensation generally takes the form gq/gm- ft niay be recalled, however, that the ratio of two vector quantities like these resolves into the ratio of their magnitudes and the difference between their phase angles. Since dead-time elements have unity gain, their ratio is also unity their only contribution is phase lag. This is why the ratio gg/gm appears as the difference t, — r between the dead times. 

For a pure dead time element, assume that a step input of magnitude A occurs. The magnitude of the output step would also be A, except displaced in time by the dead time amount. The static gain A ss would by definition be dimensionless and equal to... 

The next block is a multiplier called average that multiplies the input by 0.3333 to get the average temperature in degrees Celsius. The next block is another summer that adds 273 to obtain the average temperature in Kelvin. This signal is finally sent through a dead time element (1 min) and then to the average temperature controller. 

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