The IR transmitter datasheet can be found here:
https://www.fairchildsemi.com/datasheets/QE/QED123.pdf
Similarly, the photo-transistor datasheet can be found here:
http://datasheet.octopart.com/QSD123-Fairchild-Semiconductor-datasheet-12521714.pdf
This picture is of the second order fan system. The pennies are glued to the blades in order to slow down the feedback response time, allowing for a true second order system. The IR transmitter and photo-transistor can also be seen at the base of the fan blades facing each other looking through the fan.
Figure 1 above.) Second order fan feedback system
This is a better picture of the IR Transmitter diode and the photo-transistor facing each other. During operation, the flan blades spinning will interrupt the stream of IR light to the photo-transistor, causing it to short to ground and drop the voltage to the DMM to 0. The rate at which the blades are spinning is directly proportional to the switching frequency of the photo-transistor, and is the basis measurement for the digital feedback. Also good to note that with the simple DC operating fan used in these experiments, the voltage supplied to the fan will be directly proportional to the rpm of the fan.
Figure 2 above.) Side view of fan, IR transmitter and photo-transistor facing each other for operation.
The following schematic represents the circuit for the fan feedback system. In the experiment, R1 was 47 ohms and R2 was 100Kohms.
Figure 3 above.) Schematic for fan feedback system
The Fan Feedback schematic and simplified transfer function is depicted in the following picture.
Figure 4 above.) Transfer function for Fan Feedback
The following graphs and captures were taken using a LabView VI created by professor Birkett, used as the digital feedback implementation controlling the fan speed based on user inputs as well as the electrical measuring equipment inputs.
This is a screenshot of what the fan feedback VI looks like and how it is used to control the speed of the fan.
Figure 5 above.) Screenshot of the fan feedback VI
The first parameter necessary for our feedback system is the sensitivity of the fan. The sensitivity is a measure of how much the rpm changes in respect to the change in voltage supplied to the fan. This can be accomplished with a simple voltage sweep over the fan while measuring the frequency of the changing photo-transistor, which can be directly related to the rpm of the fan. The slope of this curve will be taken as the sensitivity.
Figure 6 above.) Frequency of photo-transistor signal vs Voltage to fan
This graph is the derivative of Figure 3, that is it is the measure of the change in frequency of the photo-transistor signal vs the change in voltage supplied to the fan.
Figure 7 above.) Change in frequency of photo-transistor signal vs change in voltage supplied to the fan
Next, since this is a second order feedback system, the actual response of the fan to a change in set rpm can be graphed along side the set frequency and the time constant for the system determined based on the Loop gain parameter used. For the time constants calculated in the following graphs, a sensitivity of 11.65 was used because that was the theoretically calculated value before running the previous testing. The time constant for this system was calculated to be 8.4 seconds
Figure 8 above.) Fan response at loop gain of -0.01 and resolution at 1.4 seconds
By changing the loop gain, the response of the fan system will also change. The smaller the loop gain, the faster the system will stabilize the fan at the desired speed. The time constant for this loop gain was found to be 6 seconds
Figure 9 above.) Fan response at loop gain of -0.02 and a resolution at 1.4 seconds
This graph represents the response of the system at a loop gain of -0.04, and is the fastest response thus far. The time constant for this loop gain was calculated to be 2.8 seconds
Figure 10 above.) Fan response at loop gain of -0.04 and a resolution at 1.4 seconds
The next loop gain of -0.1 was not required for the class, however since our fan was extremely sluggish, we decided to try a loop gain this low. The results were very interesting and yielded the fasted response time of any test, with a calculated time constant of about 1.4 seconds.
Figure 11 above.) Fan response at loop gain of -0.02 and a resolution at 1.4 seconds
The next section will be the Matlab step responses and Matlab code used to generate the plots for the step responses.
Figure 12 above left.) Response at a gain of 0.01 Figure 13 above right.) Response at a gain of 0.02
Figure 14 above left.) Response at gain of 0.04 Figure 15 above right.) Response at gain of 0.1
The next section will show the root loci plots and matlab code for the system responses at the different gains. These plots will show the dampening and stability of each system. If the x's on the plot lie to the left of the vertical axis, the system is stable. If there is only one x on the plot, the system is critically damped. If the x's both lie on the horizontal axis, the system is over damped. If the x's lie vertically, then the system is under damped. For the following responses in Matlab it is seen that all of the generated plots predicted a stable under damped system.
Figure 16 above left.) Zplot for loop gain of 0.01 Figure 17 above right.) Zplot for loop gain of 0.02
Figure 18 above left.) Zplot at loop gain of 0.04 Figure 19 above right.) Zplot at loop gain of 0.1