Practicum 3A

The goal of this practicum is to generate Bode Plots that represent the frequency response of the robot’s vertical motion. You will send sinusoidal signals of varying frequency to the robot’s thrusters and measure their effect on the output.

Once the check is complete, the proctor will add you to the list of prepared students and inform you when it is your turn to go.

If it is not your turn to go to the test tank room, read the rest of the manual carefully so you can work quickly when you get to the test tank room, then:

a. Complete section 8

b. Complete section 7 with the sample data file FrequencyResponse_sample.xlsx located on Sakai.

Follow the directions below:

• With the VI not running, set the toggle switch to the down position, and set the PWM duty cycle to be 0. This constant setting of zero means that the robot should come to rest any time the toggle switch is moved to constant mode.

• Run the VI and name the output file FrequencyResponse_XX, where XX are your initials and set it to save to the desktop.

• Change the Frequency of the sinusoid to be 0.05 Hz, and set the toggle switch to the up position.

• Watch the robot move up and down in unison with the input signal shown on the top right chart of the front panel.

  • If your robot is not in unison with the signal then your motor may be plugged in backwards. If so, turn the toggle switch off, hit the reverse button, then turn the toggle on again.

  • Make sure the output signal plot (the pressure sensor voltage) is also showing a sinusoidal response as well. The axes scrolling may make this difficult, but make sure you observe steady up and down motion in the signal.

  • See the plots in section 7 for what you should be getting.

• Let the robot move around until it achieves sinusoidal steady state, and try to minimize any drifting of the robot. After a few cycles of sinusoidal steady state, set the toggle switch to the down position so that the input single to the thruster is no longer a sinusoid.

• Repeat this process with frequencies of 0.1, 0.2, and 0.5. Pay attention to the phase and amplitude of your robot's motion relative to the applied thrust.

• Stop the VI and, if the run was successful, find the output file on the desktop and move that file to a section-appropriate folder in My Documents. If the run was not successful, delete the output file from the desktop and try again.

• Save your files to a USB drive or to the cloud so you can take them with you.

• Return to your section lab room, and inform an instructor that another team can take your spot in the test tank room.

• Dry your robot and put your robot away, returning the top spring to the general stock.

Open your frequency response data file FrequencyResponse_XX in Excel.

REMINDER: The VI timer starts when you click run, but the time doesn’t start recording to the output file until you’ve chosen the name and directory for the output file. Because of this, the time column in the output file generated from the VI will have a near 0 number in the first row, then it will jump a couple of seconds in the next row and begin recording time normally from there. When you are looking at your data, delete the first row (with the near 0 time), then make a new column where you calculate the difference between the first recorded time after the jump and the current time in each row in order to get the elapsed time starting from 0.

Using your pressure sensor calibration equation from the module 2 Practicums, convert the pressure sensor voltage data to depth in meters. If you can’t find your equation, you can use the equation below. Note that every sensor is different and values will vary between sensors.

z = 0.648v - 1.54

Using Excel’s Chart type Scatter with Smooth Lines, plot the input signal sent to the thruster (% duty cycle) and the depth as a function of time. Since we want to compare the input signal to the output signal on the same plot, it may be easiest to plot the depth signal on a secondary axis. You can do this after plotting both signals by double clicking on the depth signal and, in the menu that pops up on the right, click on “series options” and select “secondary axis," or plot a scaled version of the depth signal. E.g. plot 5x or 10x the depth signal.

Using your experimental data, you will construct a Bode plot that includes both magnitude and phase as a function of frequency. Note that for these bode plots we are comparing a depth to the duty cycle of the input signal. We are assuming the input signal is proportional to the force by some constant (F = constant*(% duty cycle)) so this is effectively a bode plot of displacement to force scaled by some constant. However this does not change the frequency response, which is what we care about.

Some helpful notes

• Recall that you should plot magnitude in dB:

• Recall that phase between two sine waves is the ratio of the delay between the signals to the signal period, scaled by degrees (360 degrees in a period).

• To make your Bode plot cover more frequencies, assume that the magnitude in dB at 0.005Hz is constant and equal to the magnitude at 0.05 Hz. Assume the phase is 0 degrees at a frequency one generation lower than 0.05 Hz. Finally, assume the phase is -180 degrees at a frequency one decade greater than 2.0 Hz.

• The magnitude of your output signal at 0.5Hz may be less than the noise level of the signal. Hence the data may be unusable and you may want to throw it out

• Also, recall that we plot Bode plots as a function of frequency on a logarithmic scale, which is easier as a function of f for this practicum. To change your Bode plot to a logarithmic scale on the x axis, right click on the axis, select Format Axis… and check the Logarithmic Scale checkbox.

Add these plots to your submission sheet (Question 2 and Question 3).

Find or re-derive your differential equation (using lumped element modeling) that represents the vertical motion of the robot. Assume the forces acting on the robot include a buoyancy spring force kx, a damping force bx ̇, and a thruster force f(t). Write your equation in canonical form, and define any standard parameters, (e.g. ζ,τ,ω_n), as a function of mass m, spring stiffness k, and linear drag coefficient b. You should have values for these parameters from Problem Set 3B. You only need spring stiffness and mass for the straight line approximation.

Derive the frequency response function G(jω).

Use the spring stiffness that corresponds to the measured diameter of your PVC tube to draw the straight line approximation Bode plot for your system. You will need to know the mass of your robot with the top spring. As we saw in part 7, we are assuming the force is proportional to the duty cycle by some constant. For your straight line approximation, you will also need to assume that your thruster force is a function of the PWM duty cycle d_PWM (t)% given by:

where

Be sure to use the semi-log graph paper provided. Double check your Bode plot makes sense with an instructor. Don’t forget to take a photo of the plot and add it to your submission sheet (Question 4 and Question 5).

1. E79 Practicum Manual 2D

2. Full Parts List (below):