Distance-velocity lag dead time

combining equations 7.58 and 7.59 gives the transfer function for a distance-velocity (DV) lag, i.e.  

This type of lag is encountered frequently in flow systems and may also be termed dead time or transportation lag. The presence of much DV lag in any control loop or configuration can lead to instability in the control action03 (see Fig. 7.49). 

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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. 

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... 

Compute the distance-velocity lag. The time in minutes needed for the thermal element to detect a change in temperature in the storage tank is the distance-velocity lag, which is also called the transportation lag or dead time. For this process, the distance-velocity lag d is the ratio of the quantity of water in the pipe between the tank and the thermal bulb, that is, 15 lb (6.8 kg), and the rate of flow of water out of the tank, that is, 25 lb/min (0.114 kg/s), or d = 15/25 = 0.667 min. 

The oversimplified picture given above is contrary to our physical experience, which dictates that whenever an input variable of a system changes, there is a time interval (short or long) during which no effect is observed on the outputs of the system. This time interval is called dead time, or transportation lag, or pure delay, or distance-velocity lag. 

Set point control Most process control is done with feedback set point control. This means that the controlled variable is measured as an output of the process and the signal is sent back to be compared with a set point (desired value). The generated error is the difference between the set point and the measured value. The error signal is acted on by the controller to make a corrective action which is sent as a command signal to a final control element. In this kind of control loop, the error is corrected only after it has occurred. The closed-loop negative feedback control works best if the distance velocity lag or dead time (DT) is very short. Fig. 17.4 illustrates atypical closed-loop, negative feedback, control loop. 

Dead time is a characteristic of a physical system that causes an input disturbance to be delayed in time, but unaffected in form. Whereas capacitance changes the form of the input disturbance (i.e. a step is filtered into a typical first-order curve), dead time is a pure delay of the input disturbance. Dead time is also referred to as transport lag, or distance velocity lag. A typical example process is the continuous weighing system shown in Figure 3.21. 

Pure delay or dead time usually occurs due to transportation lag, such as flow through a pipe. For a velocity V and distance L,9 = L / v. Another case is a measurement delay, such as for a gas or Uquid chromatograph. 

The effect resulting from a signal being transmitted over an appreciable distance at a finite velocity a kind of dead time. Also known as transportation lag and time delay. 

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