Identifying transfer functions of a hydraulic system.

[Taylor Turner]

I have seen the canned transfer functions that are used to teach and transform a function from the (s) domain to the (t) time domain, but how can these functions be identified and calculated within a hydraulic system. Light weight stuff, but getting YouTube videos to apply with my hydraulic systems seems to have gaps I cannot bridge myself.


Jumping straight into transfer functions and not considering the front-end design offers a knowledge gap. Then once that function is derived and applying it to my main control function, PID or comparable, has another gap.

I want to start with what is unclear, the examples that have no meaning.


S+2/s^2+s+2 = Y(s)/U(s) is a frequent function I have seen in examples. What universal function does this serve? Probably none of actual application. From my understanding this function describes some input that has dead time and all sorts of considerations. When designing a hydraulic system from a catalog, what can you look to that identifies these considerations from calculation. Or through testing, how can a transfer function be identified with the relationship between the output signal and the input signal of some control loop.

I have a hard time of separating PID terms, and their consequences, from transfer functions and thinking the transfer functions should support the PID, but the functions are to support the consequences of the system: valves, transducers, springs. I hope that is accurate enough and which leads me to the latter lack of understanding.


To the second part, and skipping over the transform, we use the transfer function above and solve for the second derivative, y double dot. The code would write as.

Ydd := Ud + 2 – Yd – Y;

Yd += Ydd;

Y += Yd;

U := Input;

Ud := dt;


At first I was thinking the input here applies to the feedback signal. Then I thought that was wrong and it’s definitely the PID’s CV and Ydd goes to the valve. Then I saw diagrams of Ydd of the first plant function being input to another function that is subtracted by the PID’s CV. Then I thought it could be a way of calculating PID gains. Then I realized all may be true and I’m in over my head.
With that being said can I get some help at a snail’s pace? Or perhaps I’m missing a list of universal functions and their meanings.

To describe an example hydraulic system…

Variable displacement pump: idle-2600psi, 33GMP

Proportional valve: 4WRLE16V1-250L-4X/MPT/24A1 or if there is a better example.

Cylinder: 16” bore, 10”rod

Mass: 2,000lbs*g (platen pressing down)(I suppose there is a spring here too.)
Feedback: Load cell or Linear position

 

[Peter Nachtwey]

There are a lot of good books on hydraulics itself. There are none on hydraulic control. All the people that know anything keep it to themselves.


[cpde]
S+2/s^2+s+2 = Y(s)/U(s)
[/quote]
This is very wrong. Compare with equation 2 in my pdf linked below.

What universal function does this serve?

If I can compute/estimate the controller open loop gain, damping factor and natural frequency then I can compute the controller gains too.

From my understanding this function describes some input that has dead time and all sorts of considerations.

Normally dead time is ignored because it is very small. However, if you add hose between the valve and the cylinder the dead time goes up about 1 millisecond for every 4 ft of hose or tubing.

When designing a hydraulic system from a catalog, what can you look to that identifies these considerations from calculation.

I laugh. Few hydraulic systems are actually "designed". Most are "evolved" the worst ones are kludged.

Or through testing, how can a transfer function be identified with the relationship between the output signal and the input signal of some control loop.

It is called system identification. On my YouTube channels I have 3 videos about system identification. Here is an example of using a file of time (column 0), control output (column 5) and actual position ( column 2 ) to compute the open loop gain, damping factor, natural frequency, valve offset and dead time.

https://deltamotion.com/peter/Mathcad/Mathcad - Sysid T1P2 ODE-Forum.pdf

I have a hard time of separating PID terms, and their consequences, from transfer functions and thinking the transfer functions should support the PID, but the functions are to support the consequences of the system: valves, transducers, springs. I hope that is accurate enough and which leads me to the latter lack of understanding.

The controller gains move the open loop poles to the desired location and are called closed loop poles. I use the actual characteristic equation and a desired characteristic equation to compute the controller gains. The controller gains modify the open loop characteristic equation.

Then I thought that was wrong and it’s definitely the PID’s CV and Ydd goes to the valve.

Yes, the controller output goes to the valve. The valve should be very fast compared to the rest of the system so it doesn't add any significant delay but one must be care and look at the valves Bode plot to make sure the valve is operating in a conservative region. Valve manufacturers over rate their valves.



Why such a big valve for such a small pump? You may be able to get by with that pump if you use an accumulator.



An example using Laplace transforms to make a linear model of a hydraulic system in position mode. It uses only proportional control with not feed forwards.

https://deltamotion.com/peter/Mathcad/Mathcad - T1C1 P Only Laplace.pdf


BTW, I am a member of the International Fluid Power Society's Hall of Fame. I was also the hydraulic motion contributor of Hydraulics and Pneumatics magazine. Look for my articles and down load them. The magazine will be dead at the end of the year.


Now the forum is sure I am a geek.


Also we have a hydraulic forum for motion and force control at forum.deltamotion.com
We are experienced in how to control presses.
Here we are doing press leveling.

https://youtu.be/9iSmPHpNq4w

 

[JLand]

Now the forum is sure I am a geek.

That ship sailed long, long ago.

This is all awesome info. This cleared up some knowledge gaps for me even though I am not looking specifically looking for hydraulics. Thank you very much.

 

[Taylor Turner]

There are a lot of good books on hydraulics itself. There are none on hydraulic control.

These two books are on my wish list, and look promising. That is an assumption.

ISA, A Guide to the Automation Body of Knowledge

IFPS, Modeling and Simulation for Application Engineers

1 millisecond for every 4 ft of hose or tubing.

Good to know! I'm sure diameter is a factor. I see our hydraulic guys adding check valves and, from delta's forum, I've seen that helps this.

I laugh. Few hydraulic systems are actually "designed". Most are "evolved" the worst ones are kludged.

Gunslinger Engineering. Shoot from the hip and the controls guy will move the target for you and try not to get shot.

https://deltamotion.com/peter/Mathcad/Mathcad - Sysid T1P2 ODE-Forum.pdf

https://deltamotion.com/peter/Mathcad/Mathcad - T1C1 P Only Laplace.pdf

I'll do some homework.

Now the forum is sure I am a geek.


Also we have a hydraulic forum for motion and force control at forum.deltamotion.com
We are experienced in how to control presses.
Here we are doing press leveling.

https://youtu.be/9iSmPHpNq4w

Business owners/presidents have had worse traits.





I have programmed a dozen or so 4-axis, geared systems. It sells as good platen parallelism on the marketing side. Also draw forming with an up acting cushion cylinder on a down acting ram cylinder traversing though a stationary opening has proven to be an impressive display of position/velocity and force control simultaneously. Common application, but fun to see a way around the position and force control uncertainty.


Thanks for the feedback.

 

[Peter Nachtwey]

These two books are on my wish list, and look promising. That is an assumption.

ISA, A Guide to the Automation Body of Knowledge

IFPS, Modeling and Simulation for Application Engineers

I doubt he can match this
https://deltamotion.com/peter/Mathcad/Mathcad - Hydraulic Cylinder.pdf
Real simulations require using a system of linear and non-linear differential equations. 9 of them. I use this program as a starter when I do real simulations.
https://deltamotion.com/peter/pdf/a...s drives engine research _ Machine Design.pdf
I had to model two cylinders running 180 degrees out of phase that were moving diaphragm pumps. The pumps were pressuring fuel to 43,000 psi. So there were three sets of differential equations two for each of the two cylinders in the inner loop and another set of differential equation for the outer pressure control loop. What made it tricky is that the fuel would compress by 30% as it was intensified from 150 psi to 43000 psi. The hydraulic designer botched the design.



When I do simulations for money I use differential equations.

Good to know! I'm sure diameter is a factor.

Diameter affects the ability to accelerate and the natural frequency. It does not affect the dead time which is caused by the speed of sound in oil.

I see our hydraulic guys adding check valves and, from delta's forum, I've seen that helps this.

It depends. Where? Why?

Gunslinger Engineering. Shoot from the hip and the controls guy will move the target for you and try not to get shot.

Like I said, there is designed, evolved, and kludged. I NEVER have seen a transfer function for a hydraulic system unless I generated it.

I'll do some homework.

Good for you. Start with the VCCM equation and how to calculate natural frequency. I already posted a link to a discussion about the VCCM equation. If you are working on presses with the rod pointing down there is a good possibility that the cylinder will cavitate on the blind side of the piston. Study that too.

Business owners/presidents have had worse traits.

Ouch! I am a business owner and president. I know what you mean.

I have programmed a dozen or so 4-axis, geared systems. It sells as good platen parallelism on the marketing side. Also draw forming with an up acting cushion cylinder on a down acting ram cylinder traversing though a stationary opening has proven to be an impressive display of position/velocity and force control simultaneously. Common application, but fun to see a way around the position and force control uncertainty.

Did you see the our two axis press leveling video?


If you really want to get into the control theory visit my YouTube channel "Peter Ponders PID". I get into the nitty gritty. It is not one of the many channels that says, this gain does this and that gain does that. I know what I want the response to be an place ( calculate ) the controller gains to get the response I want. To most people it looks like I am doing it backwards.