# Measurement and lag

The quality of control an automatic system gives depends initially on the accuracy of measurement of the controlled variable: tight control cannot be expected from coarse measurements. Accuracy also depends on the response of one part of the system to a signal from another and this is typified by lag—the sum of the lags of individual components in the system being its total time lag.

Consider the system in Figure 13.1. A change in heat loss from the room causes its temperature to depart from the desired value and, because of the deviation, heat is transferred between the thermostat, Cl, and the air around it. Enough heat must flow into the primary element for an adequate response to occur and this is not instantaneous, since it depends on the mass of the element, its specific heat capacity and its thermal conductivity. For example, a bimetallic strip must absorb sufficient energy to produce the thermal expansion required to make or break an electrical contact. Suppose the thermostat, Cl, in Figure 13.1 controls a heater battery by means of a two-position valve, Rl. Some time is occupied for the passage of the signal between Cl and Rl, an instance of the distance velocity lag which, for the case of a pneumatic control system, would be measurable. On arrival at the valve the signal must be translated into corrective action, with any amplification necessary. If Cl had sensed a fall in temperature and Rl were pneumatically actuated air would have to be admitted to the space above the diaphragm (see Figure 13.4(a)) in order to open the valve, time being needed for this to take place. Further time elapses because of the mechanical inertia of the valve and because the water must be accelerated to a higher flow rate. The increased flow rate of hot water gives a greater heat transfer through the tube walls and fins of the battery into the airstream, occupying more time. There is then the distance-velocity lag as the air flows along the duct from the heater battery to the supply grille. Finally, there is the air diffusion lag in the room itself, probably the largest of all the lags: the thermostat in the extract duct (or perhaps on the wall of the room) would not know that corrective action had been taken until the air delivered from the supply grille had spread throughout the room and been extracted. For example, this would occupy six minutes if the supply air change rate were ten per hour.

The total time lag is the sum of all these (and other) individual time lags and is significant, setting a limit on the speed of response of the system as the load changes. There is the possibility that the response of the system being controlled (as distinct from the automatic control system) may be out of phase with the corrective information fed from the measuring element, with implications of instability. It is also evident that the change in the value of the controlled variable will always exceed the change in the feedback, because of the time lags. Thus a thermostat may have a differential gap of only two degrees but the room temperature may fluctuate by three or more degrees because an instantaneous response is impossible.

We can also see that there are features of the system being controlled, as well as those of the automatic control system itself, that influence performance when load changes occur. The quality of the controlled system must match that of the controlling system.

Posted in Engineering Fifth Edition