Iterative Technique for PID Controller Tuning

fahad6674@googlemail.com wrote:

Have you googled?  Are you referring to a specific paper, or a specific
author's terminology?

For many plants with moderate but monotonic nonliniarities, the best
tuning procedure _is_ iterative*, because the PID tuning changes the
apparent linear model for a given system stimulus.  So you tune, test,
and tune a few times to circle in on the "best" tuning for the problem
at hand.

* Assuming you have that much access to the plant.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

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Tim Wescott wrote:


And get a huge pot of coffee before starting since this can take a long
time. Last time I did that even one of the DIP switches had enough and
broke off.

--
Regards, Joerg

http://www.analogconsultants.com

Joerg wrote:

I was going to disagree with you, but then I thought about the times
I've done this...

Some loops are well behaved enough, and have specifications that are far
enough away from the actual plant capabilities, that you can do a single
iteration of measuring the response, tuning the system in a math package
like MathCad, MatLab or SciLab, then applying the result and verifying
that yes, the system works exactly as predicted.

Many loops, however, have nonlinearities that require several spins of
the tuning at some "nominal" excitation, then require checking at
significantly different excitation levels (because with nonlinearities
the apparent linear model will change with excitation), then require
checking the time-domain behavior of the system.

Other loops require that you push them close to their limits to get the
required performance.  In a product development cycle this can mean that
one tunes the loop once, then has to tune it again and again either
because one's specifications change or because the mechanical
arrangement gets changed and you have to tune to reflect that, or
because you learn new and intriguing ways to mis-state a system's
real-world performance in terms of testable control-system performance.

So yes, keep the coffee hot while you do it.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

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Do you need to implement control loops in software?
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Tim Wescott wrote:


In this case it was a thermo-electric cooler. That would have been ok.
However the PID input was not the thermistor but the optical feedback
after it had gone through a myriad of etalons and whatnot. The numerous
staggered delays inside the DFB module were, of course, not documented
anywhere.

--
Regards, Joerg

http://www.analogconsultants.com

On Mar 28, 8:33 pm, "fahad6...@googlemail.com"

Do a search for 'PID iterative tuning'.  There are a couple of papers
that give the general concept of minimizing a cost function.
Iterative tuning doesn't require a model and just tries to calculate
PID gains the minimize a cost function between the SP and PV over a
period of time.  Iterative tuning uses a minimization program to
calculate the new gain sets at each iteration which is much faster
than the manual method where one usually changes just one gain at a
time.  This is critical if the time for each run takes a long time.
I still think it is best to find a model and tune that first because
it at least gets one in the ball park and reduces the number of
iterations.

Warning, minimizing a cost function doesn't always result in the most
stable system.  In some cases the system can be very close to being
unstable.

My first auto tuning system used iterative tuning.  I found the cost
functions had to be more complex that just the normal ITAE, ISE or
IAE.  The gains tended to be extreme unless the output effort was
added to the evaluation function.  This is why I think those that use
these simple functions are misled and mislead other.  I have made this
point on other threads.

Peter Nachtwey

On Mar 29, 6:33 am, "fahad6...@googlemail.com"

Iterative tuning is my personal favorite tuning method; usually a two
step approach as described below is adequate:

Step 1 is to find the stability limit of the closed loop system using
proportional control only.
Switch the integral and derivative control off and, starting with very
weak proportional control action, increase the proportional action in
steps with intervals in between while closely observing the response
of the system. With natural disturbances you can observe when the
system starts to show signs of becoming unstable. The point is that
you can observe the initial signs of instability without the loop
actually going unstable.
Now use a proportional controller gain equal to approximately 50% of
this value where the system starts to show signs of instability.

Step 2 is to find the stability limit of the closed loop system using
the above gain and varying the integral control action.
Similar to step 1, start with very weak integral control action and
then increase the integral control action steps with intervals between
while closely observing the response of the system, until the closed
loop system starts to show signs of becoming unstable. Generally, more
patience is required for this than the previous step; the period of
integral control instability oscillations is much longer than
proportional control oscillations.
Now use integral control action equal to approximately 50% of this
value where the system starts to show signs of becoming unstable.

Now you observe the closed loop response.
In some cases the closed loop response is good, then you're obviously
done.
In some cases the control action is too strong; the system exceeds
accuracy requirements at the expense of the controller output making
excessive moves. Then you must reduce the gain.
In some other cases the control system response is still to weak and
does not meet the accuracy requirements. No you can increase the
proportional and integral control actions and introduce some
derivative control action to prevent oscillatory response.

And yes, a great deal of patience and concentration is required. You
continuously running the risk of causing the system to go unstable -
so you have to continuously concentrate on the system's behaviour.
Especially if you introduce derivative action; noisy measurements
combined with derivative action can very easily cause the system to go
totally unstable.

Pieter Steenekamp
pietersteenekamp@gmail.com

On 31 Mar 2007 09:22:22 -0700, "pieter steenekamp"


This is the method I was taught and we used to tune the PID controls
on the main propulsion system for an aircraft carrier. I've used it
ever since for tuning PID and with practice it is very quick.

Thinking backwards from this technique helps understand PID and
develop a intuitive approach to tweaking the tuning of a system.

On Mar 31, 4:59 pm, Paul M <PaulMatWiredogdotcom> wrote:

How does this help to understand PID tuning?  I agree that a lot of
trial and error will give one a lot of experience at trial and error
but this method of tuning is not efficient. I don't think the OP was
looking for this kind ( trial and error ) of information and by now
has come to the conclusion there still is no intelligent life here but
has hopefully learned to use the search engine and found the link
below.  Before you tell me to go back to the 60 cycle hum Paul and
pieter should have taken my advice and searched for PID iterative
tuning.   Here is an article on iterative tuning.
www.inma.ucl.ac.be/~gevers/PublisMig/C119.pdf
It is obvious this this iterative tuning is not the same as the
iterative tuning you guys are talking about.

If all you guys have to offer is you tweak this gain until this
happens and then tweak that gain but watch out for the noise then
there is no point in talking about PIDs let alone more advance control
topics and I would never recommend anybody to seek information here.
One can get that kind of information or better from a PLC forum.

Doug Cooper offered one alternative ( internal model control ) but
sound method of tuning a PID and got some grief for it.  Iterative PID
tuning is an alternative method of tuning a PID.  I like my system
identification and pole placement.  Tim likes his swept sine waves
although it isn't clear to me how he calculates a system model.  Greg
Shinsky, on the Expertune forum, likes the minimum IAE which I think
is insane but am willing to debate.  As far as I know the rest of you
just use trial and error.  It would be nice if there could be an
informed and intelligent discussion as to which method is best or at
least which method is best in is certain circumstances.

Now you can flame me or try to raise the high bar.  It is your
choice.
BTW, I have tried all the tuning method but Tim's.

Peter Nachtwey

On 31 Mar 2007 20:09:04 -0700, "Peter Nachtwey"


Do you better visualize the mathematical relationships of PID by
seeing an equation or understanding what impact a small proportional
band has on the output? For me, seeing what happens when I change the
band helps more than changing a value in an equation.

You appear to be reading a lot more into my post than what I intended.
I was not dissing modeling or having the math skills necessary to
calculate what initial PID values should be. I was simply commenting
on seeing the procedure I was taught over 30 years ago. Back then, I
did not have a programmable calculator to run the values through
easily. Even if I did calculate the starting values, how would I set
them? Settings for these things even today may be no more than a one
turn pot. In the situation I was referring to the system was
pneumatic, the adjustments were to a needle valve or the fulcrum
position. We set the initial calculated values on a bench by
simulating the inputs and varying them while observing the output. It
was a slow process but worth it to get close before commissioning. So
I was not making any statement on any tuning techniques and find it
difficult to see how you took it this way.

As far as flaming each other or taking this to a higher level, I would
contribute to a discussion on PID tuning techniques using other
methods if I though I had anything to contribute. I just don't dwell
on the math much because I have found that beyond a point, it is a
waste of time. Get it close and then tune by hand. There are too many
unknowns in most electromechanical systems to do much more than that.
If the math can give the values to set within 10%, that is all that
will be helpful. This is not true in some situations. In cases where
most or all of the system is solid state such as what Tim works with,
then modeling makes a lot of sense. Now I have not flamed you at all,
but you have done this to me. Why? Have I posted stuff in the past
that irritated you? Do you feel that my participation here is out of
place somehow? I really do want to know. If I am doing something that
the group as a whole thinks is inappropriate to the group, then I will
stop.

Peter Nachtwey wrote:

"Iterative tuning" could be so broad, it's not surprising that more than
one of us mistook the meaning.

I think that sort of tuning does have a place.  Many systems can't be
meaningfully measured for plant characteristics unless they're in the
vicinity of their normal operating point, which means they have to have
loop closure.  The "twiddle the knobs" method of tuning can get you to
stability, if not high performance, pretty quickly.  It's also
appropriate if you just need _something_ resembling a closed loop,
rather than the World's Most Optimal Tuning.

Of course, it's up to the responsible system designer to recognize
what's needed out of the loop, and what they can get away with in terms
of tuning methods.

When I'm using frequency response tuning methods I don't calculate the
system model as a transfer function.  I just accept that my system model
is embodied in the plant response, and I live with it.  On the one hand
this is unsatisfying because one can't point to a transfer function and
proclaim "that's it".  On the other hand, one _can_ point to a Bode plot
and proclaim "that's accurate".


I must be fairly open-minded, because I've used a number of different
methods, as the problem at hand demanded.

If accuracy _really_ matters, and particularly if I'm looking at
frequency-domain disturbance rejection, then swept-sine is the way to go.

One of my former employers has a really nice package, that I wrote in
C++, that allows you to connect just about any small geared DC motor to
a PWM drive and a position sensor, tell it things about Kv, gear ratio
and motor inertia, then stand back while it designs all the controller
gains every time the processor powers up.  This is on it's tenth
mechanism, and I haven't had to tweak it since mechanism # 3.  ALL of
the tuning in this is done from first principals, using Newtonian
mechanics and basic motor theory -- and it includes implicit calculation
of trapezoidal velocity profiles.  This works primarily because the
tuning is quite conservative, because my goal was a universal reusable
block.

If a system isn't going to change much, and if performance is far from
critical, I'll tune by twiddling knobs.  I'll usually only do this if
the controller only needs to be a PI, and if I have strong reasons to
believe that the plant simply will not vary in production -- but I'll do
it when I feel it's necessary.

I've even double-checked frequency response data using ARMA fitting to
step-response data, ala Peter.  I haven't had occasion to use this as my
primary means of obtaining a system model, but I won't be astonished it
happens some day.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

text -

If you disregard  the effort in achieving the best PID settings, I
would support the iterative tuning as described in the paper referred
to by Peter. Some aspect of this is conceptually similar to Model
Predictive Control; the objective is to minimise a cost function that
has weighting coefficients that allow you to prioritise between
accuracy and penalising excessive control moves. I have written some
simple PID simulations in Scilab (open source Matlab-type package)
using their optimisation algorithms to find the optimum PID settings
based on this type of cost function. It is nice exercise to explain
the concepts. If somebody is interested, you can contact me and I will
email it to you.

This works very well if you have a good model of the process. All real
processes have (to some extent in any case), non-linearities and
different responses in different operating regions. Of course,
although time-consuming, it is relatively easy to model all of these,
and then use some variant of Peter's iterative tuning to find the
"best" PID tuning. But now defining the "best" becomes more complex,
just an optimisation cost function with weighting coefficients is
probably not adequate. You probably have to use concepts similar to H-
infinity robust control.

And so on. In the mean time, using the two-step iterative approach I
have outlined above, I am probably busy with my 20th loop.

Pieter Steenekamp

pieter steenekamp wrote:

What if you don't have the chance to practice?  You just need to get the
system tuned quickly and it is something that is done rarely.  What if
the next system isn't anything like the last system or anything you have
tuned before.   Tune this:

T(s)=G*Omega*Omega/(s*(s^2+2*Zeta*Omega*s+Omega*Omega))
G=3 inch/sec/volt
Omega=2*PI*10
Zeta=0.1

and make this approach the set point with a critically damped response.
  Note, this is a trick question, but this is what a hydraulic cylinder
models looks like if you linearize and simplify it.  The damping factor
is so low that it will oscillate easily if you increase the P gain to
much as suggested above.


I repeat how does trial and error approach help understand PID tuning?
There are some many different types of systems.  I cringe when I see
advice on how to tune a PID when the person giving the advice has no
idea what the other person's systems is like.  See below.


That actually isn't fair the the PLC forum.  A few years ago I got tired
of seeing the same kind of advice there like I saw here.  What I did was
make Excel spreadsheets that had different models and I asked people on
the forum to tune them.  It didn't take long to convince the people on
the forum that each model tunes up a little differently and that some
models are very difficult.  Anyway the people that took part now realize
that that giving advice is not good unless you know what kind of system
the user has.  Now only the new members that haven't been through the
Excel tuning experience make that kind of error.


Yes, but I use it only when I can't excite the system enough or it is so
non-linear that the system identification is worthless. Other people
will use the trial and error iterative approach because they have only
one system to tune and there is no pay off in investing in better tuning
methods.  I understand that.


Even then one can add this feature to the identification program so that
system like heat exchangers can be identified over a range of temperatures.


I agree, but fat chance.  The poor control guys has to put up with what
he has.  How is the system designer going to know what to do and not to
do unless he knows how to model the system? This topic is important to
me, but I will leave the rest for another time.


So what do you do with it?  Don't answer here, that is another topic but
I think everyone would like to know.


Unless you are going to shake the place apart or multiple axes are
connected to each other so they can be moved independently.  Also, the
gain on hydraulic actuator is different in the extending and retracting
directions.  I am not saying what you are doing isn't right, it just
isn't always right.  This is another example on how we should know more
about the system and the application before offering advice.

 >I've even double-checked frequency response data using ARMA fitting to
 > step-response data, ala Peter.  I haven't had occasion to use this as my
 > primary means of obtaining a system model, but I won't be astonished it
 > happens some day.

Do you do you frequency sweep in open loop?  Just curious. Yet another
topic. It would be interesting to check the Bode plot generated by the
system identification model with your sweep generated Bode plot.


That is raising the high bar.  Now problem is how can people access it
with out you e-mailing it.
I will raise high bar a little more but this will not help the OP find
his answer.
http://www.plctalk.net/qanda/showthread.php?t '057&highlight=Advanced+Control

There is a Scilab program that can identify a FOPDT and SOPDT system.
The Scilab identification program was tested using data RSTrend file of
his temperature system.  The calculated gains were then applied and
tested on the real system.  Perhaps the Newgroups will just die in favor
of forums because one can do so much more on a forum.  Yet another
topic.  BTW, I am a motion control person but dabble in other areas to
keep an open mind.  In the end it is just using math to keep track of
where the energy goes.

Actually, once you have done the work of making a good auto tuning
package then you can tune systems much faster.  That is the whole point.
  If I only had one system to tune I wouldn't bother with the math and
all  the study it took to implement something that really works.
However, in my case I sell motion controllers.  I have customers that
tell me it takes a day to start up an axis.  If I can reduce this time
from 8 hours to an hour of wiring time then I have saved a lot of time
when you multiply that by many thousands of axes a year.


I will raise the high bar some more.

For the auto tuning I use the Levenberg-Marquardt algorithm to do the
system equation.  See the link above.  Then I have a model that looks
something like the PID example on the bottom of this page:
http://www.engin.umich.edu/group/ctm/PID/PID.html
I have solved for the PID and feed forward gains symbolically.  I have
symbolically done what the Ackermann equations do.  I just find it
easier to understand the symbolic math rather than the matrix math.

For a simple type 1 first order system
T(s)=Gain*alpha/(s*(s+alpha))
the gains for a critically damped system are:
Ki=lambda^3/(Gain*alpha)
Kp=3*lambda^2/(Gain*alpha)
Kd=(3*lambda-alpha)/(Gain*alpha)
where alpha is the open loop cutoff frequency and -lambda is the desired
location of the three closed loop poles are placed.  We have a slider
bar on the auto tuning program that allows one to select the response by
moving the desired locations of the closed loop poles along the negative
real axis.

What do the equations tell you about the ratio of the integrator to
proportional gain?  Knowing this how can you change one gain without
changing the other two unless you don't care where your closed loop
poles are going?  An interesting game is to enter gains and see where
the closed loop poles end up.

Note, each model has its own set of equations and each type 1 model will
have another set for tuning without the integrator.  The weakness in my
method is that the zeros can be anywhere but there are solutions for
that too.

In the Scilab program I used the equations on www.controlguru.com to
calculate the controller gain and the integrator time constant because
temperature systems usually have dead time and my motion equations don't
allow for that.  Yet another example of how one must know the
application and the model to find the right solution.

For the manual tuning I just minimize the SSE ( sum of squared error )
between the target position and the actual position.  The error is
never very big because the target positions transition smoothly from one
set point to another. I make this a game for the customers.  If they
adjust a gain and the SSE goes down, they have made a good change in the
right direction.  If the SSE goes up the gain must be restored and
either adjusted in the opposite direction or a new gain must be
adjusted.  This is easy to teach but wasteful of time but in some cases
easy is most important.  The OP asked a question iterative tuning
technique.  If you read the document there are ways where one can
compute a gradient so the new set are adjusted in the right direction
and all gains are adjusted at once. This should result in the same
results as if one manually changes the gains one at a time.  This
iterative technique can work for me be it because takes only a second to
move an actuator.  I would not claim that is work well for other
applications, especially those with long time constants.

What if your system is a temperature control system has long time
constants so one test takes 20 minutes?  20 test will take a long time.
  If you have only the one PID then fine.  Otherwise, perhaps a method
of comparing the PV and SP and calculating the best way to change the
gains would get you much closer in 4 iterations.

Now I wish there was an advocate for calculated iterative tuning that
monitors this newsgroup. I have some questions because there are holes
or missing details in that article.  How does one find the gradient
without making extra trials just to find the gradient?

Peter Nachtwey

The is a nice and simple example to demonstrate the iterative tuning
method, thanks Peter.

Because the process includes a pure integrator (1/s), you don't
require integral control for steady state accuracy, and P-only
controller works very well. Building a Scilab model, within a small
number of iterations you find that a gain of 4.0 gives you the
required critical damping.

Pieter Steenekamp

wrote:

This is not an example of iterative tuning.  There is no iteration.  I
find the model and if it matches a type 1 first order model then I use
these equations.  There equations are an example of pole placement
using symbolic formulas that yield the same result as Ackermann's
equations for calculating gains given the desired poles.   I use
Mathcad to convert almost everything having to do with control to
symbolic form because it is easier to understand that way.

Peter Nachtwey

I do apologise, I should really have explained my iterative tuning
approach in a bit more detail.

When I tune a process like the one given, I would typically (but not
always) use an iterative method to tune it.
If I know that the process includes a pure integrator, I would use
Proportional Control only, because I know that then you don't need
Integral Control. My iterative tuning would be: with the controller in
AUTO, start with very weak Proportional Control action and observe the
closed response, you can either rely on natural process disturbances
or make setpoint changes. If you observe that there are no sign of
closed loop oscillatory behaviour, you increase the proportional
control action and repeat this action iteratively, until you observe
the initial signs of oscillatory response. If your objective is to
find critical damped closed loop response, you end your iterative
tuning process the moment you have found the strongest Proportional
Control Action before any overshoot on setpoint changes.

Let me just qualify this: I do not say this is THE way to tune
controllers. There are obviously many ways, and I will not even try to
argue that this way is better than any other way; it depends on too
many factors. All I claim is that it does work for me; not always, I
can also give you many examples of where this method does not work.
Normally my focus would be to get the loop on the real plant to work
well, with the minimum of effort. I love maths too, earlier in my
career I used to apply control theory to solve practical problems. It
did work and I did enjoy it. There is an intellectual satisfaction you
get from model a process and apply the nice maths based control theory
to design a control system and the to implement it successfully. But,
especially if you are pressurised for time, I find that there is a
place (again, not always and not for all processes) in the world for
the practical iterative tuning method explained above.

Pieter Steenekamp

pieter steenekamp wrote:

Did you notice the .1 damping factor?

 >
  because I know that then you don't need

True but you need more than the P gain.


Try getting the PV to the SP and stable in 1 second.  You should be able
to do this easily in about 0.1 seconds.

  If you observe that there are no sign of

Don't worry, you will see plenty of oscillations.

  you increase the proportional

We don't have all day to reach the set point.


Are you sure?  Have you tried it?  I don't think it will work in this case.

Peter Nachtwey

Peter Nachtwey wrote:

Disregard this post. It went to the wrong thread.

Peter Nachtwey

pieter steenekamp wrote:

How much time did you give it?   Try making a step from 0 to 1 and have
the PV reach the SP and be stable in 1 second.  It should be easy enough
to do in .1 second.  If you only have a Kp of four the PV will oscillate
even as it approaches the SP.

Peter Nachtwey

How I like this, but I guess I'm the one with egg on my face.

But I'm good with excuses. Let me see if I get away with this one:
Oh, you mean you are concerned about those small amplitude high
frequency oscillations. I mean have a heart, they do die away after a
couple of seconds, nobody will ever notice them.
Ok, I must admit, this is a feeble excuse.

But if you are finicky about those small oscillations; then just add a
filter to the controller output with time constant 0.03 seconds. Then
apply the iterative tuning to get a proportional gain of approximately
= 2.8 for critical damping.

How would you tune it Peter?

Pieter Steenekamp