- #1
Aeroeri25
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Homework Statement
F = Fahrenheit
A particular temperature control system uses electrical heaters, exterior thermal insulation and a thermostat for maintaining the temperature at 170 F +/- 1 F. The thermostat turns the heater on when the temperature drops to 169 F and on at 171 F. Heater consists of a 3 ohm resistor supplied by a 28 volt source (1 watt = 3.4 Btu/hr). The heat capacity of the device is 0.1 But/F. Heat is lost to the environment by conductive heat transfer, the constant of the process being 3.6 But/F/hr.
(1)Prepare a block diagram of the control system.
(2) Sketch the variation of the device temp vs. time through a complete control cycle, for environmental temperature of 70 and -20 F, taking the initial temperature to be that of the environment.
(3) What is the lowest environmental temperature for which the desired temperature can be maintained?
Homework Equations
This is where I am having problems. None are given, maybe they were in the previous week, but i was out. I tried asking the TA but to no avail.
The Attempt at a Solution
I drew a block diagram similar to the attached picture.
Parts two and three aren't that hard if I knew the transfer functions in part 1.
When i solve for T(s) i get this:
T(s) = (Q(s)C(s)T_desired)/(1+Q(s)C(s)T_desired)
but my problem is finding Q(s) and C(s).
Any help on how to get started?