Modelling Hydraulic Systems

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.

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

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.

On Jul 20, 2:37 am, "Peter Nachtwey" wrote:

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?topic=612.0>

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

On Fri, 20 Jul 2007 00:27:58 -0500, Tim Wescott 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.

Spool valve: see fig.5-13 at

Springiness arises from compressibility of the oil and from compliance of the hoses and tubing. (Do you know that the lines from fuel pump to injector on a Diesel engine are cut to the same length regardless of the actual run? The amount of delivered fuel is less than the pumped volume because of the compliance, and equalizing the lines delivers the same amount of fuel to each cylinder.)

When building precision machinery, it is well to design and think as if all structural elements are made of rubber. Homework problem: A steel cylinder, full of hydraulic oil at zero (gauge) pressure is 3.000 ID with .250 wall. When the pressure is increased to 4,000 PSI, what is the new diameter? If the fluid were truly incompressible, how much would need to be added? (Which is more compressible; hydraulic oil of steel?)

Jerry

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?topic=612.0>

Peter Nachtwey

I like to browse here but most of the topics are well beyond the stuff that I used to get involved in. Having said that, I did get to play around with hydraulic control systems. We kept things pretty basic--defining the system dynamics using the gain of the spool valve (Flow as a f(inlet stroke), the characteristics of the various components, actuator, the various flows in the circuit and the feedback mechanics. Obviously, one of the biggest factors was "air" and the manner in which it affected the stability and the transient response of the system. Calculations are nice (if you can predict everything) but nothing did the job better than a good set of instructions for bleeding the air out of the system and then a means of verifying it with the system running. As noted in another post, at times things move pretty fast and I've seen a 30-50 millisec delay (no actuator movement due to compressible flow) cause a control parameter tracking error which eventually resulted in compressor blade failures (jet engine). In this case, putting a .010 dia hole at the top of the actuator pistons was enough to allow the trapped air a way of getting out of the actuator lines. Cheap solution for such an expensive, catastrophic failure. MLD

This is another good site. It has the differential equations like those used by 20Sim.

This is why system identification is so important.

Peter Nachtwey

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.

Where does the oil go?

and equalizing the lines delivers the same : amount of fuel to each cylinder.) : : When building precision machinery, it is well to design and think as if : all structural elements are made of rubber.

: Homework problem: A steel : cylinder, full of hydraulic oil at zero (gauge) pressure is 3.000 ID : with .250 wall. When the pressure is increased to 4,000 PSI, what is the : new diameter?

The diamater would increase by about 0.002. I have been asked about the hydraulic capacitance of the cylinder. It is too small to worry about. See

: If the fluid were truly incompressible, how much would : need to be added? (Which is more compressible; hydraulic oil of steel?)

If the fluid is incompressible then anything over of the volume required to fill the cylinder would cause the pressure to increase infinitely. The formula for calculating the change in pressure is

DeltaPressue = BulkModulusOfOil*deltaVolume/Volume

Oil is much more compressible.

Peter Nachtwey

Peter Nachtwey

The injector creates a large back pressure. The steel line expands (increasing its volume) and the fuel compresses. Think of a constant-displacement pump intermittently pushing air into a gum-rubber hose that has a relief valve at the far end.

Most of the reason for making the pump-to-injector lines the same length is so that they hold the same amount of fuel. Expansion of the lines is secondary. but measurable.

Jerry

Bleeding air out of the system is basic hydraulics 101. If designed right the air will flow out of the cylinder on its own. See below. What gets tricky is keeping entrained air out of the oil. A major culprit is the return line to the tank. The oil must be returned without any splashing. Usually the return oil is released below the level in the tank and baffles slow down the motion of the oil.

As noted in another post, at times things move pretty

You didn't describe your system but I recommend putting the hydraulic servo valve directly on top of the cylinder for two reasons. One is the trap volume of oil between the valve and the piston is minimized and the other is that trapped air will naturally flow out the valve because the lines are at the top of the cylinder.

I see too many take the easy way out and put the valve on a manifold that is often below the cylinder and then hose is run to the cylinder. This is bad for three reasons. Air can't escape easily, the trapped volume of oil is larger than it needs to be, and the hose adds capacitance. All three factors lower the natural frequency of the actuator.

Peter Nachtwey

instructions

Peter: I didn't get into too much detail but what you're referring to applies well to something that is usually large and stationary. Jet engine control systems are fairly complex and today's digital controls are complimented with many hydromechanical components. Most (almost all) gear driven components are at the bottom of the engine and the actuator locations are dictated by their function (moving inlet guide vanes, jet nozzle etc) as well as the envelope constraints and are usually not very close to the high pressure source. I agree that getting air out of a system should be "basic hydraulics 101" as you put it. Again, not so basic or simple when the system is all assembled and then is filled with oil or fuel. No tank but a complete closed system; return flow just goes to the low pressure side of the system (pump inlet); maybe there is an accumulator. Arbitrarily cracking fittings or lines to bleed them is not acceptable and is not allowed. It usually takes a systematic series of steps to ensure air is removed--in some systems, there are means to extract the air via push button type of relief valves as it is being filled. A well defined specification has to be in place since this is done world-wide using skill levels from experienced to basic rookie, and can't be left to everyone's own idea of how to do it. MLD

The link is to a Mathcad worksheet where I used data from our hydraulic test system and compute the model. The columns are time, target position, actual position,?,?, control output. The target and actual positions are the same because I used a an open loop output. I only used the control output (5) and the actual position (2) to generate this data. ftp://ftp.deltamotion.com/public/NG/Mathcad%20-%20Sysid2A2BV70%20T02.pdf

One can see there is some oscillation when the control output changes rapidly. First order lag systems would not overshoot the steady state velocities. One can also see my model generated an estimated velocity which closely matched the actual velocity. This is more than good enough to use for tuning. I would use a PIDD with velocity, acceleration and jerk feed forwards to tune this system. All those following my posts know I have formulas, where I plug the actuator gain, damping factor, frequency and the desired closed loop pole locations, to generate the controller gains.

One must design the hydraulic system properly to identify a hydraulic system this well. Hose, long tubing, non-linear valves and not enough accumulator capacity will make identification harder or less accurate. A well designed system tunes easily and is easy to keep tuned. A poorly designed system will be a nightmare until it is ripped out.

Peter Nachtwey

On Fri, 20 Jul 2007 22:29:20 -0400, 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 s*it. 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.

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, 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?

On Sep 26, 11:44 pm, Paul M 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

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