Modelling Hydraulic Systems

:I was about to respond to a comment by Peter in the PIDD thread, then I
: realized it'd hijack the thread.  So...
:
: Peter mentioned in his response that a hydraulic system can be modeled as
: a mass between two springs.  I'll believe that -- but what's the
: underlying physics?  Where does the 'spring' come from -- is there an
: accumulator somewhere (springiness in a pneumatic system I can understand,
: but not a hydraulic)?

See
ftp://ftp.deltacompsys.com/public/PDF/SpringEffectEffBulkModl.pdf
ftp://ftp.deltacompsys.com/public/PDF/Mathcad%20-%20Natural%20Frequency.pdf

The oil on either side of the piston are the 'spring'.   Oil compresses, so
does water.   The bulk modulus of oil is about 200,000 psi under ideal
conditions.  This value will drop if there is air in the oil.

Here is a thread that show the effect of compressing oil.
http://www.patchn.com/SMF/index.php?topica2.0

When I get serious I use a system of non-linear differential equations.  We
have 20Sim for that.

  What changes in the model as you change the
: actuator -- the position of the endpoint of one or another of the springs,
: the spring constants, what?
You can see that the natural frequency changes depending on where the piston
is.   The natural frequncy is lowest close to the middle of the stroke.
:
: Finally, if there's a web page that details the workings of the sort of
: hydraulic system you're talking about, with the plumbing, the actuators
: (spool valves, right?  Whatever a 'spool valve' is?)
Actually, servo valves.   The idea is to have the flow proportional to the
control signal but this also depends on the pressure drop across the valve.

 and any other things
: that are pertinent to the control of such systems, I'd be interested in
: reading up on it.
This is a big topic.  Jack Johnson has some books on hydraulic motion
control but they are written from a more academic point of view.


I will try to find some good websites..  We have some stuff on our website
but it is mostly marketing.

Peter Nachtwey

Seeftp://ftp.deltacompsys.com/public/PDF/SpringEffectEffBulkModl.pdfftp://ftp.deltacompsys.com/public/PDF/Mathcad%20-%20Natural%20Frequen ...

oil.http://www.patchn.com/SMF/index.php?topica2.0

I have just been asked to help build/advise on the controls design of
a "human flight simulator" at my school. At first I didn't know if a
motor, spring/clutch system or hydraulic system would be best, but I
have now concluded that hydraulics is indeed the way to go. The
problem is I have little experience working with hydraulics. As an
example of what we want to accomplish, think of the control stick of
an aircraft, and we want to use a hydraulic system to simulate the
force feedback a pilot would feel while flying. We have a simulator
for the pilot/aircraft dynamics which can simulate, for example, if
the pilot pulls back on the stick with a force of 2 N, the aircraft
will climb at a certain rate. Or if a pilot is trying to pull out of a
high G manuver, the stick needs to be able to "pull back" indicating
its really hard to pull out of said maneuver.  We would like to keep
the actual controller within matlab (because as we tweek the aircraft
model, we need to tweek the controller), so I am thinking we need some
sort of electromechanical actuator that can push/pull a hydraulic
servo valve which in turn will allow a cylinder to move back and
forth. Can you advise on what kind of servo valve we could use? I just
looked on the Parker Hannifin web site, but it was pretty useless.
Additionally, I am assuming we are going to have to model the dynamics
of the servo valve and cylinder because I am willing to bet it is not
linear. You mentioned the author, Jack Johnson... is any one of his
books better than the other?

Thanks,

James Forbes

Seeftp://ftp.deltacompsys.com/public/PDF/SpringEffectEffBulkModl.pdfftp://ftp.deltacompsys.com/public/PDF/Mathcad%20-%20Natural%20Frequen ...

oil.http://www.patchn.com/SMF/index.php?topica2.0

http://www.mech.uwa.edu.au/jpt/mecha/MD/handouts/Hydraulic%20Servo.pdf

This is a start.  It is very basic.
I will find more when I am at work.

Peter Nachtwey

This is another good site.  It has the differential equations like
those used by 20Sim.
http://servomaster.sblo.jp/

Once you get the differential equations set up use RK4 to do the
integration.  The trick part is simulating the pressure going to 0 or
the piston hitting the ends of the cylinder.   From a practical stand
point the hard part is getting good values or models for all the
components that make up the complete system.   This is one of the big
pet peeves I have with the hydraulic industry.  The manufacturers
don't provide very good specificiations for their valves, pumps, hoses
etc.  The engineers must do too much guestimating to do serious design
work.  The companies that are serious about hydraulic like Caterpillar
and Boeing will analyze the parts themseleves and not rely on the poor
and incomplete data provide by the manufacturers.

This is why system identification is so important.

Peter Nachtwey

The response time of hydraulics tends to be pretty quick. I've found when
I've had to deal with them (on machine controls for large industrial
turbines and compressors) that you can generally ignore the dynamics in the
hydraulics. That depends on what your 'plant' is, of course.

: The response time of hydraulics tends to be pretty quick. I've found when
: I've had to deal with them (on machine controls for large industrial
: turbines and compressors) that you can generally ignore the dynamics in
the
: hydraulics. That depends on what your 'plant' is, of course.
If the valve is mounted directly on the cylinder then it take little time to
increase pressure/force.   This is analogous to the resistance and
inductance in a DC motor armature keeping the current/torque from changing
instantaneously.

Peter Nachtwey

proclaimed to the world:


A spool valve is a piston and cylinder with ports cut into them so
that a linear motion of the piston causes a change in flow volume or
direction. The ports can be cut so that flow is proportional to linear
motion. The valve can also be designed so that the linear force acting
against the control motion can be canceled out (a small force will
change the position of the spool).

Here is a page with a simple explanation and some pictures of
different spool valves.

I also question the accuracy of a hydraulic model based on spring
elements. Springs most accurately represent pneumatics.

On Fri, 20 Jul 2007 09:19:50 -0400, Paul M <PaulMatWiredogdotcom>
wrote:


Why.  A hydraulic system is stiff, but it's not infinitely stiff, so
there's still a spring.  Practically though, there may be lower
frequency dynamics that dominate, making it not so important.  
If it is important, air in the oil is a huge factor in the stiffness,
and that's pretty variable.  

Actually the big issue is the assumption of linearity, which is not so
good in hydraulic systems.  Presure drops are proportional to the
square of flow, so you have to decide if you linearize or not.

dave y.

proclaimed to the world:


Sorry I took so long to reply. My reasons for doubting the validity of
a spring model for a hydraulic system are mainly what you bring up.
Most hydraulic systems I came across during my career were designed
around minimal springiness. Air in the system is a bad thing and
minimized. If you need it, you add spring function via spring or air
accumulators. I can envision a system designed for high speed
actuations needing to take things like air and the overall system
expansion into calculations, but again these characteristics are the
smallest components in a hydraulic systems response.

Since I spent the majority of my career without the aid of computer
models, they are far from the primary tool I use to design a system.

One models in general. They can be very useful to someone who
understands from experience how a system works. A model allows them to
quickly test out how changes to the system will affect it's
performance. Using a model to learn how a system works actually
teaches you how the model works, and the model never, I repeat, never
performs the way the actual system does. It might be close or it might
be completely wrong.

Each and every time I have brought up PID tuning and mention that I
normally use starting settings I know will be close from experience
and then tune to optimal, I get this deluge of responses that could
best be described as hate mail. I understand now that I stepped into a
subject that has some history here. Tough shit. Unlike the detractors,
I don't tune by making a guess and most likely I could analyze how I
do this and put it down in a few simple rules. Why should I bother?
There appears to be only a handful of people here I have any respect
for and I am not willing to waste my time responding to the others.

On Sep 26, 7:46 am, Paul M <PaulMatWiredogdotcom> wrote:

Did you see the link above about natural frequency?

That is a safe statement


II have posted a link to a to this .pdf before.
ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20Sysid2A2BV70%20T02.pdf
It shows the results of doing a system ID on my hydraulic system.  The
graph shows how the estimated model responds to a control signal
compared to how the actual hydraulic system responds to the same
signal. I have no illusions that this model takes into account
everything.  The valve is assumed to be fast compared to the
actuator.  If I had a more detailed model, what could I do with it?
To properly control this system requires a PID2D controller.  Adding
more gains for more poles is not practical.  This kind of modeling
does work extremely well for for finding system parameters that I need
to plug into the formulas for calculating the gains.

My hydraulic system is well designed.   If one uses valves with non-
linear spools then all bets are off. When I get serious I use a system
of non-linear differential equations for my model.

Peter Nachtwey

On Wed, 26 Sep 2007 18:45:31 -0700, pnachtwey@gmail.com proclaimed to
the world:


I did look at the mathcad data. I can see how a model is helpful in
some cases. I believe you hydraulics work.

But what is your typical system used for. Is it typical to hydraulics
systems in general? I can see doing some modeling and testing in high
performance hydraulic systems, something really fast or with dampening
added to lower stress on mechanical systems.

Also the question was using a spring model for a hydraulic system. Why
not use a model designed for hydraulics instead. I guess you can set
the spring parameter to zero or infinite and this will make that
virtual spring act like a cylinder with no air entrapment, but is this
really adequate, necessary, useful?

Can you think of a reason for using nonlinear spools other than cost?

On Sep 26, 11:44 pm, Paul M <PaulMatWiredogdotcom> wrote:

Here is another one of my worksheets.  I wrote this when a student
asked for help about hydraulic shock absorbers.  The student was told
to find the equations on the internet.  My 'integrator wound up into
saturation' since I knew there was little if any information on this
topic.  This student asked a question that was like the answer to
'life the universe and everything' for hydraulics. I didn't think he
deserved the response he got so generated this worksheet to point out
that the answer isn't simple.  I work on this worksheet when I have
time and post an update to it just so the thread goes to the top to
remind those of their embarrassing answers.  Yes, I like to tweak
noses not gains:)
ftp://ftp.deltamotion.com/public/PDF/Mathcad%20-%20Oddball.pdf
Notice how much the oil compresses.
Next I will add modify the delta p = B * delta v / v equation take
into account the flow of oil through the orifice and how the changing
volume affects the delta p.   On a hydraulic simulator for a cylinder.
one must do this for each side of the piston.   Also, as you pointed
out the supply pressure does not stay constant.  One must also model
the flow into and the flow out of the accumulator to get the
instantaneous pressure at anytime.


Point to point moves of large masses and pressure force applications.


My company makes motion controllers and we specialize in industrial
hydraulic servo control so I don't get involved with aircraft or
mobile applications too much.   You are correct about the testing
applications this is growing business.   You also correctly point out
the fact that there is lower stress with smooth motion and therefore
fewer if any leaks.  We got our start moving logs and saws in the
sawmills of the Pacific North West and that is still a big part of our
business.  Now we try to convert bang-bang hydraulics and misapplied
servo motor application to servo hydraulics using the same kind of
motion control the servo motor applications use and yes we can control
servo motors and electric cylinders too.   Hydraulics is used in
aluminum and steel plants ( square trees ), presses,  motion platforms
for movies and entertainment.   Servo hydraulics and servo motors have
different strengths and weakness.   In a press application a hydraulic
system uses very little power to maintain pressure or force whereas a
motor requires lots of current to maintain torque.  Another advantage
servo hydraulics has is that the actuators are small relative to the
work rate they do.  Another big advantage is that one motor can run at
a constant speed and supply the oil for many actuators.  This one
motor/pump only needs to be able to convert the average amount energy
required for a machine cycle.   An accumulator can store energy during
the dwell times.   Servo systems require a motor for each actuator and
each much be sized for the peak instead of the average load.  However,
this advantage goes away and shifts to the motors in applications like
conveyors where this is no dwell time to store energy and the load is
fairly constant anyway.

Here is an example of a servo hydraulic system and a lot more.
ftp://ftp.deltamotion.com/public/movies/JAN-04%20VSS_0001.wmv
There is a scanner upstream that scans the wood.  This information is
used by the optimizer to figure out how best to cut the wood.  Notice
the actuators do not cut straight boards.  The actuators follow the
grain or curve of the wood and the cut wood is dried straight in
theory. The curves or electronic cams are downloaded for every piece
of wood.   The motion controller waits for a photo eye to be blocked
and then makes the actuators follow the curves ( electronic
camming ).   This cuts the wood in the optimal way for best recovery.


Again, you should look at the links I posted in response to Tim's
original request.  Oil, like most other materials, has a modulus of
compression.   200,000 PSI is ideal.  Reality can be much lower like
160,000 or even 120,000 PSI.  Oil appears incompressible until you
start trying to position an actuator moving tons to 0.001 inch
accuracy.   I wouldn't put the effort into modeling if it isn't
useful.  I have saved customers many 100,000 of dollars with models.
Not because I can tell them the model works but because I can tell
them that it doesn't and why.   I am very cautious about models
because I don't get all the facts and unmodelled feature will degrade
performance. If an ideal model does work you can assume a real system
will not.  I can't ever assume that if the model works that the real
system will.


Not for servo position or pressure/force applications.  Some valve
manufacturer claim their dual gain valves provide more resolution at
lower flows but the need for this has long gone with 16 bit DACs on
the output. Also,  anyone that has spent just a little time in motion
controller realizes that errors due to quantizing of the feedback
cause quantizing in the output such that 16 bit resolution is often
wasted.  I like tweaking the valve manufacturer's noses about linear
valves too.  A linear servo valve will be very easy to tune over a
wide range of speeds.   Non-linear valves are a hastle.  What every
you think you save in price is paid for in lost time tuning and
performance for a the time the non-linear valve is installed.

Manual applications that use joy sticks like to have a dead band so
one can let go of the joystick and the spool will shut all the ports.
In some applications where hydraulics is used for speed control of a
conveyor it is nice to have a dead band because the conveyor will not
drift.  These are not usually controlled by a controller like ours and
as I pointed out, continuous moton and load applications are best done
with a motor.

Peter Nachtwey

On Thu, 27 Sep 2007 10:33:18 -0700, pnachtwey@gmail.com proclaimed to
the world:


Peter, thanks for this response. I want to continue, but will need to
do this at a later time. I don't have any major disagreement with
anything you have said. It's ironic that your experience quoted is in
the lumber industry as the only major problems I have had with
hydraulics in one of my designs was in a similar application back in
the early 90's. It involved a very similar project, automating an
operation that produced fence posts and the company hired me to design
and build a system to sort incoming precut timber, debarked and fed
via conveyor into a peeling operation where they hand sorted the stock
to be fed to the peeler set to the largest post possible for the
stock. Eventually the sorting operation was to be automated using
visual inspection systems and X-ray scanners. There were to be eight
peelers for different size posts. We completed the first stage, which
was to automate a single peeler using one of the first PLCs, the Atcom
64. I actually loved that little PLC and the SNAP programming
language. I had little problems with the programming side of the job,
but did have lots of hydraulic woes. I spent weeks arguing with the
supplier and ended up having to switch to his control valves and
working around their limitations.

We never got past the single peeler automation and the conveyor/sort
system. The project was scaled back because the company had no
infrastructure to move and make use of the chippings being produced by
a machine that worked at 10 times the manual rate. The added cost of
waste disposal stretched their budget. I felt it was short sighted as
they had one of the east coast's major paper mills within 60 miles of
the facility and a contract to supply all of the fence posts supplied
to Lowes. They could have leveraged that into supplying landscape
timbers.

The visual inspection and sorting system was going to be challenging
for me in the early 90's. A big gamble that I could produce a working
system.  I had just started researching what was available at the
time. It would have been an interesting gamble.

I have not kept up with the wood industry but I wonder if there is not
a lot of opportunity still in my area.

Anyway, give me some time to look at this better and I will comment
some more.  My major concern with models is this. Students in many
fields are now being taught science and engineering using computer
models. HS chemistry and physics classes now do not even have the
equipment to carry out basic experiments. They learn about inertia,
mass and motion on a screen instead of bricks, roller skates and
pulleys. Does this new approach develop the mind's ability to model on
it's own. I know models help me understand aspects of systems quickly,
but without the real life experience, I don't know this would be true.

For me to defend or abandon this position, I need to investigate the
modeling being used a little better.

On Thu, 27 Sep 2007 16:11:58 -0400, Paul M wrote:


-- snip --


Personally, I don't think a model is much use unless I also have an
intuitive grasp of how the system is going to work.  That intuitive grasp
comes from actually working with real hardware.  I have successfully
closed loops around systems where I only understood the math*, but it's
chancy at best -- more often failing to close the loop properly will lead
me to that "aha!" moment where I intuitively grasp what is going on (and
therefore what's wrong with the model).

* Always after being backed into it, or where I _thought_ I understood the
real thing.  Never as a first choice, ever.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

I think an accurate model is always useful. The more accurate the
model and the less intuitive feel one has the more useful the model
is.  I can tell how accuate a model is by looking the mean squared
error between the estimated and actual response.  In the link to the
system ID you can see the error was 0.102183.  That is the sum of
squared errors.  If I divide that by 1500 samples I get a means square
error that is very small.   It is easy to see estimated velocity is
matching the actual velocity very well.  I know I can use the gain,
damping factor and natural frequency to plug into my gain calculation
equations and the results will be very good.  Since I am measuring the
position with a Temposonic rod with a resolution of about 0.001 inches
every millisecond you would think my speed measurements would be very
coarse.  It makes one wonder what is more accuate, calculating the
speed from the Tempsonic rod or using the model to estimate the
speed.  Which would you rather use for calculating the derivative gain
term of the control output, the model velocity or the velocity
calculated from the Temposonic rod?

Peter Nachtwey

pnachtwey@gmail.com wrote:

True, but the less of an intuitive feel I have for the system, the less
I trust my ability to make an accurate model.  When I have to approach a
system this way -- by modeling it, then developing an intuitive
understanding from the model -- I make darn sure that I do tests (like
your MSE error between estimated and actual response) to verify my model
before I go building systems that may be blunders.


Do you mean your derivative _gain_ term or the derivative term itself.
Using a model to calculate a velocity is all well and good if the model
is accurate, but when reality diverges from the model you can be
applying some really wrong control signals if you depend too much on the
model.

I'm not putting down using a well-constructed observer here -- just
pointing out that you need to take care that it is, indeed,
well-constructed and not just a flight of your own imagination.

--

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

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

proclaimed to the world:


This pretty well states a lot of my uneasy feelings about models. I
fear that a student that uses models supplied them without any
intuitive feel, has no way to know if the model is giving them junk or
something useful. Without any experience seeing the control system
built and running, how do they get the intuitive understanding?

"Paul M" <PaulMatWiredogdotcom> schrieb im Newsbeitrag

... by using models. See also how to get the necessary process transfer
function:
http://home.arcor.de/janch/janch/_news/20071001-identification/


--
Regards/Grüße    http://home.arcor.de/janch/janch/menue.htm
Jan C. Hoffmann  eMail aktuell: janch@nospam.arcornews.de
                 Microsoft-kompatibel/optimiert für IE7+OE7

I meant the derivative term but I also use the model to calculate the
derivative gain.


Obviously the model needs some feedback to keep from going astray.  As
you pointed out below the result is an well-constructed observer or
possibly Kalman or H-infinity filter.  The difference between them is
small especially if you are talking about steady state filters.

That applies to Kalman filters and H-infinity filters too doesn't it?
I have seen the terms Kalman and H Infinity filter used on this and
other forums but it is all just big talk unless one can get past the
basics and both filters start with the system transition matrix.

I wonder if the astronaut landing on the moon would have had an
intuitive feel for landing without models and simulators.

Peter Nachtwey