Thermal Systems II

Deliverables 1 and 2

The heatsim program produced a curve that has a sharper increase in temperature compared to the testthermal graph which is derived from heating the physical heater.  It appears that the physical heater increases at a gradual rate which makes sense given that metal increases its temperature at a gradual rate rather than at a sharp increase.

Using the formulas given to us from the previous lab and this lab, we determined that our heat capacity was 21.6W and thermal resistance was 2.05 if our heater ran at its maximum power of 6.5W
(313.25-300)/6.5 = 2.05 for Rth
C = P/(dT/dt) = 6.5/ [(3.5-312.3)/100] = 21.6w

Using the formula (Rth*C) to determine the time constant, the amount of time it would take to reach 63.2% of the heater's final temperature, we calculated that it was 26.65.  Our graph matches that estimate as well so we were assured that the values we calculated were correct.

Bang-bang control

In comparison to our heatsim, the actual heater yielded a much more gradual rise in temperature.  The heatsim program does not take material properties into account which is why the two yield different graphs. The difference is again most likely due to the fact that metal heats gradually rather than with sharp increases in temperature.

Proportional control
We used the gains given to us to calculate the varying coefficients for each time.  For a gain of 0.05, the coefficient was 0.7679; for a gain of 0.2, the coefficient was 3.077; and for a gain of 0.5, the coefficient was 7.692.  We also determined that the proportionality ratio was 6.5/100 = 0.05a/x

However, using gains of 0.05 and 0.2 were insufficient for the heater to reach its desired temperature of 340.  Using a gain of 0.5 yielded the closest result.  However, as we saw with using proportional control in the heatsim, using this type of control is insufficient for achieving our desired goal.

Heatsim with proportional control:

Gain = 0.05

Gain = 0.2

 Gain = 0.5 

PI Control
The PI control utilizes both proportional control and integral control to heat the system.  It initially begins with using proportional control but then uses integral control to counter the error that the system encounters.  Using this type of control, the system responded instantaneously to any error.  We used the formula given to us: P_desired = Kp * error + Ki * integral error.  To get the temperature to 350, we had to use a Ki of 0.5 and a Kp of 11.