Modelling control valve

[Pandiani]

Hello guys,

it's time to talk about modeling and simulation again. I've been doing some research and saw different models. I noticed that in many cases control valves are used but never modeled. I know that when control valve is in good working condition that is not necessary. But nontheless, I'd like to discuss about control valve modeling. Control valves can have different types of flow charactersitcs. Most of them are shown in the attcahed picture:
http://www.plctalk.net/qanda/uploads...ve_Flow_Ch.gif

Now, if valve is motorised, then DC or AC motor model should be taken into modeling phase. For now, we can exclude motorised valves.

I was playing in Matlab trying to make simple but effective model of a control valve and I came to the following structure:
http://www.plctalk.net/qanda/uploads/C_valve_model.jpg

Now, I made little test with ramp input and here's the result:
http://www.plctalk.net/qanda/uploads/Response.jpg

Of course, these time constants and gains are parameters that can be adjusted depending on the real situation in the field.
Saturation block is necessary and because of backlash this can be use to analyze prformanse of control loop in case if controller is used to minimize bad effect of valve with backlash.

Do you have time and will to try to make different models and design controllers to minimize negative effect of backlash?

Do you agree with this model?

[Tom Jenkins]

Which control valve characteristic did you use? There are several shown in your first figure. The most commonly used valves are going to be non-linear, with a characteristic similar to the quick opening curve. A small change in the valve near closed makes a big change in the flow. A large change in the valve near full open makes a small or no change in the flow.

Why do you exlcued motorized valves?

[Pandiani]

Well, I thought first to try to achieve good model and test it and then add new transfer function block that representts motor and learn about its influence.

I also used nonlinear, exponential characteristic of flow. It is just my guess, maybe you used more sophisticated models? I don't have much experience myself...

[Peter Nachtwey]

A valve where the spool is moved by the fluid or by a solenoid can be modeled by 1/(tau*s+1) where the control signal is -1 to +1 and the spool position is -1 to +1.

When you added the integrator you are then turning the system into a motorized valve. In this case the valve stays where it is when power is turned off. Would the valve really have a time constant of 2 seconds? Does it really take 10 seconds to get up to speed? That seems very long. Wouldn't the biggest problem be the speed of the valve?

I think a valve might get up to full speed which might be only 10% per second. It would get up to that speed rather quickly. But it would take 10 seconds to fully open or fully close. The time constant only affects the time it takes to respond to a control signal.

Is the speed of the valve closing or opening variable? I can see where the motors are just simple on/off controls. Look at your valve response. You can see the valve slows down as it approaches then end of travel. I would expect the valve to slam against the end of travel at the opening or closing speed.

I would bet that a lot of these valve don't even have feedback. You just close the valve at set the position to 0 and then keep track of the time the motor runs in either direction to estimate where the valve is.

Finally there is the matter of the spool. Is the flow linear as a function of how open the valve is? Chances are it isn't. A look up table or formula may be needed to convert the spool position to a percentage of flow.

[Pandiani]

Peter, these are right questions. I just made up time constants. You're right about motorised valve. At first I made it open loop, but then I wanted to stay at some point and in effect I made it look that way. I also think that transfer function of motor must be incorporated somewehere.
I'll think about you've just written. It needs a lot of work, it's far from useful, but it's a start. I'll get back when I figure out more...

[kamenges]

You will need different models based on the actuator type you are dealing with.

One of the actuator types is the motorised actuator. However another type is the spring balanced pneumatic actuator. This would have a more typical first order transfer function. However, these valves are typically driven using an E/P or I/P transducer, which have flow limits and transfer functions of their own.

I would personally stick with the pneumatic style for right now as they tend to model 'better'. Once you move to the motorised actuators the response is governed largely by the motor speed and will be very non-linear. However, these are also the actuator types where backlash really become a problem. That can be fun on it's own.

Keith

[Peter Nachtwey]

The model for a motorized valve would be

K/(s*(tau*s+1)

The velocity response is K/(tau*s+1). The 1/s just integrate velocity into position. I don't understand why you had two gains in the numerator above. If the time constants are small you could model the valve as just K/s

I would expect tau to be on the order of 0.1 seconds or smaller. I would be there are specifications that say the valve must close within a second or two. This would put the gain at 0.5 to 1 /sec.

[kamenges]

I'm a little confused by the structure of the model. It looks like it is modeling a motorized valve positioner with built-in feedback. I don't know enough about those to know if the structure is correct. It appears a little simple for one of those.

On the other hand a simple three-state motorized valve wouldn't have the feedback in the valve model. That (if it is even present) would have to go back to the control system. So this seems like kind of a hybrid between the two.

Is the output of the model intended to be flow or valve position? I am guessing valve position. Depending on the valve design the backlash may need to be moved around. If the feedback device is on the valve stem the backlash would be inside the feedback loop.

Keith

[Peter Nachtwey]

In the models I present the feedback would be position. That is why the model is K/s or K/(s*(tau*s+1)). Velocity is proportional to the control signal and the integrator integrates velocity to position. This is a type 1 system. Type 1 systems do not move back to a steady state. They just stop. Type 0 systems like temperature or velocity systems will go back to a steady state like 0 velocity or ******t temperature. They do not hold the state.

I wonder what the program is with a m b i e n t

[Pandiani]

Ok, I have added closed loop and integrator to keep steady value of flow, when there is stop command. This means that when valve is opening and stops, flow through valve is not going to start decreasing, it must be kept at current value. I have also saw one model of control valve by browsing the Internet for these models.

I tried to mimic quick opening behavior of control valve. This way I was actually developing model of motirised valve.
There are many motorised control valves in my plant and their running time depends on the actual appication and appropriate mechanical euipment (level, gears...) but it is about 30 - 40 sec from one end to other. There are of course, pneumatic positioners which runing time is measured in a second or two...

[Pandiani]

I've continue searching for the different models and found model as shown in the attached file. It is interesting that it used a lookup table (it is possible to use approx. nonlinear relationship). Complete article can be found here

This is really interesting. I wasn't able to find much models of control valves no nearly as much as I expected.

[Peter Nachtwey]

Originally Posted by Pandiani

This is really interesting. I wasn't able to find much models of control valves no nearly as much as I expected.

The article is good but basic so that most can understand it.

Your model should look something like this

x(s)=K/(s*(tau*s+1)

Where:
x is the valve state. x[0] is the Valve position. You should be able to find K which is the rate if valve opening or close per % of control output or full output.
tau is the time constant to reach the desired closing speed.

Next you need to model the valve

Flow(t)=ValvePosition(t)*Kv(ValvePosition(t))*sqrt (Delta P)
The flow is dependent on the valve position as it goes from 0 to 1. Kv, is the flow consant, is not usually linear. See the bottom of page 2. There is a look up table for the valve position and Kv relationship.

If it is then this equation can be simplified to just
Flow(t)=ValvePosition(t)*Kv*sqrt(Delta P)

So Pandiani, do you have a flow curve for the valves? The manufacturers should have this information. Look for the transfer function stamped on the valve.

What you end up with is a system of NON-linear differential equations that you solve by using RK4 or similar.

This thread and the other about the Rockwell PIDE and creating vacuums are related.

Welcome to my world. I don't usually control motorized valves but when we do we are just interest in the valve position. Sometimes the valve has a big spool with about 12 inches of travel.