Thermal Systems II

Michelle and I expanded Thermal Systems I to a thermistor system, which measures the heat dissipated across a resistor through altering the output system.

Deliverable 1: Heating Curve
Our first experiment was to determine the physical constants (Rth and C) from our simulated heating experiment in order to conduct our experimental run.

Using Rth = (T-Tair)/p and a maximum power of 6.5 V, we found the thermal resistance to be 2.05:
(313.25 - 300)/6.5 = 2.05 T/W. Also, C = P/(dT/dt) =  6.5/ [(3.5-312.3)/(100)) = 21.6 W/(T/s)

Deliverable 2: Simulation Differences
(Rth*C) = the time constant, or time in which it would take our system to reach 63.2% of its 'plateau' value:  (2.05)*(13) =  26.65. Our own graph was approximately less than 2/3 of the way to that point, so we were on the right track.

Deliverable 3: Bang Bang Controller
The simulation cleanly levels off and maintains a constant temperature, whereas the experimental situation has a much rougher incline, which could be because of a slight breeze from the environment. Unlike the simulation, the experimental graph fluctuates to different values around the desired temperature (like a realistic system).

Deliverable 4: Proportional Controller
We experimented with various proportional gains (.05, .2, and .5) and had to calculate the coefficients each time. We set up a proportionality ratio: 6.5/100 =  a.05/x. We found the coefficients to be: .7679 for .05, 3.077 for .2, and 7.692 for .5

The experimental system never reaches 340. When the proportional gain is small, the system does not add enough power to reach 340, but a large coefficient (like ~7.7) comes close.

 Deliverable 5: PI Controller
Simulation (Thermal Systems I)
A Pi Controller incorporates both integral and proportional control to achieve and maintain a certain temperature: P_desired = Kp * error + Ki * integral_error. At Ki = .5, we had to increase Kp to 11 for the system to reach 350K. Even when we blew on the resistor, the temperature remained pretty constant while the power fluctuated heavily. Unlike the last PI Controller, this controller did not fluctuate dramatically.




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