The purpose of on/off control is to keep agiven physical variable, e.g. the ambient
temperature, within certain limits or to change
it according to a predetermined programme.
A control system serves to measure the value
of the controlled variable, compare it with the
desired value, and adjust the control unit, by
which a possible deviation is reduced.
Thermostats and pressure controls for on/off
control are two-position regulators where the
manipulated variable can only lead to two
conditions: cut-in or cut-out.
The temperature sequence for a room
controlled by a thermostat is shown in fig. 1.
The rise in the ambient temperature will not
occur at the same time as the valve opens,
as some time will pass before this happens,
i.e. the dead time Tt. The dead time is defined
as the time which will pass from when the
valve opens until the bulb begins to register
the temperature increase.
At the measuring point the increase will follow
an exponential function. The tangent to the
starting point of the curve intersects the
tangent to the final value of the curve at
Tt + Ts.
Ts is denoted the time constant and indicates
the time it takes for the temperature to
increase to 63% of the final value.
In other words, the time constant is an
expression of the rate at which the controlled
variable changes as a result of a sudden
change of the manipulated variable.
Because of the great difference in
temperature the curve of temperature will
increase most rapidly at the beginning, to
fade out gradually and approach the final
value tangentially.
When the temperature has increased to the
point A the thermostat will cut-in and the
cooling begins. However, it takes some time -
τ1 - before the ambient temperature begins to
fall.
T1 depends on the following factors among
others:
• Bulb position
• Air circulation at the bulb
• Sizing of the refrigeration plant.
During cooling the temperature drops to the
point B where the thermostats cut out the
refrigeration system. Because of the cold
accumulated there will, however, be a certain
after-cooling - τ2 - before the temperature
increases again. The cooling is restarted at
the point A, and a new cycle begins.
td (= the section A to B) denotes the thermal
differential of the thermostat, whereas tmax
indicates the maximum temperature
fluctuations.
Source
http://www.danfoss.com/NR/rdonlyres/8524B02A-
CA67-43C5-B491-907BE25E9647/0/RF5XA102.pdf
