A while back when I was working on tuning the control loops for the expressive degrees of freedom of our robot I thought I’d make a video showing a more fun example of classical controls tuning when you don’t know your system than what I typically see in classrooms.
For this, I’m using a DC motor as an actuator, hall effect quadrature encoder for position sensing, ROS with rqt_plot to visualize the position input and output, dynamic reconfigure to change the control gains, and have a few python scripts to generate and publish reference trajectories.
Step Response
I begin by just publishing a reference step function between 0 and 600 encoder ticks and start twiddling control gains! I’m doing this as quickly as I can to illustrate that you can tune things without actually looking at time domain step response parameters like rise time, settling time, etc.
PID Tuning Via Step Response
Note: at 3:27 I mispoke and say “proportional term” when I actually meant “integral term”.
Frequency Response
After first tuning my gains via visual inspection from a step response, I move on to a frequency response to illustrate what tracking of a varying frequency sinusoidal position input looks like.
The basic thing that I’m trying to convey to students is that the rise time and overshoot from our step response can in a way be translated to our frequency response. When the inverse of the frequency is faster than our rise time, we begin to see that the magnitude of our frequency response decreases. When the inverse of the frequency is at about the time that we see an overshoot in step response we begin to see the beginning of a resonant peak in our frequency response.
Frequency Response
Putting It All Together
I’m just kidding, this is me goofing off, but system dynamics and controls don’t need be dry and boring! Ignore the commentary, we were delirious from working long hours.
OK. This one was SUPER annoying to debug, but basically what was happening is the controls for some D.O.F.s of a previous product looked really bad, almost like we were missing encoder ticks. Looking at the position control loop, it certainly looked like we were missing ticks, but where did they go?
Since we were using ROS for trajectory generation I basically worked my way from that level down, figuring that computational burden was just causing us to not be able to keep up with things in real time. After working ALL THE WAY THROUGH the software side and concluding everything looked fine, I had to turn to the motors and encoders themselves. Now, unbeknownst to me, we had just changed the model of the magnetic disc we were using as an encoder (paired with a hall effect sensor). With almost everything else tested, I resolved to test the magnetic (B) field strength of the magnetic discs.
Experimental Setup
Magnetic field strength of the permanent magnet encoder discs were characterized as a function of angular position using a quadrature encoder and digital Gaussmeter. Discs were mounted via very small 3D printed couplers to a Koyo TRD-MX1024BD quadrature encoder to measure angular position, while B field strength was measured with an F.W. Bell 5180 Gauss meter. The disc was then rotated by hand while the Gauss meter probe was fixtured so that it was in contact with the disc surface. Data was collected with a Saleae pro 16 logic analyzer. The encoder was powered with 12 v from a benchtop power supply, and outputs of the A, B, and Z channels were pulled up to 5v via a 1.5k ohm pullup resistor.
After data collection, data sets were analyzed by python scripts that extracted one full revolution of B-field strength and angular position, matched the angular position in 0.1 degree intervals using a binary search tree, filtered the data, extracted local extrema, and carried out statistical analysis on the identified positive and negative magnetic poles. The test apparatus is shown below, without the rigid fixture between encoder and Gauss meter. Data collect showing A, B, Z channels of the encoder and B field strength from the Gauss meter are shown on the screen.
Output Plots and Analysis
Let’s begin by looking at some of the magnetic discs that we used in the past that have not given us any trouble.
Good Magnetic Disc
POSITIVE POLES: Angular differences between positive magnetic poles (degrees): [ 29.1796875 29.35546875 30.9375 31.81640625 30.76171875 30.5859375 29.53125 31.81640625 31.55273438 26.015625 27.59765625]
Magnitude differences between positive magnetic poles (Gauss): [ -31.06543128 -37.91607879 48.9585365 -13.01091485 55.52667332 -25.77534475 139.50712186 -107.25554613 1.97638668 73.26621106 -42.15276701]
Magnitudes of positive magnetic poles (Gauss): [ 803.04389588 771.97846459 734.0623858 783.0209223 770.01000745 825.53668077 799.76133602 939.26845788 832.01291175 833.98929843 907.2555095 865.10274249]
Standard deviation of difference in angular position of positive magnetic poles (degrees): 1.75035138526
Standard deviation of difference in positive magnetic field strength (Gauss): 65.0042394818
Standard deviation of positive pole magnetic field strength (Gauss): 56.6024562212
Mean magnetic field strength of positive poles (Gauss): 822.086884405
Mean angular displacement between positive magnetic poles (degrees): 29.9227627841
NEGATIVE POLES: Angular differences between negative magnetic poles (degrees): [ 29.70703125 30.05859375 31.20117188 31.55273438 30.76171875 29.8828125 30.14648438 30.84960938 30.76171875 26.3671875 27.24609375]
Magnitude differences between negative magnetic poles (Gauss): [ 56.61348071 -26.47935011 -17.37341869 -51.85460574 46.539964 -1.21482977 -78.56630343 45.94343868 -91.39098625 40.87246128 18.49249138]
Magnitudes of negative magnetic poles (Gauss): [-808.25615348 -751.64267277 -778.12202288 -795.49544157 -847.35004731 -800.81008331 -802.02491308 -880.59121651 -834.64777783 -926.03876408 -885.1663028 -866.67381142]
Standard deviation of difference in angular position of negative magnetic poles (degrees): 1.55056517428
Standard deviation of difference in negative magnetic field strength (Gauss): 49.9112757447
Standard deviation of negative pole magnetic field strength (Gauss): 48.8189412974
Mean magnetic field strength of negative poles (Gauss): -831.401600587
Mean angular displacement between negative magnetic poles (degrees): 29.8668323864T
Bad Magnetic Disc
And now, let’s take a look at a representative “bad” magnetic disc.
Woah, it looks like there’s a big difference in B-field strength here…
POSITIVE POLES: Angular differences between positive magnetic poles (degrees): [ 22.41210938 23.37890625 23.203125 22.32421875 22.06054688 24.08203125 21.62109375 23.37890625 21.88476562 22.93945312 25.6640625 18.80859375 22.93945312 22.8515625 21.62109375]
Magnitude differences between positive magnetic poles (Gauss): [ -47.8981468 -29.24181437 -56.77963869 -104.24687756 16.93935508 -48.46134758 -28.67192289 81.30195449 22.73229587 80.86085334 69.16778126 -1.74263368 87.44192205 -1.72612453 5.0340433 ]
Magnitudes of positive magnetic poles (Gauss): [ 480.6194911 432.7213443 403.47952994 346.69989124 242.45301368 259.39236876 210.93102118 182.25909829 263.56105278 286.29334864 367.15420199 436.32198325 434.57934957 522.02127162 520.29514709 525.32919039]
Standard deviation of difference in angular position of positive magnetic poles (degrees): 1.42966348597
Standard deviation of difference in positive magnetic field strength (Gauss): 55.7923451036
Standard deviation of positive pole magnetic field strength (Gauss): 112.811684507
Mean magnetic field strength of positive poles (Gauss): 369.631956489
Mean angular displacement between positive magnetic poles (degrees): 22.611328125
NEGATIVE POLES: Angular differences between negative magnetic poles (degrees): [ 23.203125 23.11523438 23.29101562 22.93945312 21.4453125 23.5546875 23.02734375 22.58789062 22.06054688 22.32421875 23.11523438 23.29101562 21.26953125 20.7421875 24.43359375]
Magnitude differences between negative magnetic poles (Gauss): [ -31.87032808 61.11857653 16.26178864 122.02554834 2.7446541 80.43354251 -28.80379618 72.50021235 -75.90017174 -51.9568724 -61.59044252 -43.34832509 -25.8054608 -36.74159058 -54.81136214]
Magnitudes of negative magnetic poles (Gauss): [-521.8299272 -553.70025528 -492.58167875 -476.31989011 -354.29434177 -351.54968767 -271.11614517 -299.91994134 -227.41972899 -303.31990073 -355.27677313 -416.86721565 -460.21554074 -486.02100154 -522.76259212 -577.57395426]
Standard deviation of difference in angular position of negative magnetic poles (degrees): 0.938524830477
Standard deviation of difference in negative magnetic field strength (Gauss): 58.5461130337
Standard deviation of negative pole magnetic field strength (Gauss): 105.59001526
Mean magnetic field strength of negative poles (Gauss): -416.923035904
Mean angular displacement between negative magnetic poles (degrees): 22.693359375
Indeed, upon further verification we were missing that low B-field magnitude tick.
Conclusions
After repeating the tests on 15 magnetic wheels from each class, it was determined that all of the new, supposedly better, magnetic wheels were causing us to miss ticks due to their very non-uniform B-field strength.
The amount of time that it took to debug this was a VERY annoying setback for the control systems, one that I have not had to deal with before. With this discovery there was quite a bit of back and forth with the vendor, to say the least. Ultimately, due to timeline compression, we had to proceed using the same vendor, but used the “old” discs as they appeared to have better quality control.
