Matlab 3, Thermal Systems Part 2

So in part 1 we simulated coffee cooling, and now we are going to actually test it.

Deliverables

1: experimentally measured heating curve 

First we found Rth and C (correct calculations at the bottom of the page)

 We found our values [ C=5.7 J/K an Rth=19.23 K/W) and then solved for Tau, which equaled 109.6 seconds. As expected this was about 62.3 % of our asymptotic value. 

so looking at the graph, it is 2/3s done heating at 110 seconds

other variables:
Tair = 317 K      T (300) -= 442K

Though our graph only goes until 300 [the time we wanted] matlab actually measures until 311 seconds

Deliverable
2: Simulated heating curve

Here is the simulated graph. Our graphs have similar shapes except the simulation more perfect. The original graph has a few seconds delay before the heat has an effect on the 'coffee'. Also our final temp was 433K in the simulation vs 442K in the actual test

3: Bang-­‐Bang control

So here we used Bang-Bang control to control the temperature. Instead of the temperature rising or falling and overshooting, we used bang-bang control to more or less keep the temp constant. We added an If-Else statement telling the system to add power if the temperature is below 340K and to set power to 0 if the temperature is above 340K. In our graph, our temperature started above 340K so it decreased until it hit 340K- though technically below 340K. Bang-Bang control has the tendency to overshoot its target, especially if it has high levels of power, so even if the system turned to 0 power at 340K, the residual power would affect the temperature. This creates the up-and-down zig-zag- it bounces up and then at a slower rate cools.