Second Time Derivative Of Current

I don't think there's even a name for the first derivative of current. We call that one "dee eye dee tee."

John

then it must be dee squared aye (over) dee tee squared

I suppose, but it has so little physical use in electronics that it's usually not referred to at all.

di/dt is commonly of concern because it induces voltage drop in intended or parasitic inductances.

I don't recall using the second derivative of voltage much, either. dv/dt is real common, as in opamp slew rate.

John

I use the term "accelericity" for d2i/dt2.

Bob

Yeah, little use for second derivatives of i or v. I remember my old math prof said that there was a physical use for, I think it was the fourth derivative of position (some derivative beyond acceleration). Something called "bounce," like in an elevator.

The term I was taught was 'jerk' for anything at the 3rd derivate of time and beyond. And yes, for elevators.. but also cars.

Jon

I would assume that you haven't worked on control methods for switched power conversion, then.

Jon

I have done a lot of switching regs, servo motor controllers, microsteppers, and a few ballpark 32,000 horsepower/80,000 ton control loops. Lots of temperature controllers, too, where the process dynamics can be really dreadful: transport plus diffusion.

Even derivative control is tricky... gets unstable in a lot of real-life situations. 2nd derivative sounds really hairy.

John

I gathered from reading (not doing) that it is NECESSARY in some cases. For some things like uninterruptable supplies, active power factor compensation, power filters and gyrators, the control input itself, as a function of time, doesn't appear in the first time derivative of the output voltage, which is something like:

d/dt V_out = (I_in - I_out) / C_out

But the control term it does appear in the second derivative. (I just tried to work it out on paper, again, and it's 'longish' but the term including the input control function of time, del(t), is:

d/dt [(I_in - I_out) / C_out] = V/(L_out*C_out)*del(t) - ....

Apparently, it's necessary to recover that term to apply switching law and devise a control strategy. I remember reading something about choosing a "sliding surface" here.

Sounded interesting on skimming before, but I've never required that level of understand for anything so never went any further than to just remember a few interesting tidbits. The one thing I definitely remember well is that the second derivative was absolutely required in order to even begin to develop a proper control strategy, though.

Jon

Depends on the system. Most control loops (power supplies, industrial process) are happy with just proportional and integral terms. Derivative amplifies noise and can do nasty things in cases like deadbands and static friction.

A prudent amount of lead/lag compensation can improve phase margin; every situation is different.

Derivative is often necessary in maximum-dynamics electro-mechanical servos, like high-performance aircraft controls. Everything else - actuators, sensors, machanics - must be precise enough to allow serious derivative action.

One alternate to a tight control loop is to apply feed-forward corrections from known error sources, like the unregulated input to a voltage regulator, or ambient temperature into the control loop of a crystal oven. That can buy you a 5 or 10x improvement without adding the potential instabilities of a very tight loop.

John

Yes, that's why I took a moment in the earlier post to include some of the systems that I was reading about, at the time. Apparently, for those it is important to consider. I agree that "not always" is also true.

I've done a LOT of PID control. Not as much as Tim W., I'm sure (I like reading his posts on control theory and feel as though I learn things from him here and there), but enough. There are some commonly found problems where it works horribly, if at all. It's dirt easy, for example, to make it to "go to hell in a hand-basket" merely by making the output function a nice, time-delayed copy of the input. Like maybe a second's delay.

One of my favorite tricks, in fact, when presented with a "difficult" case with PID control is to take a quick look at the delays and their variability, as well, from measurement source to closed loop control signal output. If there is any way to shorten it, I do that first. Not infrequently, it starts working well enough with nothing more done to it.

Yes. However, in the cases I cited above, I remember the author making an excellent case that this was the ONLY way to set up the state-space equation and then properly design the control system for it. If he's right about it, you bite the noise to get there.

I don't think I said it was appropriate in all cases (nor would I know, to be honest) and instead chose to list those where the author discussed needing the 2nd derivative to develop proper control theory for them.

I understand and agree with this much.

To my unpracticed eye, feed-forward is a very important tool to be aware of and able to apply. I didn't mean to take anything away from that and I'm glad you brought it in. But that's a separate subject.

Because I saw the equation development by the author, mentioned earlier, I definitely accept the author's assertion in those cases that the 2nd derivative of output voltage was necessary for proper control loop design. I don't know better from experience, but the equation development looked solid to me if and only if the assumptions the author brought into it were valid, too. I simply accepted those, at the time.

Jon

Generally they have better, more agreed upon names and symbols in EE than any other field except math.

On the other hand the names that appear in software are so bad you wonder when they'll form a committee to purge them from the language.

The French have some expression for using the exact right word. It's really a waste of time wondering over some post on heat exchange equipment and then realize usage is different in the U.K.

Bret Cahill

"The human mind invents things more easily than words; that is why many improper terms and inadequate expressions gain currency."

-- Tocqueville

"Le mot juste" was Flaubert's big thing, as I recall.