# Does anyone know this simple lead compensator design procedure?

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#### throbscottle

##### Well-Known Member
I found a page on the web last year that gave a procedure for lead compensator design without all the heavy maths, and now that I want to find it again I can't.
It was at the end of a nice tutorial that went through designing a motor control system which introduced an integrator (for stability) and then a lead compensator (for speed), for a fictional customer.
It was something along the lines of
"simulate your system, and plot the main pole and zero, choose your capacitor and series resistor based on one of these (I can't remember how this bit worked), and the feedback resistor is based on something ten times what you got, then you simulate it again and trim the values a bit"
Anyway, I did it and it worked and it was quite easy, but now I want to document the procedure for other non-mathematical people, and can't find the page!

Can anyone help re-create the procedure?

#### throbscottle

##### Member
My experience in this is with disk-drive actuators: the input is a force (acceleration) and the output is a displacement , or acceleration integrated twice, giving an s-plane equation A/s^2: 2 poles at f=DC.

Response of this will go to Amp=1, phase=180 at some frequency F0. Inputs at this frequency will cause oscillation because of the phase=180 degrees
A compensator is used to
1 Add phase-margin (make phase < 180 at F0)
2 Decrease response at frequencies above F0
The response must be pushed greater in phase before this frequency and lower in amplitude above it, so a zero is added at Fz<F0 and a pole at Fp>F0

(Here it gets squishy, if it was not before)

The frequencies chosen were F0/sqrt(10) and F0*sqrt(10). There was list of a dozen or so sets of coefficients for a digital compensator: the F0 of a drive could be picked off the step-response on the scope (sometimes the manufacturer wouldn't or couldn't give us the actual number.)

#### throbscottle

##### Well-Known Member
Okay, that's something to squirrel away for future reference! I've never heard of an s-plane equation. Is the F0 * or / sqrt(10) peculiar to digital compensators and disk drives, or will it also apply to the general/analogue case? It's a narrower range than in the article I read, and my own design ended up with the pole being the zero *11. Perhaps I have mis-understood - I'm on the edge of my understanding here...
I think the site I found is the same one I looked at originally, it just looks different, like some stuff has been removed...

##### Member
The method outlined was for the case where the transfer function is A/s^2: the output is the input integrated twice times a constant.
It's easy to see how it applies to the disk-drive actuator: all you can do to affect it is to accelerate it by increasing the current to the arm and all you know of the result is its position.
I'm told that many physical systems fit this model, but this was the only one I ever used it on: I'm at the edge of my understanding, too.
You say
It's a narrower range than in the article I read, and my own design ended up with the pole being the zero *11
.... a pole/zero ratio of 11 is pretty close to 10

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