Imagine you had a long length of pipe through which a fluid was flowing in a plug flow manner. At the end of the pipe is a temperature sensor. Now imagine that the inlet temperature of the fluid increased suddenly in a step, what would happen at the outlet of the pipe?
The answer is that nothing at all would happen immediately at the pipe outlet - it would take time (equal to the distance divided by the fluid velocity) for the first element of fluid with the increased temperature to flow down the pipe. When the element reached the end of the pipe, the measured temperature would suddenly increase in a step. This is an example of a pure dead-time process. When the input to such a process changes the output is 'dead' to that change until the dead-time has passed.
Although long pipes with measuring instruments at the end are generally avoided in the process industries, dead-time is a very common phenomenon. The reason for this is that in real processes perfect mixing does not occur. In imperfectly mixed systems it takes time for changes in conditions in particular parts of the vessel to transfer themselves to the rest of the vessel - this appears as some element of dead-time superimposed on some other (e.g. first-order) dynamic response. Also, pure dead-time can arise in real systems as a result of using analytical instruments which take time to produce a response - this time can range from seconds to hours.
Dead-time causes us two problems. The first is that it is impossible to analyse systems containing dead-time using the mathematical tools we have available in this course. The second, and more serious, is that dead-time causes real problems in feedback control systems. Even at relatively low levels of dead-time, the decoupling between the controller taking an action and seeing its response means that controller performance is reduced and instability becomes more likely. At high levels of dead-time (when the dead-time approaches or exceeds the process time constant) adequate feedback control using conventional techniques may become impossible and special model-based methods may be required.
Although we don't cover dead-time any further (except in some simulation work), it doesn't mean that it isn't important!