Systems (Intro): From Circuits and Buildings

Howdy from the homefront!

I’ve had a lot of experience with systems since the beginning of freshman year. I am currently working for Doctor Tolle on control systems, we learned about them in differential equations, derived them in circuits 1, had to create them from scratch in mechatronics, and finally are required to know how to derive transfer functions and make bode plots from circuits in circuits 2.

One thing that is consistent with every professor here is that they do an awful job explaining systems. I don’t know what it is. They can perfectly explain away differential equations and phasors but the second we try to tie the two together, there’s a major gap that’s left.

That’s the purpose of this post is to aid future SDSM&T students in the solving and deriving of systems.  I’ll first approach systems from a circuits point of view (since I’m an EE), later I’ll be transitioning into more physical examples.

This tutorial expects you to have taken circuits 1.

Let’s get started:

The circuit below is what is called a low-pass filter. In other words, it only lets low frequencies pass through undistorted and unattenuated.low pass

With this type of filter, we incidentally create a first-order system (but let’s not think of it as such just yet). As a result, our output will always differ from our input in both phase and magnitude.

What we’ve just done was create a voltage divider in the phasor domain.

CodeCogsEqn
Voltage divider in the DC domain.

 

Practically, we use this configuration for filtering out noise in a DC circuit or smoothing a rectified sine wave into a more DC-like signal.

smooth

 

First, lets model and solve this circuit in the phasor domain. If you’ve taken circuits 1 (from Montoya) this should be second nature and therefore the easiest way to solve. It goes as follows and is exactly the same as voltage division above. This method, also, gives us phase information.

CodeCogsEqn (1)
Phasor Voltage Division

Let’s take the same circuit from above and apply various frequencies (ω) and see what happens to the amplitude and the phase of the output waveform. For this example, we’ll use a 4.7μF capacitor and a 1k resistor.  The input waveform will be 15sin(ωt). Pay special attention to  the magnitude and the phase shift.

for ω=20

CodeCogsEqn (3)

for ω=200

CodeCogsEqn (1)

for ω=2000

CodeCogsEqn (2)

Congratulations! You’ve done a really low resolution frequency response analysis. These are important because now you know how the filter will respond to different input frequencies.  You can use this data to help determine the correct resistor-capacitor combination for your filter. And while it isn’t entirely useful to plot this information with first order systems, I’ll use this as a segue into Bode Plots because they’re entirely important for systems greater than 1st order.

As mentioned earlier, the data we collected from the three ω values gave us a low-res view on what the frequency response of that circuit looked like. But what happens if we take a bunch of magnitude and phase information and plot it? Well that’s a bode plot!

bode

As you can see, our low pass filter is doing exactly that, passing the lows! At very low frequencies there is essentially no attenuation or phase distortion (just how we like it) but the high frequencies dramatically drop out of the output signal. While this graph sure is pretty, it doesn’t tell us much that we didn’t already know or could easily find out. They do have their uses, however for higher order systems!

Part 2 will cover a second-order system example. Please let me know what you think or what I should improve on!

Ultra-Mega-Super Project Update for the Blog

Howdy everyone! The semester is over, has been for a week now. Been busy getting things checked off of my to-do list, as far as projects go. Most of the projects are blog worthy!! So instead of posting promises I can’t keep, this entire post is filled with real pages of projects!

(Click on the pictures to go to the respective pages)

I’ve been working on a business:

business

System Projects:

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Magnetic Flux Field Scanner
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Laser Keypad
DSC03170
I updated the page for Lux Æterna
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Meteorite Necklace
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Boris the .50 caliber cannon
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MK III (The Beam Lab)
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Inverted Pendulum for Automated System Identification
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Why do digital if you can do it easier with analog?
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Bullet Proof Wallets
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Ratchet the Tape Library

 

Untitled
Water-Analog Molten Salt Reactor

 

 

Culinary Projects:

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Dippin Dots
eggs on a cloud
Eggs on a Cloud
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COOKING WITH SCIENCE!!! (Sous Vide)

 

Differential Equations Tutoring Series:

This section is still in progress. I kind of got overwhelmed during the semester and stopped.

Tutoring

This update took me two solid work days to complete. I hope you’ve enjoyed clicking through my projects so far. I’m going to do a much better job blogging as I go. It’s much easier to keep a page private and add to it as I go and then publish than it is to try to remember everything about every project I’ve worked on for the past two years.

God Bless, Merry Christmas,

-Conrad

But You’re Catholic…

“…how can you be a scientist and a Catholic?”

Surprisingly, this is a question I often encounter and I’d like to address it with the following three images and a short explanation.

georgelemaitre
George Lemaitre – Father of the Big Bang
Gregor_Mendel_oval
Gregor Mendel – Father of Genetics
Br. Consolmagno
Guy Consolmagno – Carl Sagan Medal Winner

 

There is a plethora written on the subject of “faith vs science”, however I am writing this as a short primer/response to my personal friends (the ones who read my blog anyway).

There is this stereotype that asking questions in religion is discouraged. In some denominations, it makes sense.  In Catholicism, there’s an entire order (the Jesuits) dedicated to research and education in both our faith and the physical world. In fact, two of the three men shown above are Jesuits.

What it all boils down to: The search for the truth will never contradict the truth that God is.

The only time this search is forbidden is when it is immoral. Fetal stem cell research, for example is grossly immoral and unnecessary.

[2275] It is immoral to produce human embryos intended for exploitation as disposable biological material.
[2295] Research or experimentation on the human being cannot legitimate acts that are in themselves contrary to the dignity of persons and to the moral law.

The USCCB goes into greater depth on both of those short snippets, but they’ve been truncated for brevity’s sake.

My faith is exactly that, faith, but it has withstood the crumbling of entire empires and the test of time. There should be no contradiction between my faith and my yearning for the truth, save for the methods used to obtain said truth.

I’ve closed comments (and will continue to keep them closed) on all of my posts pertaining to religion as it is all to easy to get on a tangential-debate that I don’t have the will to entertain. If you have legitimate questions, I am sure there have been terabytes written on the matter.

The Seven Stages of Project Development

Denial

T=0 hours

“I need you to ________”

Your first thoughts are “Oh yeah this’ll be easy.”

You get a basic sketch drawn up, and begin hunting for parts.

initial
I <3 OneNote and LaTeX

 

Pain

T=40 hours

The parts you’re wanting don’t spec up to the others. The design gets revised. Nothing unexpected. You never typed an A+ essay the first time.

second
Okay we need more supports…I get it.

 

Anger/Panic/Insanity

T=120 hours into the project you’ve come to regret taking on this “weekend project” that started out as a joke. More revision requests come in and you only have a week until the expected date where you present the DATA you’ve gathered on your project. You still hold out hope that you can source the parts, next-day air them, and assemble the experiment on time. Your file naming and revision hierarchy has gone to hell in a handbasket.

file paths
Now was it DoYouWantToBuildAPendulum/OkayBuild/SW Parts & Drawings/FlatpackPendulum or DoYouWantToBuildAPendulum/OkayBuild/SW Parts & Drawings/FlatpackPendulumFinal? Which revision is this??

Depression

T=160 hours the conference is over, you brought what you could to the table. You presented the concept. Nobody seemed too interested, and the project is still nothing more than a CAD drawing nicknamed “McPendulum”

mcpendulum
The customer is always right. Keep repeating that to yourself. The customer is always right.

Reconstruction

T=240 hours.

“This looks good! Let’s build it!”

Finally satisfied with your design, the boss signs off on the quickest possible method of construction, because, you know, the project is 3 weeks late. You begin construction and the project is starting to look acceptable.

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“You’re the guy who brought in $200 in gold coins for the deposit on the liquid nitrogen. Don’t worry about the deposit. We’re sick of holding on to those.”

Acceptance

You’re behind time, but thankfully not over budget. The conference is long over and the school year has started so you’re only able to put in what time you can put in between studying and sleep.

20140926_132523

Hello Kitty Bandaids: Because rounding corners removes an opportunity to shame the injured.

Don’t freak. Focus.

This summer has been an amazing experience for me in learning how to professionally develop projects and see them through to the end. I’ve never been one to shift the blame to anyone other than myself when it comes to my own failures. This project did have a lot of its own unique obstacles, and I’d say I did fairly well considering the circumstances of starting two weeks late, working with another researcher on another project, working with another researcher on yet another project, revising and finalizing various PCBs, and babysitting mentoring. Currently, the pendulum project is nearing completion, and is in it’s early stages of testing. If you’re interested in learning more about the systems experimentation platform, I will have a page for it after the apparatus is up and running.

What I learned:

  • Multiply all projections by 3
  • Time management
  • Have fun (see below)
  • Have even more patience
  • Solidworks is unstable on school-sponsored laptops
  • Save often and to multiple locations

Have Fun!

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My buddy Adrian next to my buddipole.
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Amanda, Jack, and David at Hippie Hole.
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Father Sparks with a 3D printed version of himself.

Boldly Going Where No Man Has Gone Before

It’s not really that bold, but it is pretty cool. I’ve been doing research under my professor throughout the entire year and right now progress has slowed to a halt, but I have gathered some interesting data so far! Right now we’re working on a magnetic flux leakage material evaluation method. The technology isn’t at all new, but how we’re going to be applying the method is entirely novel.

The application will not be discussed here.

It all started with Ghettoscanner, my three-dimensional topographic mapping scanner.

V1 was ugly as sin, but it worked.

And ended with Ghettoscanner 2.0, my three-dimensional magnetic flux scanner.

2014-03-06_01-08-37_862

I have an entire page I am preparing on ghetto scanner and its uses, but for the purpose of brevity, Ghettoscanner 2.0 is able to take “layers” of measurements, and software I wrote takes that data and compiles it into images.

WE CAN USE THIS TO SEE THE UNSEEN!

Mapping has been done before using a different method.

Three-Dimensional mapping (my approach)? Never been done outside of simulations and calculations. Neat.

There is a lot more work to be done in the way of processing the data into an actual three dimensional model (lots-o-vector calc), but as of a few months ago, I was able to compile the slices of the field into various .gifs which gave a really neat visualization of the field.

RECRIPROCATING100bigscan

Above are the fields, as measured (no altering of the data)

highcontrast RECRIPROCATING

Below are two more scans with a contrast function implemented to better pronounce the field.

I collected around 5 megabytes of data per slice stack. This doesn’t sound like much, but when you break it down, that’s 180X180X100 points of data, 3,240,000 points. Not really bad for servos.

I still have a long way to go before I get any decent data, such as correcting the strange overlap in my scans, and finding the actual magnitudes of the flux by implementing the other 3 axis of measurement I have available.

As soon as I stop being lazy, I’ll have new software written in C++ that will turn my point cloud into an .STL file.

The Tribulations of the Scatter-Brain.

I have, sitting in my post queue, about 5 really awesome projects that I’ve mostly finished. They’re not ready to publish yet because they are not up to the quality that I want them at. They should hopefully be finished up here-fore-too-long. With any hope you’ll be able to see some of the neat work I’ve been doing.

Like how I got this scan of Han Solo...
Like how I got this scan of Han Solo…

If I have one piece of advice for you all, it’s to just pick one project and finish the darn thing.

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Seriously, I sous vide’d some hamburgers today. Like I didn’t have enough on my plate already *ba-dum-tss*

“Get it working, get it working better, make it pretty.” -David H.

The pit I am in is deep. It’s a really cool pit, but it’s deep. And if I don’t craw out of it (I.E. finish my projects) then I’ve successfully wasted an entire year’s worth of time toiling about with proof-of-concept projects, but no finished products.

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My wallets can stop bullets…but they’re not ready to be pitched yet!

How all of you guys blog regularly is a complete mystery to me. I feel like I have a decently rigorous course load, combined with my extracurricular activities (learning LaTeX as of recently).

"Rigorous."
“Rigorous.”

Provided I am actually able to focus, I can turn out an entire system in a night. One of my projects was an XY plotter with a piezoelectric topography sensor I designed around two servos I had lying around. The proof-of-concept materialized right in front of me in a matter of 8 hours (designing, printing, and coding). I’ve since then spiffed up the design, and am working on publishing it on Thingiverse before somebody else decides that they can 3D print something that works around servos.

V1 was ugly as sin, but it worked.
V1 was ugly as sin, but it worked.

That’s it for now, I’m hoping I can push aside my filled schedule (looking at funny pictures of cats) to do some more posts, because hey, why not?

Warmest regards,

-C

 

 

 

Sexy Axe Murderers, Lab Entertainment Systems, and My First Semester of College

As finals draw near I am constantly in awe as to how fast time flies when I’m busy. These past months have all been blurred together which has caused me to abandon some of my projects (this website included). All I can say is WOW! I’ve been welcomed into my department and have been offered new opportunities! I’ll divulge a little later this month in the event that I remember to blog. Spiritually, I’ve never been stronger which blew my expectations of this school out of the water. Like any institution there is more than enough to complain about, but I’d say that I’m making the best of it by picking the brains of my professors.

As far as being busy, it isn’t so much the work load of school as all of the extra projects I’ve taken on.

I’m happy I started out with a smaller work load as it has allowed me to design, build, and program my mechanical fusor controller.

After spending several nights designing, printing, editing, and reprinting the design. I showed it to my professor who kindly said “That’s cute, now use a DAC.”

I’ve since abandoned the fusor as there is no reason the jump through the hoops of bureaucracy to “just run the thing”.

 

In between work on the fusor and school I managed to work on a bunch of personal projects which included the coolest beanie cap on campus, a lab entertainment system, and an axe murderer costume that I wore pretty well! On top of all of this I am on board with the school’s first hybrid rocket project and the HAM radio club. Can you say exhausting?

 

The cellphone allows me to draw energy from the atmosphere and recharge faster.
The cellphone allows me to draw energy from the atmosphere and recharge faster.

 

Granted, none of this is even close to what my friends over at RIT, MIT, or any of the other 3-lettered institutions are experiencing for a work load right now.

Here’s some eye-candy. I’ll start posting the cool stuffs as semester break rolls around!

sexyaxeman  beanie     A real chick magnet I tell you what. .

 

 

Nuclear Farnsworth Now Powered by Arvixe!

So I finally left the house both physically and electronically. All of my projects and hobbies have been transplanted to the South Dakota School of Mines and Technology. After I got everything unloaded, I saw a professor attempting to access my slow server. Since I already had purchased a professional server (and 6 domains/websites) I figured I would transfer everything over and use this always-available, reliable, maintenance-free resource. At $8/month it is a little pricey, but I will also be piggybacking other organizations’ websites on this server (hence the 6 slots I purchased) and that should be enough to pay for my blog, their blog, and all of hair I will be saving not trying to kick an old computer back into service.

I am honestly looking forward to putting more projects on here (and there are quite a few good ones). There will be some free time I will encounter once I get settled into this collegiate groove. As for now. Enjoy the new speeds!

arvixe

Fantastic company! Check them out sometime!

The Blog That’s Not Updated Often Enough To Be Read

Here we (my, myself, and I, and probably you) are. Several months from my last post looking back and asking myself…Where are all of the cool things? I keep reading this one depressing post about this kid who insulted a science fair director and made national news. Well fret no more. The reason I’ve been gone these past few months was because I was to busy doing awesome things!

So, some things to look out for:

  • Europe
  • Science
  • Underground Science
  • Engineering
  • Programming
  • Kevlar
  • Molten metal
  • More science
  • Firearms

I’ll also probably be transferring nuclearfarnsworth over to a more stable server service that I’m paying for. The amount of traffic I’ve been getting and the amount of down time I’ve been having were determining factors!

I can’t post without pictures!

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