Deliverable 1:
A blog post (or section of a post) containing a MATLAB figure,
such as the one below, showing your experimentally measured heating curve along
with a derivation of the thermal parameters that you have deduced from the figure.
You should also document your time constant, and how the expected time for the
system to respond, based on that time constant, matches the actual time.
Our experimentally measured heating curve
Values deduced from the curve above:
Rth (thermal resistance) = 18.897 K/W
C (heat capacity) = 5.476 J/K
time constant = Rth * C = 103.479972 J/W (expected)
actual time constant = 63.2% (426.5633 K - 303.7299 K) = 77.6307 J/K
They didn't match because there were several areas of possible errors (such as the error from calculating the initial slope).
In physical terms, the time constant is defined as the time required for the system
to reach ~63.2% of its final asymptotic value.
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Deliverable 2:
Your modified heatsim.m program, which generates
simulated heating curve. Comment on the ways in which the results of the
simulation agree and / or disagree with the experimentally measured results.
Modified program. (Title should be %simulation of resistor.)
Plot for the program above.
Our simulated heat curve was a lot smoother with a steeper slope until the temperature stabilized. It was a lot smoother because in real life, temperature is constantly changing due to various factors, which is why the experimentally measured plot has more oscillations.
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Deliverable 3:
Implement a bang-bang controller in MATLAB with a target
temperature of 340 K. How does the behavior of bang-bang control in actual
thermal system compare to the simulation you did last time? (You’ll need to insert
the correct values of the thermal parameters into your simulation.) Include the
answer to this last question as a comment at the beginning of the MATLAB script
you submit.
The bang-bang control causes more obvious oscillations, which is reasonable. The heat curve above showed the heating of the metal resistor until it reached its hottest point. Here, with the bang-bang controller, we had a target temperature, and in order to reach that target, power was turned on and off depending on the "current" temperature at the moment (of course, there would be some delays).
Bang-bang controller program (We need to include more comments next time.)
Plot from our bang-bang controller
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Deliverable 4:
You should turn in your results, the main one being the graphical
comparison of the simulation and experiment. Provide a short description of each figure so we
know what the data are. You should also include the MATLAB scripts that you
used to create these figures, identifying the values of the heat capacity and thermal
resistance that you deduced. Also make sure to answer the bulleted questions
below.
• Can you explain why the system does not reach the control set point when
the proportional gain is small?
This is because if the gain is too small, the system errors or disturbances become significant and prevents the system from reaching the set point. Even when the error is large, not enough power is supplied.
• How does the system behave when the proportional gain is high?
When the proportional gain is too high, too much power is applied even when that amount of power is not desired (when the error is small). We do not want full or large amounts of power for the whole time.
• What seems to be the “optimal” gain setting for your system?
To determine the "optimal" gain for our system, first, we thought about the initial point. Our starting temperature was about 303K, while our target temperature was 340 K. This meant that the difference in temperature or our error was about 37K. To reach 340K, we needed full power which would be 100 (in percent but is actually 6.5 W in real life).
gain = 2.7
Our program for the Proportional Controller
Plot for the Proportional Controller
The proportional controller definitely had smaller, more unnoticeable oscillations than the bang-bang controller had. Also, compared to the experimentally obtained plot which immediately started heating up, the proportional controller had a smoother rise to this target temperature.
Our proportional controller (with blows)
You can see that the blows caused larger oscillations, but the temperature returned to 340K or a value close to 340 K, which was what we wanted.
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Deliverable 5:
Your final MATLAB script that controls the temperature of the system. Make
sure to add lots of comments explaining what your program is doing.
• Relevant experimental data, in the form of well-labeled graphs, from your
constant temperature hot-wire anemometer experiments. Your graphs should
make a compelling case for how well (or perhaps not well) your hot-wire
anemometer is working.
• Your simulation of a PI controller and a comparison to the experimental
data.
Our program using PI controller (both proportional and integral)
At first, we struggled with the gain values and noticed our target temperature was not reached or was surpassed. We realized that the "error" was significant in our "if then" statement because this "error" affected the integral error. (At first, we used integral error in our if then statement.) Also, we were initially experimenting with only the integral gain values. However, we realized we also had to change the normal gain (proportional gain) also.
Final Values:
proportional gain = 2 (slightly less than 2.7, which was what we used for our proportional controller)
integral gain = 0.35 (after experimenting with 0.2 and 0.5).
Plot for our PI controller
We noticed the oscillations were fewer and more spread out compared to our proportional controller and bang-bang controller. Also, compared to our experimentally obtained plot, this plot was a lot smoother.
Plot after blowing
The blow caused some oscillations, but the controller made the temperature return to a value close to 340 K, the target temperature. This plot looked similar to the plot created by the proportional controller after blowing.
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