MATLAB: Thermal Systems Part 2

Heating Curve:

Using a given code in class, test_thermal.m, we ran our code producing the graph on the right.

Our graph ran for 300 seconds and paused every half second to plot the graph.

1: Calculating The Physical Constants

Using test_thermal.m from above, we took the slope at the beginning of the curve and the initial and final temperature to calculate the time constant: t = Rth*C.

• Rth = (deltaT / P) = ((R * deltaT) / V^2)
• used: change in temperature, voltage
• Rth = 6.9
• C = (P / slope) = (V^2 / (R * slope))
• used: voltage, resistance, slope
• C = 16.2
• t = 112.1

Our calculated time constant was 112.1 seconds and the temperature at that time should be 334.4 K.  The actual temperature from the graph above at 112.1 seconds is 338.6 K, which was a bit higher than expected, although still approximately 63.2% of the final asymptotic value.

2: Simulation

We modified the heatsim.m code by putting in our calculated values from above and resulted with the graph to the right.

The generated graph had a very similar curve to the our experimentally measured results from the initial test_thermal.m graph.

3: Bang-Bang Control

Magnolia, Vivian and I modified test_thermal.m to contain bang bang control with a target temperature of 340 K.

Compared to the behavior of last bang bang simulation, this simulation reached a close 340 K through smooth increase.  In Thermal 1, our bang bang started and stayed at 0 for a bit, immediately increased with no warning and once goal temperature was reached, began dropping and increasing in little segments.

Above shows the code and the graph produced from the graph.  Below shows the values of the temperatures at the plateau of the graph.

4: Proportional Control

error = target state - present state
setpower = Kp x (target - T)

We modified a second test_thermal.m code to include proportional control.  We ran the code for three different proportional gains: 0.05, 0.2, 0.5.  The smaller the proportional constant, the smaller the increase in temperature.  The larger the proportional constant, the more significant the increase in temperature of a system.


The proportional constant cannot be too big or it will act like bang bang control and will basically be on full power from the beginning and will stay on full power until when the target temperature is reached.

The optimal proportional gain constant is between 0.2 and 0.5 for the target temperature can be reached while using the power efficiently.

Reflection:

This activity allowed us to see the differences between simulations and actual experiments.  Although the numbers and graphs produced were very similar, differences were ubiquitous.  There are many limitations due to the natural nature of Earth causing the difference between actual and theoretical data.

Examples of thermal systems can be seen in many things we do everyday including heaters and air conditioners.  Having some control over them is important in creating and designing safe devices.