# Control loop design

• posted

Hi,

I found the control loop design

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

• posted

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.

• posted

Am Samstag, 3. M=E4rz 2012 16:09:40 UTC+1 schrieb Tim Wescott:

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

pt

• posted

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.

• posted

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

• posted

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

• posted

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

• posted

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.=20

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.= =20

pt

pt

• posted

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

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