[EE] Help understanding a "Loop Transfer Function" from ST application note AN1626, brushless motor driver

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[EE] Help understanding a "Loop Transfer Function" from ST application note AN1626, brushless motor driver

Jason White-20
Hi everyone,

ST makes a handful of brushless DC motor driver ICs. In application note
AN1626 (page 27) ST describes how to implement speed/torque regulation
using a voltage integrator on the tachometer output from one of their
brushless drivers. I am designing a system around the driver described in
the app. note and aim to verify the phase margin. However, first I have two
fundamental questions I am struggling with.

Question (1):
I am having trouble deciphering how they obtained the "loop transfer
function" from the block diagram. I have attached a screenshot showing the
transfer function, block diagram, and schematic, in the same photograph.

Question (2):
What is the precise definition of "loop transfer function" in this context?
In this context it seems to be something distinct from the closed-loop,
open-loop and error transfer functions. My online searching plus some
guestesmation suggests that it is the error signal divided by reference
(command) signal for a 0 torque load. Although, when I wrote out the
equations from the graph it did not seem to even remotely match the
structure of the provided loop transfer function in ST's application note.

Thanks everyone!
--Jason White

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Re: [EE] Help understanding a "Loop Transfer Function" from ST application note AN1626, brushless motor driver

Jason White-20
Addendum to original post:

I believe I found the answer question (2). I now strongly suspect that
"Loop transfer function" is referring to the "open loop transfer function"
although I am unsure where exactly they are cutting the loop. Particularly
since the whole "loop transfer function" is negative - which I find to be
unexpected given the contents of the block diagram.
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Re: [EE] Help understanding a "Loop Transfer Function" from ST application note AN1626, brushless motor driver

Sean Breheny
Hi Jason,

I am pretty sure that Gloop refers to the transfer function you get by
considering cutting the feedback loop, considering zero command input, and
just multiplying all the gain factors as you go around the loop back to
where you started. I think they cut the loop just before the feedback
summing junction - and since the feedback input to that junction has a
negative sign, that's where the negative comes from. Please see the
attached image.

Sean


On Thu, Jun 11, 2020 at 4:12 PM Jason White <
[hidden email]> wrote:

> Addendum to original post:
>
> I believe I found the answer question (2). I now strongly suspect that
> "Loop transfer function" is referring to the "open loop transfer function"
> although I am unsure where exactly they are cutting the loop. Particularly
> since the whole "loop transfer function" is negative - which I find to be
> unexpected given the contents of the block diagram.
> --
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> http://mailman.mit.edu/mailman/listinfo/piclist
>

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Re: [EE] Help understanding a "Loop Transfer Function" from ST application note AN1626, brushless motor driver

RussellMc
In reply to this post by Jason White-20
On Fri, 12 Jun 2020 at 07:23, Jason White <[hidden email]>
wrote:

> ST makes a handful of brushless DC motor driver ICs. In application note
> AN1626 (page 27) ST describes how to implement speed/torque regulation
> using a voltage integrator on the tachometer output from one of their
> brushless drivers.
>

For those wishing to see the context it appears to be AN1625 (not 1626) -
"L6235 THREE PHASE BRUSHLESS DC MOTOR DRIVER "

https://www.st.com/resource/en/application_note/cd00004396-l6235-three-phase-brushless-dc-motor-driver-stmicroelectronics.pdf


or  https://www.mouser.com/datasheet/2/389/cd00004396-953604.pdf


        Russell
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Re: [EE] Help understanding a "Loop Transfer Function" from ST application note AN1626, brushless motor driver

Jason White-20
In reply to this post by Sean Breheny
Hi Sean,

Thanks, I'm pretty sure you're right.

I had initially thought exactly what you said - but had changed my mind
because at the time I was convinced "information" (pole/zeros in the
characteristic equation) was being lost by ignoring the summing junctions
and setting all the inputs to 0.

I wrote out the transfer functions and have managed to convince myself that
"all is well." Specifically that the characteristic equation is totally
unaffected by the summing junctions in this case

I attached my "proof" should someone else in the future find themselves in
my shoes.

-Jason White

On Thu, Jun 11, 2020 at 8:23 PM Sean Breheny <[hidden email]> wrote:

> Hi Jason,
>
> I am pretty sure that Gloop refers to the transfer function you get by
> considering cutting the feedback loop, considering zero command input, and
> just multiplying all the gain factors as you go around the loop back to
> where you started. I think they cut the loop just before the feedback
> summing junction - and since the feedback input to that junction has a
> negative sign, that's where the negative comes from. Please see the
> attached image.
>
> Sean

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