|
Deadband--the thermostat
starts or stops the furnace only when the difference between
set-point and room temperature is greater than about 1.0 degree.
Without this deadband, the furnace would cycle every few seconds
with the minute temperature changes. The deadband produces small
temperature variance.
Time Delay--there is a time
delay while the heat exchanger heats or cools and this causes a
further variation in room temperature. While the heat exchanger
is warming, the room temperature continues to fall; when the
heat exchanger is cooling it continues to heat the room even
after the thermostat calls for shutdown.
This illustrates two reasons
why feedback systems become unstable:
time delays and
non-linearity.
Non-linearity refers to a
response that is not proportional to input. The dead-band is non
linear. A small temperature change brings no response from the
thermostat. A slightly larger change starts the burner at full
heat. The burner is either on or off and is also non-linear. A
burner that could modulate and produce heat in proportion to the
temperature difference between set-point and room temperature
would be more linear and, thus, more stable.
In
this heating system, operating on its own, the time delays and
non-linearity produce only small oscillations and system
instability is small. At times, an
additional feedback loop is introduced into a
formerly stable heating system. This takes the form of a
thermostat fiddler-- people
who attempt to improve on the control system by changing the
set-point frequently. |
The red line
in figure 2 shows the result. When the fiddler
detects a slight decrease in temperature, he/she raises the
set-point to a very high setting, say 85 degrees. The thermostat
responds, the burner ignites and room temperature rises.
Fiddlers rarely notice the rising temperature until it reaches,
say 80 degrees. They then respond by excessively lowering the of
set-point while cursing the defective furnace.
This illustrates amplification in the
feedback loop. The temperature difference is
amplified disproportionately and over-correction results. The
thermostat fiddler also adds complexity and additional
non-linearity.
Amplification is common when humans are
part of a control system. With scheduling and
inventory systems, it results in excessively large batches of
product and excessively large inventory alternating with
shortages.
Our
heating system example illustrates several
fundamental causes of instability and chaos:
-
Non-Linearity
-
Amplification
-
Time Delays
These factors can produce instability
and chaos when present in
any part of the system. However,
feedback loops are especially sensitive. |
