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From: KING%KESTREL@sri-unix.UUCP
Newsgroups: net.physics
Subject: Re: Why don't thermostats work?
Message-ID: <16485@sri-arpa.UUCP>
Date: Tue, 7-Feb-84 12:18:00 EST
Article-I.D.: sri-arpa.16485
Posted: Tue Feb  7 12:18:00 1984
Date-Received: Fri, 10-Feb-84 03:17:03 EST
Lines: 64

From:  Richard M. King 


2)  A closed loop control system (such as a room-thermostat-furnace-room)
    regulates the "process" by creating an error term.  A thermostat
    is a relatively dumb control unit.  There must be an error in room
    temperature in order for the thermostat to call for heat.  The
    thermostat does not know how much heat is leaving the room, it only
    knows that there is an error in desired the temperature.  The average
    error will be proportional to the rate of heat loss in the room.  So,
    on colder days, the average room temperature will be lower.

	I think this is incorrect.  It would be correct if the thermostat
were "proportionally controlled", which means that it can set the furnace to
"partially on" as well as on or off.  In a proportionally controlled unit,
the heat generated (or, more generally, the equilibrium restoration effort)
is proportional to the error term.  The human body's temerature control
mechanism is proportionally controlled; you don't go from maximum shivering
to maximum sweating several times per day.  Indeed, as Jeff writes, there
are additional inputs besides body temperature.  Humans hypothalmi have skin
temperature inputs, and I recall in a Scientific American article a few
years ago that dogs have exercise transducers (but humans don't).

	However, a house thermostat has only an on/off setting.  Because of
this it has to have a hysteresis, or a range of temperatures over which it
will not change state.  Otherwise it would change state rapidly, reducing
contact life and furnace life.  If you set the thermostat to 20C, and it has
a hysteresis of 1C (a reasonably realistic number), it will start the
furnace at 19.5C and turn it off when the temperature has risen to 20.5C.
The anticipator is an attempt to account for the heat stored in the
radiator or whatever.

	Assuming that the difference between the indoor and outdoor
temperatures is large compared to the width of the hysteresis band, we
observe that the temperature will fall at a constand rate within that band
when the furnace is off, following which it will rise at a constant rate
when the furnace is on.  The average temperature is always halfway between
the ends of the hysteresis band.

	So why does the room feel colder when the outside is colder?  It has
been shown that a major reason is that the walls are colder, and a human
loses heat by radiation.  The thermostat is comparitively insensitive to
radiation for two reasons; the active elements do not give off heat when the
furnace is off, so they radiate a lot less than a person, and they are
usually enclosed in a little metal box which prevents them from "seeing" the
walls.  I've always thought that thermostats should be mounted on exterior
walls with just the right amount of insulation behind them so they would
take (a linear approximation of) the proper amount of notice of this effect.

	Minor note: if your home is heated by a "heat pump" (a central air
conditioning unit that reverses in the winter to bring heat INTO the house
rather than take heat OUT) the thermostat has not two but three positions;
no heat, heat pump only, and heat pump plus auxiliary electric resistance
heaters.  In this case, there are two hysteresis bands; the resistance
heater might turn off at 20C and on at 19.5C, and the heat pump might turn
off at 20.5C and on at 20C.  In this case, on a cool day the heat pump might
cycle on and off and the resistance heat might never run, making the average
room temperature (20+20.5)/2=20.25, and on a frigid day the heat pump might
run continuously and the resistance heater cycle, making the average
temperature (19.5+20)/2=19.75.  This form of heat is relatively rare.  Note
that it is "closer" to proportional control than the usual thermostat.

						Dick
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