Control loop design

pt

unread,

Mar 3, 2012, 7:53:36 AM3/3/12

to

Hi,

I found the control loop design

http://imageshack.us/photo/my-images/209/controlloop.png

containing the controller C with proportional and integral part. The
controller output is added to the reference value r with the result
processed in D. D is kind of linearization but only for the gain and
not for the dynamics. P is the plant. The process P is non-linear.

Does somebody know about the pro's and con's of using such structure
in comparison to a common PI controller with additional feed-forward
control?

What would happen if D uses feedback from the process P?

As I couldn't remember where I saw this structure, there may be errors
in my painting. I would be glad if somebody could give me a hint to
some literature which deals with such structure.

pt

Tim Wescott

unread,

Mar 3, 2012, 10:09:40 AM3/3/12

to

I don't know if that structure has any particular name. If the plant
nonlinearity is predominantly at the input then what you're showing would
do a pretty good job of linearizing the whole thing.

If, for instance, you were controlling the temperature of something, and
your plant input were a voltage or current command, and the heater was
both resistive and didn't change temperature dramatically itself, and the
plant was otherwise linear, then at the plant the system would be
something like y = h(x^2) where h is an LTI system. Then making D into x
= sqrt(x_c) where x_c is the controller output would really make the
system design easy.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

pt

unread,

Mar 3, 2012, 12:25:49 PM3/3/12

to

Am Samstag, 3. März 2012 16:09:40 UTC+1 schrieb Tim Wescott:

> I don't know if that structure has any particular name. If the plant
> nonlinearity is predominantly at the input then what you're showing would
> do a pretty good job of linearizing the whole thing.

Can this be successful even the dynamics, i.e. poles and zeros, is not taken into account? Would you allow feedback of sensor signals from P(s) into D(s)? Some of them are quite fast.

pt

Tim Wescott

unread,

Mar 3, 2012, 2:49:40 PM3/3/12

to

Well, I already bounded my answer, in the part that you snipped. I'll
repeat, in hopes that it sticks this time:

_If_ the system has _just one_ nonlinearity _at the input_ and _is
otherwise substantially linear_ then this method will work well.

Does it make sense now?

If you have a (or some) nonlinearity right on the edge of the plant, i.e.
right at the input or right at the output, and the nonlinearity is
memoryless, and the nonlinearity provides a reasonable one-one mapping
between the command and the internal force exerted (on the input side) or
the plant state(s) and what you read back (on the output side) then
negating the nonlinearity is trivial.

In other words, if your system equation can be expressed as

d
-- x = A x + b(u(t)), y(t) = c(x(t), u(t))
dt

and if b and c are easy functions to "undo", then you can just undo them
and proceed with a linear system design.

On the other hand, if you cannot separate out your system function that
way, then until you know more, all bets are off.

Bruce Varley

unread,

Mar 4, 2012, 5:23:09 AM3/4/12

to

"Tim Wescott" <t...@seemywebsite.please> wrote in message
news:qLmdnfO-LcxJ6M_S...@web-ster.com...

Nice explanation of something that I've struggled to communicate to
youngsters for a long time, Tim. Thanks!

pt

unread,

Mar 11, 2012, 11:09:04 AM3/11/12

to

Am Samstag, 3. März 2012 20:49:40 UTC+1 schrieb Tim Wescott:
> On Sat, 03 Mar 2012 09:25:49 -0800, pt wrote:
> > Am Samstag, 3. März 2012 16:09:40 UTC+1 schrieb Tim Wescott:
> >
> >> I don't know if that structure has any particular name. If the plant
> >> nonlinearity is predominantly at the input then what you're showing
> >> would do a pretty good job of linearizing the whole thing.
> >
> > Can this be successful even the dynamics, i.e. poles and zeros, is not
> > taken into account? Would you allow feedback of sensor signals from P(s)
> > into D(s)? Some of them are quite fast.
>
> Well, I already bounded my answer, in the part that you snipped. I'll
> repeat, in hopes that it sticks this time:
>
> _If_ the system has _just one_ nonlinearity _at the input_ and _is
> otherwise substantially linear_ then this method will work well.
>
> Does it make sense now?

I have not yet converted the process P into state space form and thus could not say if the nonlinearity is at the input. Do you have an advice in non-state-space-form?

pt

Tim Wescott

unread,

Mar 11, 2012, 12:59:33 PM3/11/12

to

Do you have a set of differential equations that describe the process?
If so, where are the nonlinearities? If not -- get cracking!

pt

unread,

Mar 11, 2012, 1:40:30 PM3/11/12

to

I have algebraic equations which describe the gain of the process. The gain already is non-linear. Furthermore, I have step responses and local linear models. I don't expect that I could develop differential equations (other than those of the local linear models) of the process.

I still wonder if the gain linearization in D is a good idea iv it does not handle dynamics and if it requires significant feedback from the process.

pt

pt

pt

unread,

Mar 14, 2012, 3:45:15 PM3/14/12

to

I think the fast feedbacks would screw up the system. But I wonder if
there are mechanisms to use current measured values in the
linearization block without getting in trouble.

pt