My experience is more hands-on than theory, but here is the answer I gave my classes:
In N years of setting up servos, I have never once found a use for it, nor have I found any literature that explains when it might be of some use. I think that somewhere back in the early days someone was told to put in a jumper that reverses the phase of the entire servo (quite handy when someone miswired a section that is really hard to get to), got it wrong, and some other manufacturers have been copying the "feature" ever since.
If one of the theory boys has a better answer, I am all ears.
Being able to reverse the sign of the whole thing is good -- one of the old curmudgeonly engineers from whom I learned practical control liked to say that when designing one of these things you should count up all the sign changes in the loop -- then throw in one extra for the one you missed. His circuits always had at least one spot where you could rearrange the inputs to an op amp and reverse the sense of a signal. I follow that now: there's always at least one place in my software where one can insert a '-' and change the sign of the whole thing.
Sounds like it has more to do with ingenuity than pistons and connecting rods. Of course, the Latin root "ingenium" (ability?) is the same for both words.
I'll search for that. Have you ever used it? It seems like introducing a low-pass would be a much better way to kill noise and add lag at the same time.
True negative derivative is called (negative) velocity feedback and is used to decrease response time at the expense of overshoot. The frequency response of the system goes up. The system becomes stiff but 'nervous'. Can be used to stabilize systems as the same stiffness can be had with a lower proportional gain.
This is just what one would expect as plain-ole' derivative feedback is used to lessen overshoot at the expense of slower response time.
Think of D as oil: it can be used to slow something down by being thick and greasy or it can speed something up by lubricating it.
Speculation: if the controller is configurable to use derivative on error _or_ derivative on process then the sign of the derivative at the summing junction must change, most modern controllers do this automatically in software but I suppose there are those that don't. The same is true if feed-forward on SP is available.
Not so simple ... it doesn't necessarily make the system unstable: think Nyquist diagram.
I'm not sure what this has to do with software, except to know to shout 'Hardware Error!' and go for a cup of coffee.
FWIW: dual slope and V/F are preferred conversion techniques for process control as there are no 'bad spots'. Also work a charm if synched to the line frequency.
Er, maybe a new audience is needed?
The only requirements for control are monotonicity and repeatability, everything else is icing on the cake (though some sort of linearity is _really_ nice to have).
Shortly after VJ day, Japanese military electronic software began turning up in the surplus stores on Cortland Street (razed to make way for the World Trade Center). I bought a small panel meter, probably out of an airplane cockpit, that had Japanese markings molded into the inside of the case. The design itself had been blindly copied. Prominent in the inside center of the back cover were the letters, "Simpson".
With few exceptions, hyphens are equally effective--perhaps more so, because e.g., it finds things with 'online' when you enter 'on-line'.
When posting a link, hyphenated search strings are superior. (A double-quote mark tacks a '%A' onto the front of a search term making it difficult to search the Google archive for that term.)
I tried to sell them an article a couple of months after the dot-com bubble burst. The word then was that advertising revenue was down, so they had to thin it out. The reduced page-count plus all the suddenly unemployed engineers writing stuff nixed my article for a while (but I have published there recently).
All controllers I've seen, be they in software or hardware, have a flag or switch to reverse the controller action. Some even let you reverse the output action. Eases up a lot in initial implementation.
I've seen the ones that let you reverse the terms individually but haven't found a need for trying them out. One accidentally had the integral term reversed and I went bonkers trying to tune it before finding the error.
The derivative term is useful when you have a slow process with inertia. Once the controlled variable starts to respond it puts a lid on further controller action which might cause unacceptable overshoot. On the few occasions I do apply it it's usually in homeopathic doses.
The "D" part of PID refers to the presence of a rate-of-change term, often able to be interpreted as a derivative of a position (or similar) quantity. Derivatives are a concept deriving (!!) from the differential calculus. Either term refers to the notion of infinitesimal differences whose ratios are considered as they approach (under suitable existence conditions) some limiting value.
Thus either version of the acronym is fine. Elsewhere in this thread is a timely reminder about the danger of reliance upon statistics (eg: Google hits) to "prove" something. I've come to the conclusion that if the majority agree upon something, it's probably false (works great in the stock market, but you have to be careful about your audience when defining the principle as "the fallacy of democracy"......)
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