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)? 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?
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?) and any other things that are pertinent to the control of such systems, I'd be interested in reading up on it.
--
Tim Wescott
Control systems and communications consulting
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: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
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Seeftp://ftp.deltacompsys.com/public/PDF/SpringEffectEffBulkModl.pdfftp://ftp.deltacompsys.com/public/PDF/Mathcad%20-%20Natural%20Frequen ...
Peter,
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
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Seeftp://ftp.deltacompsys.com/public/PDF/SpringEffectEffBulkModl.pdfftp://ftp.deltacompsys.com/public/PDF/Mathcad%20-%20Natural%20Frequen ...
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
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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
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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.
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: 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
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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.
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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.
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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.
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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
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On Wed, 26 Sep 2007 18:45:31 -0700, snipped-for-privacy@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?
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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.

Industrial hydraulics.

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
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On Thu, 27 Sep 2007 10:33:18 -0700, snipped-for-privacy@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.
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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
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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
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snipped-for-privacy@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
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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?
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"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/Gre http://home.arcor.de/janch/janch/menue.htm
Jan C. Hoffmann eMail aktuell: snipped-for-privacy@nospam.arcornews.de
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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
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