# Designing a control system for a heating system

1. Apr 12, 2009

### Aeroeri25

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

This is where im 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.

3. 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?

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