One thing - in the text for Figure 5, you say "magnet is attached to the stage, which moves with an acceleration proportional to the coil current."
I've done exactly this with a large voice coil (4" diameter, 4" throw) with a constant *voltage*, and you get a *speed* proportional to the voltage, although the current quickly settles to a constant (-ish). I'm sure I don't need to explain why - but it might be worth mentioning back EMF at some point. It was a surprise to me, initially.
Embedded Systems Design (or whatever they call themselves) kept moving this around -- so I've revamped it, updated it, and posted it on the web.
Take a gander. Please comment on anything you like/don't like. I'm not sure if the way that I'm setting off the math is a Really Good Idea or a Really Bad Idea -- I'm trying to make it easy for the math-averse to skip over it, without breaking up the flow too much for folks who can read math without breaking stride.
You leave out math but include C code, I think that's defeating the purpose. If you can't explain it in non-technical words or a simple picture... well, try harder :-)
You spend only one page on tuning, and give no examples of "If you see this, try this" which is much more useful to the practical user.
You don't mention feed-forward terms at all.
In short, it looks much like all the other PID papers out there, and wouldn't have helped me "get" PID back when I was trying to figure it out.
The section on I - the last paragraph should go first, since the point of the I term is to correct for long-term errors, and you don't even mention it in the first paragraph.
The second paragraph in D should be first, and is probably the most useful paragraph in the paper, if you don't already understand PID.
The other thing I always hated about PID papers is that they never gave solid examples of the difference between controlling speed and controlling position, or the more complicated case of torque/speed/position nested PID loops for CNC control.
I'm reminded of a YouTube video about how NOT to weld - the guy would intentionally do it wrong various ways so you could compare his results with your results, so you could figure out what you were doing wrong and how to fix it. Something like that for PID would be more useful than showing an ideal situation.
I don't know if color is something that will be preserved, but that bright green for links actually hurts for me to look at. Hard to miss though.
The PDF page numbering is off 1 from the text page numbers. I'm pretty sure there is a way to deal with that.
Page 2 (text page number) paragraph 2, "Some command is given to a controller, and the determines a drive signal to be applied to the plant." Is "the" the word you want?
Page 4, equation 1, you might explain the basis of this equation. I assume the voltage actually controls the torque. Friction force is a result of velocity and the acceleration is from the excess force until the motor speeds up. Contrasted to the equation for the frictionless platform.
Page 6, paragraph 1, figure 5, you write "The magnet is attached to the stage", but the diagram calls it a "platform". That is not hugely distracting, but if I know nothing about optical systems (which I don't) I might be thinking the "stage" is something different and start looking for what it means (I did).
Just for completeness, you might include the "position transducer" in your diagram. I assume it measures the position of the platform rather than the magnet.
Page 6, paragraph 2, showing my ignorance I don't understand, "With this arrangement the force on the magnet is independent of the stage motion." Doesn't a magnet moving in the coil create a current/voltage that interacts with the applied current/voltage? Are we assuming the "good current-output amplifier" deals with this?
Page 6, equation 2, I don't see where Vp is defined. It does not seem to be used anywhere else in the paper.
Page 8, equation 3, you define Th twice but don't say what units. I assume it needs to be absolute temperature, Kelvin? Two time constants are given, but no explanation for why two or what is different about them. I don't know about others, but I have a hard time considering an equation I don't understand. It keeps me from getting an understanding of how the controller would work.
I need to go now. Please take this for what it is worth, free advice.
The intended audience is writers of software for embedded processors, so the 'C' code may be easier to understand than English for some readers. This was implied when it was in its original context -- I think I'll at least put in an expanded forward.
Hmm. I'm trying to keep the math stuff short -- people write entire white papers on the behavior of motors alone. Maybe put all the math into a several-page appendix?
To unpack a bit, the difference between the applied voltage and the motor's back-emf, divided by the armature resistance, determine the motor's armature current. Torque is armature current times the motor's torque constant, and acceleration is torque divided by the motor's moment of inertia. All of that is rolled into the kv and the time constant, in this case.
You're right, the nomenclature should be consistent. I don't know about other people, but this is incredibly difficult for me. It's a subset of the "don't toss jargon around" rule. (Sometimes, the multiple-language problem is a consequence of incomplete solutions to removing jargon, at least for me).
The good current-output amplifier, and the frictionless support of the platform, deals with this.
Vp comes out of the position transducer that I left off of the drawing. Yup, need to change something!
Well, I pulled the time constants out of my ear. Or my donkey (I _do not_ get that cliche :P ). Or something.
Te temperature of the load (Th) is determined by both the driving input (Vd) and the ambient temperature (Ta). Again, I need to think about making that more clear without making the math-averse reader run away screaming.
I appreciate your time and trouble you've taken to read the thing and write your comments.
I don't think tucking away the math into an appendix is the answer. Maybe derivations or something not essential to understanding the problem. All I would need is an understanding of the meaning of the terms of the equation. Typically each term of the equation comes from some specific "thing" in the problem. I don't get what those "things" are in these equations.
I'm not sure I understand this. I'd need to write out the equations. The back-emf is proportional to what, the rate of change of the current? Or the speed of the motor? It's been a long time and I forget. I think saying it "is rolled into the kv and the time constant" is a bit simplified. Again, I'd like to know the meaning of each term in the equation. d theta/dt is the speed of the motor, but why is that in this spot of the equation? Does this represent the friction? Then I would get that the friction force balances with the motor torque and the acceleration would become zero.
Then where did this equation come from? I find it very hard to follow the rest of the approach if I can't understand the equation. I guess I'm not the target audience.
Seems to me the equation would be
dTh/dt = ka * (Ta - Th) + kh * Vd
kh * Vd is the heat applied by the heater with kh the constant for the heater watts vs the thermal mass of the container. ka * (Ta -Th) is the heat entering (or leaving) the container with ka accounting for the thermal mass and the amount of surface area, etc. The heat moving into/out of the container is proportional to the temperature rate of change, no?
How does this get to be a second order differential equation?
I appreciate you writing this. I'm sure I will learn a lot from reading it.
I just spotted an error. If the heater is controlled by volts, it would have to be voltage squared to get power. Unless the volts is out of the ADC and the heater is controlled by a voltage to watts control, lol.
I've gotten this report before, and I think it's something about the way that LaTeX renders pdf files, and then the way that Adobe renders those pdf files on some screens. I would really appreciate it if you could email me a screen shot so that I can file a bug report with the LaTeX folks, or ask for a work-around.
A very nice work. I seem to remember that you already had a previous version of it, didn't you?
It was a surprise to see that the D box input (and pehaps P) is taken from the feedback and not the error signal, as os usual in most textbooks. For constant or slow varying commands, it makes no difference. Is this arrangement an empirical result?
Every motor is also a generator. For a motor with constant magnetization, the back EMF is proportional to the speed and the motor torque is proportional to the current.
You can model such a motor with a series connection of the supply voltage, the motor (and line) resistance and the back EMF. The motor settles to a speed near such speed that the difference between supply voltage and back EMF runs just enough current in the circuit to compensate for torque needed to keep the speed.
If you feed a constant-magnetized motor with a constant current supply, the torque stays constant until the compliance limit of the feed supply.
Well in general good other comments people have stated I would add these points -
1/ Code layout on page 14 of the integral state is UGLY, belongs in obfuscated C better laid out out that is easier to read at a glance is better for those trying to understand.
2/ Sampling time and loop delay, the closed loop problem that many people overlook is not mentioned in any manner until into the maths. Most people forget that digital control systems have a time lag and time between calculations, sampling and worst of all ALL systems have a delay between command -> error -> drive -> feedback Each part has its own intrinsic delays/inertia and other effects that most people never MEASURE.
Increasing sampling rate or precision does NOT guarantee being able to get to target faster.
A classic problem I saw was a remotely operated vehicle, with a video link and command back to vehicle. Everybody was annoyed that it could not be driven faster than 30 mph so were looking at using 3D cameras to make it faster. No one had obviously measured delays in system
Camera frame integration time Camera frame transmission time Camera frame acquisition time frame compression encryption time frame radio link transmission time frame receive time (missed/corrupt data) frame decryption time frame network transfer time (multi-computer setup) Frame ROTATION by 90 degrees time Frame mixing with other graphics Frame buffer switching
Then Operator response time Controls delay to data time Controls network transfer Controls radio link transmission Controls receive time (what about missed/corrupt data) Controls entered as new commands into drive control loops Controls being applied Vehicle lag to changes in drive
So how was 2 video feeds going to speed this up
3/ Limits (especially integrator)
Limits, limits, limits how often overlooked and bear NO relation to reality.
If you have a motor with NO direction control, under what circumstances do you need a NEGATIVE limit ?
If you have a maximum drive (output level) under what circumstances do you need a larger limit ?
Real world as in your heater example if you measure ambient unless you have some cooling system your minimum IS AMBIENT.
Light drives can you really have negative light without use of mirrors or other light sources. Ambient light or black is your minimum.
Case I saw was some control software 30 years ago where a PI example program had
Oven Heater constant heat drive Door that could be open or closed 2 temperature readings Oven Ambient
If you left the door closed the integrator would easily reach 50,000 degrees C
If you opened the door it would 'cool' to -500 degrees C and beyond
Just some random ramblings from a nutter to bear in mind
Paul Carpenter | email@example.com