DT and furnace/thermostat models
Posted: Tue Nov 02, 1999 12:20 pm
Should we use 0-off, 1=on to indicate an on-off switch in a thermostat?
To what extent does this require incorporating DT into the equation?
Is this good SD practice?
Wayne W and I have discussed this issue in the past and have never quite
resolved it. But this discussion rekindles some thoughts.
In the normal residential heating system we dont want the thermostat to
detect room temperatures to within 0.1 degrees, thus turning the furnace on
and off minute by minute. The average "system" is therefore designed to
maintain the temp within +/1 one or two degrees of the "set point". Any
more than this becomes noticeably uncomfortable.
Traditional thermostat:
Consider a traditional thermostat with a bi-metallic coil. Start with a
cool room. The coil contracts, hits a contact, turns on the furnace, and
the room begins to warm. With some delay, the coil begins to warm and
expand, releasing the contact and turning off the furnace. The room begins
to cool, starting the cycle again.
Rather than model one stock (room temp) and one on-off switch, I would use
two stocks. One illustrates room temp, the other illustrates the temp of
the bi-metallic coil.
The size of the coil, the amount of expansion per degree, etc. will
contribute to the "lag" in the system, thus damping the response of the
furnace to very small changes in room temp.
We could demonstrate this (physically, and in the SD model), by placing a
paper cup over the thermostat. The furnace heats the room, but additional
time is required for this information to get to the sensor. This lag leaves
the furnace on too long, and the room overheats before the coil gets warm
enough to turn it off. Once the furnace is turned off the room cools below
the desired temperature. Heat is trapped within the cup and the coil does
not turn the furnace on again until the room is well below the desired
temperature.
We have thus converted a comfortable system with a +/- 1 degree "dead zone"
into an uncomfortable system with a +/- 5 degree dead zone. More
importantly, we have captured the true dynamic structure of the system if
we model it in this way, rather than by using a mathematical on-off switch
to simulate the thermostat switch.
Question: Before continuing below, does the above analysis make sense?
High Tech thermostat:
We now have a digital thermostat at home. It has a semi-conductor
temperature probe rather than a bi-metallic coil.
(It is possible that this probe was designed with a very small mass and
therefore a very rapid time constant. If undamped this would lead to rapid
on-off cycles. OR the mass of the probe might be designed to take this into
account. I am ignorant about this design issue. Does anyone know the
answer?)
I bring this up because if the temperature sensor indeed has a very rapid
time constant, the damping might be introduced in software (or rather,
firmware). The damping might literally be produced by an IF-THEN statement
within the thermostat controller!
e.g. Algorithm says --> If the temp is rising, turn OFF at 71 degrees; if
the temp is falling, turn ON at 69 degrees.
These logic statements would create a dead band of +/- 1 degree around the
desired temperature of 70 deg.
Back to the philosophy and practice of SD modeling and simulation:In this
case the "correct" model would explicitly -require- the use IF-THEN
statements!
{BTW, I bought a "cheap" ($19.95) digital thermostat several years ago. It
was quite uncomfortable, with a dead band of at least +/- 2 degrees. After
a year or so I upgraded to a "deluxe" version ($29.95). Much better!}
This is an intriguing question, because I often use descriptions of the
familiar (and reasonably intuitive?) home heating system as an introduction
to mammalian thermoregulation. If my students are not familiar with
bi-metallic coils then the introduction becomes a bit strained.
Ed Gallaher
Oregon Health Sciences University
From: Ed Gallaher <gallaher@mail.teleport.com>
(PS As an aside, technology is creating a new set of generation gaps.)
Example I.
School children were asked to form a circle and then rotate the circle
clockwise.
Kids: "Whats clockwise?"
Teacher: "Thats the way the hands turn on the clock."
Kids: "What are hands?"
Example 2.
Mom: "Would you tie a bow on that package?"
Billie: "Whats a bow?"
Mom: "Thats what you use to tie your shoelaces."
Billie: "What are shoe laces?" (looking down at his Velcro . . . )
To what extent does this require incorporating DT into the equation?
Is this good SD practice?
Wayne W and I have discussed this issue in the past and have never quite
resolved it. But this discussion rekindles some thoughts.
In the normal residential heating system we dont want the thermostat to
detect room temperatures to within 0.1 degrees, thus turning the furnace on
and off minute by minute. The average "system" is therefore designed to
maintain the temp within +/1 one or two degrees of the "set point". Any
more than this becomes noticeably uncomfortable.
Traditional thermostat:
Consider a traditional thermostat with a bi-metallic coil. Start with a
cool room. The coil contracts, hits a contact, turns on the furnace, and
the room begins to warm. With some delay, the coil begins to warm and
expand, releasing the contact and turning off the furnace. The room begins
to cool, starting the cycle again.
Rather than model one stock (room temp) and one on-off switch, I would use
two stocks. One illustrates room temp, the other illustrates the temp of
the bi-metallic coil.
The size of the coil, the amount of expansion per degree, etc. will
contribute to the "lag" in the system, thus damping the response of the
furnace to very small changes in room temp.
We could demonstrate this (physically, and in the SD model), by placing a
paper cup over the thermostat. The furnace heats the room, but additional
time is required for this information to get to the sensor. This lag leaves
the furnace on too long, and the room overheats before the coil gets warm
enough to turn it off. Once the furnace is turned off the room cools below
the desired temperature. Heat is trapped within the cup and the coil does
not turn the furnace on again until the room is well below the desired
temperature.
We have thus converted a comfortable system with a +/- 1 degree "dead zone"
into an uncomfortable system with a +/- 5 degree dead zone. More
importantly, we have captured the true dynamic structure of the system if
we model it in this way, rather than by using a mathematical on-off switch
to simulate the thermostat switch.
Question: Before continuing below, does the above analysis make sense?
High Tech thermostat:
We now have a digital thermostat at home. It has a semi-conductor
temperature probe rather than a bi-metallic coil.
(It is possible that this probe was designed with a very small mass and
therefore a very rapid time constant. If undamped this would lead to rapid
on-off cycles. OR the mass of the probe might be designed to take this into
account. I am ignorant about this design issue. Does anyone know the
answer?)
I bring this up because if the temperature sensor indeed has a very rapid
time constant, the damping might be introduced in software (or rather,
firmware). The damping might literally be produced by an IF-THEN statement
within the thermostat controller!
e.g. Algorithm says --> If the temp is rising, turn OFF at 71 degrees; if
the temp is falling, turn ON at 69 degrees.
These logic statements would create a dead band of +/- 1 degree around the
desired temperature of 70 deg.
Back to the philosophy and practice of SD modeling and simulation:In this
case the "correct" model would explicitly -require- the use IF-THEN
statements!
{BTW, I bought a "cheap" ($19.95) digital thermostat several years ago. It
was quite uncomfortable, with a dead band of at least +/- 2 degrees. After
a year or so I upgraded to a "deluxe" version ($29.95). Much better!}
This is an intriguing question, because I often use descriptions of the
familiar (and reasonably intuitive?) home heating system as an introduction
to mammalian thermoregulation. If my students are not familiar with
bi-metallic coils then the introduction becomes a bit strained.
Ed Gallaher
Oregon Health Sciences University
From: Ed Gallaher <gallaher@mail.teleport.com>
(PS As an aside, technology is creating a new set of generation gaps.)
Example I.
School children were asked to form a circle and then rotate the circle
clockwise.
Kids: "Whats clockwise?"
Teacher: "Thats the way the hands turn on the clock."
Kids: "What are hands?"
Example 2.
Mom: "Would you tie a bow on that package?"
Billie: "Whats a bow?"
Mom: "Thats what you use to tie your shoelaces."
Billie: "What are shoe laces?" (looking down at his Velcro . . . )