Cascade Loop Specifications
ssylee
assuming the reference and disturbances are step-like signals, is it
fairly common for the inner loop to be running much faster than the
outer loop? If so, why is this the case? Thanks in advance.
Tim Wescott
Define "faster".
The inner loop often has a higher bandwidth, and in a sampled-time
system has a greater need for a high sampling rate. In some systems it
is convenient to have a high bandwidth, high sample rate, simple loop
surrounded by a low bandwidth, low sample rate, complex loop.
So if your "faster" means "higher bandwidth", then yes. If your
"faster" means "higher sampling rate" -- well, maybe not as often, but
it's still going to be a valid technique.
When this is the case it is because one has a system that just plain
needs two loops, either because it has two inputs to the plant or
because it has two measurements of the plant behavior. Often these are
arranged as they are because you'd really like to have the fine control
that the 'slow' input or output offers, but things just plain won't work
without the coarse -- and fast -- control that the 'fast' input or
output offers.
--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
Vladimir Vassilevsky
Tim Wescott wrote:
Nested loops are everywhere: almost every sensor or actuator has inside
a control loop of its own. In nested loop configurations, a seemingly
paradoxical result can happen: if the inner loop gain is reduced, then
the outer loop can loose stability.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
Vladimir Vassilevsky
ssylee wrote:
Inner loop -> local feedback -> less phase shift -> higher bandwidth.
VLV
Bruce Varley
"ssylee" <stani...@gmail.com> wrote in message
news:d2c36e99-8543-415d...@z1g2000prc.googlegroups.com...
Theory aside, it's common for outer loops in industry to scan more slowly
than inner loops. An inner flow controller may have a process response time
of a few seconds, and require a control scan rate of < 1 second, whereas a
level controller that writes to the flow controller setpoint may have a
response time of an hour or more, and be able to function fine with a scan
rate of a minute or so.
Slower scan rates are more commonly seen when controlling 'complex'
variables, where there may be a large amount of computing involved.
Processor load can be conserved by only running calculations as often as
necessary.
Remember that one of the key functions of cascade controls is to buffer them
from *fast* disturbances.
JCH
"ssylee" <stani...@gmail.com> schrieb im Newsbeitrag
news:d2c36e99-8543-415d...@z1g2000prc.googlegroups.com...
The inner loop must have faster dynamics and is used to pre-control the
system using an auxiliary process value that leads to improved performance.
Disturbance d2 is instantly feed-back controlled.
See
* http://www.bgu.ac.il/chem_eng/pages/Courses/oren%20courses/Chapter_10.pdf
Figure 10.4
--
Regards JCH
Tim Wescott
What you say here is pretty much in line with what I was trying to
express in my post. The only real difference in my experience is that
my 'fast' loops are often sampled at or above 10kHz, and my 'slow' loops
(except for the odd thermal control) are sampled no lower than 100Hz.
Same theory, different worlds...
pnachtwey
> "ssylee" <staniga...@gmail.com> schrieb im Newsbeitragnews:d2c36e99-8543-415d...@z1g2000prc.googlegroups.com...
>
> > In a cascade control architecture with an inner and outer loop,
> > assuming the reference and disturbances are step-like signals, is it
> > fairly common for the inner loop to be running much faster than the
> > outer loop? If so, why is this the case? Thanks in advance.
>
> The inner loop must have faster dynamics and is used to pre-control the
> system
to?
It said otherwise.
Now who is right? Better yet who can prove it one way or the other
so that ssylee has the right answer. One example is not a proof.
Would this work on my favorite type 1 under damped second order
systems?
Peter Nachtwey
JCH
"pnachtwey" <pnac...@gmail.com> schrieb im Newsbeitrag
news:d945f2d5-ed8b-4113...@l11g2000pro.googlegroups.com...
I refered to 'Figure 10.4 Traditional cascade block diagram'.
Traditional! Nothing else.
For more difficult systems I would use State Observer techniques.
EXAMPLE
Real process transfer function of 6th order:
* http://home.arcor.de/janch/janch/_control/20100323-system-of-order-6/
Page 1: Process identification
Page 2: PID without feedforward and compensation
Page 3: With state observer techniques
That makes cascade control obsolete!
--
Regards JCH
Dr. Ebert
Dear Sir,
the disturbance type must not be limited to step-like ones. Assume the
RST reguator of Professor Aström or the one of Professor Landau, the
inherent D-polynomial gives the internal (disturbance) model (not to
think on IMC of Professor Morari)
Constant D=1-q^-1
Ramp D=(1-q^-1)^2
Parabola D=(1-q^-1)^3
Sinusoid D=1-2q^-1cos(omega Tsampling) + q^-2
For further reading I propose my new book on www.wolfram-ebert.com
Dr.-Ing. W. Ebert, PhD
Systemdesign
George
To avoid interaction between the loops, the inner control loop should
respond AT LEAST 3 times faster than the outer loop. We cover cascade
controls, and tuning of cascade loops, in this recorded webinar:
ssylee
more resources to better understand the operation of cascade
architectures.
RRogers
I haven't read the paper but lets think about the alternative. If the
inner loop was slower than the outer loop then the outer loop would be
trying to correct at higher frequencies than the inner loop was
conditioned for. This might lead to forcing unconsidered inner loop
poles being forced active; resulting in control thrashing. While you
might deal with it; it would be more complex. The only case where I
could imagine it is if your trying to reject high frequency
disturbances in the inner loop; and avoid saturation effects. Even in
that case making the outer loop faster should be done only in the
context of a full system analysis to avoid problems.
Ray
pnachtwey
Because it simply works out that way mathematically. At least in one
case.
I can prove that for a single pole system, such as a motor with a
velocity loop and a position loop, that the position loop must have a
lower bandwidth than the inner loop. This is not a general proof but
for a single pole system a few things should be obvious. First, the
closed loop transfer function of the inner loop will have two poles.
One for the system and on for the integrator that comes with the inner
loop integrator gain. The output loop will have 4 poles. There
will be two from the inner velocity loop. One for integrating
velocity to position and one from the outer loop integrator gain. It
should be obvious that the inner loop two poles system will be much
faster than the outer loop four pole systems unless the outer loop
poles are very fast relative to the inner loop poles. So how much
faster can the outer loop poles be made relative to the inner loop
poles? The answer is not fast enough. I tried an example where the
inner loop was tuned to be critically damped with the characteristic
equation being (s+lambda)^2 and then tried to chose outer loop poles
that would be faster. I chose a desired characteristic equation of (s
+mu)^2*(s+delta)*(s+gamma) and found the symbolic solutions for
them. I found there was a narrow range for mu relative to the inner
loop poles at -lambda. mu cannot be made to be greater than lambda
without moving delta and gamma to the right hand side and therefor
unstable. Also, mu had to be less than 1/3*lambda for Ki to be
positive and mu had to be less than 1/2*lambda for Kp to be positive.
By taking the derivative of either the formula for Ki or the formula
for Kp I found the relative value of mu compared to lambda that
provided the highest gains is about 0.21132*lambda. This is less than
1/3 lambda. As it turned out gamma=0.21132*lambda too but delta
turned out to be 1.366*lambda so the characteristic equation for the
outer loop turned out to be (s+0.21132*lambda)^3*(s+1.366*lambda)
which is much slower than the inner loop's characteristic equation of
(s+lambda)^2.
I don't consider this a proof but just one example but I can show
symbolically that the inner loop is going to be much faster than the
outer loop. I am pretty sure that more complicated systems will have
similar results for similar reasons. I don't agree with with the
statement on page 257 in the document JCH posted a link too. I can
prove the statement is wrong at least in this case.
Note, as a by product of this work it was found that inner loop AND
the outer loop can be tuned once I know the system gain and bandwidth
and by choosing inner closed loop pole locations at -lambda. The
outer loop Ki=0.01289*lambda^2 and outer loop Kp=0.192459*lambda
Peter Nachtwey
JCH
"pnachtwey" <pnac...@gmail.com> schrieb im Newsbeitrag
news:d945f2d5-ed8b-4113...@l11g2000pro.googlegroups.com...
Be aware that my solutions are not simulations. They are 'solved'
differential equations on the basis of process identification methods.
EXAMPLE
Non-self regulating difficult system 3rd order:
Process: 0,001 v1''' + 0,03 v1'' + 0 v1' + 0 v1 = v2
Disturbance: 50%
* http://home.arcor.de/janch/janch/_control/20100326-non-self-regulating/
This system can't be controlled better by using traditional cascade control.
--
Regards JCH
pnachtwey
> "pnachtwey" <pnacht...@gmail.com> schrieb im Newsbeitragnews:d945f2d5-ed8b-4113...@l11g2000pro.googlegroups.com...
>
>
>
>
>
> > On Mar 22, 3:46 am, "JCH" <ja...@nospam.arcornews.de> wrote:
> >> "ssylee" <staniga...@gmail.com> schrieb im
> >> Newsbeitragnews:d2c36e99-8543-415d...@z1g2000prc.googlegroups.com...
>
> >> > In a cascade control architecture with an inner and outer loop,
> >> > assuming the reference and disturbances are step-like signals, is it
> >> > fairly common for the inner loop to be running much faster than the
> >> > outer loop? If so, why is this the case? Thanks in advance.
>
> >> The inner loop must have faster dynamics and is used to pre-control the
> >> system
> > Did you read the bottom of page 257 in the pdf file you posted a link
> > to?
> > It said otherwise.
> > Now who is right? Better yet who can prove it one way or the other
> > so that ssylee has the right answer. One example is not a proof.
> > Would this work on my favorite type 1 under damped second order
> > systems?
>
> Be aware that my solutions are not simulations. They are 'solved'
> differential equations on the basis of process identification methods.
>
> EXAMPLE
>
> Non-self regulating difficult system 3rd order:
>
> Process: 0,001 v1''' + 0,03 v1'' + 0 v1' + 0 v1 = v2
> Disturbance: 50%
>
>
> This system can't be controlled better by using traditional cascade control.
>
> --
> Regards JCH
multiple feed back devices. Second, you still haven't learned how to
tune a PID. Let alone two PIDs in cascaded loop.
Third, that is a simulation unless real hardware is being controlled.
System identification is never perfect and your simulations shows a
system where the acceleration or second derivative is being controlled
and that is being integrated to provide velocity. There is no
viscous damping term for v1', the velocity. Now what REAL system
doesn't have friction?
Fourth, what do you do when the set point is an arbitrary function of
time or something other than a step change?
Peter Nachtwey
JCH
[...]
> There is no
> viscous damping term for v1', the velocity. Now what REAL system
> doesn't have friction?
Sometimes you can neglect small values or superfluous digits. (No one uses
pi
with infinity digits.)
Compare Page 1 (without) with Page 2 (with friction)
* http://home.arcor.de/janch/janch/_control/20100327-non-self-regulating/
Remark: Don't argue, show comparable solution!
--
Regards JCH
pnachtwey
> Remark: Don't argue, show comparable solution!
JCH, do you really want me to embarras you again? I don't think any
body cares or really wants to move beyond the myths.
Peter Nachtwey
JCH
No one is obliged to accept my solution. I'd just like to see YOUR solution!
Don't just argue.
AGAIN
Process transfer function and benchmark: Example Page 2
* http://home.arcor.de/janch/janch/_control/20100327-non-self-regulating/
--
Regards JCH
pnachtwey
> "pnachtwey" <pnacht...@gmail.com> schrieb im Newsbeitragnews:fed60e73-4a07-403c...@u15g2000prd.googlegroups.com...
with cascaded loop is wrong, so why bother? What is in it for me?
You never seem to learn from what I have posted before or even
admitted that you were beat. You keep on posting your nonsense.
If you are willing to do the math yourself then this is how I approach
problems like this.
The outer closed loop transfer function has 3 poles if I don't use an
integrator and four poles if I do. I simply place the three or four
poles on the negative real axis and move them far enough in the
negative direction to get a faster response than what you have. You
have seen this before. I always get a faster response than what you
do because I am not limiting the response with a target generator
filter like you do. The inner loop , velocity, is just another system
to be tuned in a similar manner but obviously the inner loop is tuned
first.
Peter Nachtwey
JCH
*PLONK*
pnachtwey
> *PLONK*
What do you want? I told you the procedure I use. Do the math
yourself or admit you don't really know if your method is better than
cascaded closed loop control because you don't know how how to
implement cascaded control properly.
The key is what I call alpha or 30 from your equation. For a
critically damped response, the inner loop closed loop poles must be
at -30/2 or more negative. The outer loop poles must be at 2/3 of the
inner loop poles or greater in magnitude.
This shoots holes in George's ascertion that the inner loop must be 3
times greater than the outer loop. George must not do motion
control. OK, we know he doesn't. George's ascertion that the inner
loop must be 3 times greater than the outer loop may apply to the few
types of systems that he is familiear with but not to all systems.
The math must be done on a case by case basis. JCH's system is much
different from a temperature control system.
The point is do the math or stop misleading by spreading false myths.
Question everything. I don't believe anything until I prove if for
myself. Question me too but I have posted links to pdf files for the
last five years that show the techniques I use. It is time that
someone else puts some effort into finding the truth because I think
this news group is just a social club where people post opinions and
not hard facts or math.
I have JCH's problem worked out in great detail. JCH, if the inner
loop is set to the slowest response where the inner loop poles are at
-30/2 and the outer loop poles are set at 2/3 of that or -10 the
response is still much faster that what you have shown.
Here is my cascaded loop response using your equation with
http://www.deltamotion.com/peter/Mathcad/Mathcad%20-%20t2p1%20pid2%20JCH%20cascade%204+.pdf
This is pdf was made with the gains as low as possible for a
critically damped response.
The inner loop poles are at -30/2 or -15 and the outer loop poles are
at -10. Even so the outer loop bandwith is not 1/3 of the inner loop
bandwith. Even the slowest critically damped response beats JCH's
best.
Now do the math your self and see if you get the same results. It
should be obvious if you truly know what your are doing.
This news group should consider this a thumb in its eye for not
backing up anything they said with real facts or calculations. Okay,
I haven't either but atleast I have done the calculations. I am just
showing the results. This can't be a one way street. Someone worthy
is going to have to show me that they have put some effort into this
before I spill more info.
Peter Nachtwey
pnachtwey
> *PLONK*
JCH you are beat again but no one cares.
It wasn't worth my time. I know that it is easy to beat your
responses because they are limited by your target filter.
No one bothered to ask why the actual position is leading the target
position in the sine wave simulation. ( The answer is zeros in the
outer loop). I have shown my gains. It does take much to translate
what I did to Scilab script to verify my gains.
I did discover a few things. The double integrator make simulating
this system, using state space, prone to integration errors. The
response appears to change a lot when the sample time in changed. The
response is much slower at low sample times because of the integrating
error. I wonder if using RK4 would be better. I will try that out.
I have alway wondered which would be better,
I get exactly the same response when I don't use just a single loop
when I place the closed loop poles at -10 IF I only have the P gain in
the forward path. Otherwise there is a difference in the zero
locations which adversely affect the sine wave significantly.
The response you see is the slowest. If I move the inner closed loop
poles to -30 then the response is very quick.
Peter Nachtwey
pnachtwey
> *PLONK*
Now I *PLONK* the JCH and the whole news group that gave opinions
instead of hard facts and calculations.
What's wrong JCH? I haven't got a reply. Are you ever going to admit
defeat and go away?
Tim, your statement
"So if your "faster" means "higher bandwidth", then yes"
This is right most of the time but not all of the time. It is the
times where it isn't right that bother me.
Mr Vladifilter man
"Inner loop -> local feedback -> less phase shift -> higher bandwidth"
This doesn't make sense and you can't justify it?
JCH
"The inner loop must have faster dynamics and is used to pre-control
the
system using an auxiliary process value that leads to improved
performance.
Disturbance d2 is instantly feed-back controlled. "
And you you posted a link to a page that said it wasn't necessarily
true. I pointed that out and even then you ignored it. Apparently
you to read and understand the documents you post links too.
Dr Ebert just wants to sell his e-book. It is too bad Dr Ebert didn't
post something I could challenge. I love picking on PhDs.
George
"To avoid interaction between the loops, the inner control loop
should
respond AT LEAST 3 times faster than the outer loop. "
George just wants to sell expertune but I wonder where the expert in
the tuning is.
George, did you work through JCH's problem? It is obvious that your
are wrong about the 3/1 ratio. What you say may apply to process
control application but you should not say the inner loop must be
faster than the outer by 3/1 as a general case. I can prove that in
some cases the ratio must be greater than 10/1. It all depends on the
system and the choices in how it is going to be controlled. In JCH's
problem the inner loop can be slower than the outer loop.
Consider this. A hydraulic system has a outer position loop control
and an inner acceleration/force loop control. The inner loop is two
derivatives from the postion so don't you think the acceleation loop
would be MUCH higher that 3/1?
ssylee shoud be careful about who he listens too.
The whole point of this 'thumb in the news groups eye is' that too
often people repeat what they have heard or read on the web. Too
often people think that their experience is true for all cases when it
it not. Too often people provide opinions instead of facts.
Do the math guys. If you do it right you will find that if the inner
loop for JCH's problem can have two inner loop poles at -30 then the
outer loop can have just one pole at -30 and one the one pole outer
loop at -30 will be faster than the two pole inner loop poles at -30.
JCH may still be saved. At least he is still willing to put some time
into his posts and do some math. He only needs to listen.
Peter Nachtwey