Frequency Response

I have finally finished processing all of the data and calculated the frequency, it ranges from 0 to a little bit above 2 Hz. The blue line is the motion of the KUKA, the green line above is the maching frequency.

 The plot below is the frequency response of the raw data. I am not very sure why there is this large spike towards the end of the graph.

I will now use these data to conduct a Bode Plot.

Constructing the Bode Plot

In the process of drawing a Bode Plot, I have construct a plot including 400 times the frequency of the KUKA and 100 times of the force data.

The x-axis marks the period of the peaks and troughs of the increasing frequency of the KUKA robot. I am assuming the rate of increasing frequency is constant within each period, using that to calculate the frequency of each point to plot the frequency response which leads to the Bode Plot.

The Bode Plot

Using the experimental data, a bode plot was constructed to examine the dynamic response of the probe. It requires the performance of the probe as well as the frequency at witch the system was moving at. As I do not know the transfer function of the system, I will need to use the experimental data along. After searching online, I have found a fast way of plotting, this requires an input frequency and measures the output of the system under that specific frequency. By changing the input, a set of output can be obtained. Plotting the output against the input would yield a frequency response of the system. In order to get a Bode Plot, the output need to be log transformed.

My problem is that I do not have an steady output for a specific frequency. The system is constantly adjusting its output while the frequency increases continuously. The best I can do is to calculate an average of the output for a period of time while dividing the constantly increasing frequency into blocks. As there are more than 55000 data points to go through, this may take quite a while.

Performance of the Probe

After studying the statistics obtained during the experiment, I found the performance of the probe is not as appealing as when it is hold vertically. I have taken all the components apart and trying to figure out why. I think there are a few causes. Firstly due to the nature of the motor and the spindle, when there is no force applied on them, the tolerance in between the two components works fine. However once a force perpendicular to the tolerance is applied, it forces the motor and spindle to come in close contact in one side but with lose tolerance in the other. This in fact would lead to inaccurate performance of the motor that the output speed does not equal to the desired speed when it is high. The second conclusion I draw is that as the probe was hold horizontally, the feeling of the same force to me is different to when it was held in a more vertical fashion. Human error may have also been introduced in the experiment. As it is sometime necessary to hold the probe horizontally during a ultrasound examination, how to increase the performance of the probe might be a development point.

Filtering the Experimental Data

As the vibration of the motor induce vibration on the sensor, it needs to be taken out of the raw data. This will need a high-pass filter.

To remove the vibration of the motor from the experimental data, I use a low pass filter which has a Matlab function of "function y=lowp(x,f1,f3,rp,rs,Fs)". In which x is the input, f1 is the frequency at the start of the pass band and f3 is the end of the band. rp is the cutoff frequency for the point 3 dB point below the passband value and rs being the cutoff frequency for the point 6 dB point below the passband value. Finally, Fs marks the sampling rate of the filter.

I have also involved a high pass filter to remove the shaking of my hand holding the probe, the function is essentially the same, "function y=highp(x,f1,f3,rp,rs,Fs)".

After applying the filters, the experimental data are plotted.

The first figure is increasing frequency and the second is increasing amplitude. It can be seen in both figures that the the early stages where the change is small, the probe could maintain a relatively constant level of force. It could also be observed that the probe performs better when the change is in frequency.

Experiment Result

The experiment was taken place on Monday with the help of Yang and Lin. The KUKA robort was facing downwards originally, as I explained what I would like to do, Yang tried to move the end-effector upward. Yang struggled for nearly twenty minutes but it was unsuccessful in the end. The best we could achieve was to have the end-effector perpendicular to ground, thus the end-effector moves parallel to ground. In this case, I had to held the probe away form its normal position but lying down. Due to the tolerance in between the motor and the spindle, stronger vibration could be felt immediately.

In the first experiment, we have set the KUKA to oscillate with increasing frequency. We started slow, having it move one cycle per second. The performance of the probe was very good. However, as we increase the frequency to 5 cycles, the performance started to degrade. This started  earlier than I originally thought, after a little fettle around, I discovered having the probe in a flattened position decrease the effective speed of the motor. I tried to increase the speed in the program to improve the performance, however this also introduced some extra vibration to the system. With the vibration, the raw data looks very noisy, they need to be filtered before moving onto plotting a Bode plot.

In the second experiment, the probe was set to follow the motion of the KUKA when the position of the holder was kept constant. The probe followed the end-effector closely with a phase shift.

Experiment Plan

After a discussion with my supervisor, we believe building a system from scratch and install a force sensor is too time consuming, using an existing system is a more effective option. The KUKA robot has been incorporated widely with a number of other projects, it has a force sensor mounted on the end-effector. The now plan is to press the probe against the sensor while oscillating the end-effector. Two tests will be carried out, one with constant frequency with increasing amplitude and another with constant amplitude but to vary the frequency of oscillation. Both data from the external force sensor and the load cell on the probe is to be recorded. I will need to find out how to export data from the serial monitor of arduino to a manageable format like excel.