# Flow control system using proportional valve

#### Crogla

Hi guys, I have this as school project and I am stuck at the moment and any help would be great. So I need to make simulation of flow regulating system that will have proportional valve as element of control. System needs to take in consideration transport delay and non-linearity of valve (dead-band mainly, histeresys and asymmetry should not be taken in consideration). I need to make software for it in TIA portal and simulation in WinCC. So far I made system which is shown in picture below and if I can I would like to keep it like that(elements of system), if not it can be changed of course. Frictions from pipes don't have to be taken in consideration also and whole system is in one line but I didn't have room to draw it properly(tanks should be aligned).
I made some mathematical modeling and came with this:
P = dp * Q (pump power)(1)
pPump = p1 + dp (pressure on pump exit)(2)
Q = Cd0 * i / i_max * A0 * sqrt(2*(pPump - p2)/rho), (prop. valve equation)(3)
Implementing equation 1 into equation 2 into equation 3 I get this:
Q^2 = (Cd0 * i / i_max * A0)^2 * (2*( p1 + P / Q - p2)/rho)
which is:
Q^3 - (Cd0 * i / i_max * A0)^2 * (2*( (p1 - p2) * Q + P)/rho) = 0
and that is qubic equation
Q^3 + a1 * Q + a0 = 0, (4)
with coefficients:
a1 = - (Cd0 * i / i_max * A0)^2 * 2 * (p1 - p2) / rho
a0 = - (Cd0 * i / i_max * A0)^2 * 2 * P / rho
when solved it should give value of flow in system but I get some weird values for flow rate with that or I get good result but in weird measuring unit. I also made HMI in simulation to enter parameters for valve, pump, etc. and I get some values for flow but I am not sure that is correct. Also I have PID regulator made in software so I just need to enter parameters for it. Don't know if I need to make some linearisation or it is already linearized system? So any help with this would mean so much to me. And sorry for my bad english.

#### ControlsGuy25

Hi guys, I have this as school project and I am stuck at the moment and any help would be great. So I need to make simulation of flow regulating system that will have proportional valve as element of control. System needs to take in consideration transport delay and non-linearity of valve (dead-band mainly, histeresys and asymmetry should not be taken in consideration). I need to make software for it in TIA portal and simulation in WinCC. So far I made system which is shown in picture below and if I can I would like to keep it like that(elements of system), if not it can be changed of course. Frictions from pipes don't have to be taken in consideration also and whole system is in one line but I didn't have room to draw it properly(tanks should be aligned).View attachment 240
I made some mathematical modeling and came with this:
P = dp * Q (pump power)(1)
pPump = p1 + dp (pressure on pump exit)(2)
Q = Cd0 * i / i_max * A0 * sqrt(2*(pPump - p2)/rho), (prop. valve equation)(3)
Implementing equation 1 into equation 2 into equation 3 I get this:
Q^2 = (Cd0 * i / i_max * A0)^2 * (2*( p1 + P / Q - p2)/rho)
which is:
Q^3 - (Cd0 * i / i_max * A0)^2 * (2*( (p1 - p2) * Q + P)/rho) = 0
and that is qubic equation
Q^3 + a1 * Q + a0 = 0, (4)
with coefficients:
a1 = - (Cd0 * i / i_max * A0)^2 * 2 * (p1 - p2) / rho
a0 = - (Cd0 * i / i_max * A0)^2 * 2 * P / rho
when solved it should give value of flow in system but I get some weird values for flow rate with that or I get good result but in weird measuring unit. I also made HMI in simulation to enter parameters for valve, pump, etc. and I get some values for flow but I am not sure that is correct. Also I have PID regulator made in software so I just need to enter parameters for it. Don't know if I need to make some linearisation or it is already linearized system? So any help with this would mean so much to me. And sorry for my bad english.
Crogla,

What is meaning of "pressure on pump exit" in the equation 2 ?? is that pressure discharge??

We can try to assist you if you ask you the right questions.
It is simple as that.

Let me have a research on that subject, I will be back to you .

Controlsguy25

#### Crogla

Crogla,

What is meaning of "pressure on pump exit" in the equation 2 ?? is that pressure discharge??

We can try to assist you if you ask you the right questions.
It is simple as that.

Let me have a research on that subject, I will be back to you .

Controlsguy25
Yes, it is discharge pressure of pump and in this case it is same pressure that is valve inlet pressure.

#### ControlsGuy25

Yes, it is discharge pressure of pump and in this case it is same pressure that is valve inlet pressure.
So you can check out some videos on the web explaining modelisation of fluid system first .

Here is one video and a slideshare :
1-
2-https://www.slideshare.net/PracheeSharma/fluids-25896167

Then try to see if you schematic is matching ( if something needed to be added or removed like valve or other equipment)

Also is there any piping slope , tank height to take account on this system??

Regards,
Controlsguy25

#### Crogla

So you can check out some videos on the web explaining modelisation of fluid system first .

Here is one of them:

Then try to see if you schematic is matching ( if something needed to be added or removed like valve or other equipment)

Also is there any piping slope , tank height to take account on this system??

Regards,
Controlsguy25
Tank height and tank base radius is entered through HMI for both of the tanks separately and asumption is that at the start of simulation, tank 1 is full of liquid(water) and tank 2 is empty. I didn't asume piping slope as I mentioned that tanks are aligned and pump and valve are on the same level(height) but I drew them accidentaly like I did in thumbnail I posted earlier as I was just trying to describe system in shortest time possible(my bad). Also I made HMI inputs for pipe length after each element of system as I taught it will be needed for transport delay such as pipe diammeter input.

EDIT:
Here are my HMI elements so you can have better picture about system.

There is also regulation screen made for regulation parameters but there is long way before configuring that.

#### ControlsGuy25

Tank height and tank base radius is entered through HMI for both of the tanks separately and asumption is that at the start of simulation, tank 1 is full of liquid(water) and tank 2 is empty. I didn't asume piping slope as I mentioned that tanks are aligned and pump and valve are on the same level(height) but I drew them accidentaly like I did in thumbnail I posted earlier as I was just trying to describe system in shortest time possible(my bad). Also I made HMI inputs for pipe length after each element of system as I taught it will be needed for transport delay such as pipe diammeter input.

EDIT:
Here are my HMI elements so you can have better picture about system.
View attachment 241
View attachment 242
There is also regulation screen made for regulation parameters but there is long way before configuring that.
Crogla,

You will find here after some precious informations on the subject that you posted here:
Valve Sizing and Selection

What is Cv?

The definition of Cv factor is the number of G.P.M. that will pass through a valve with a
pressure drop of one (1) psi. A unit of measure for comparing valve flows.

STEP #1: Define the system

The system is pumping water from one tank to another through a piping system with a total
pressure drop of 150 psi. The fluid is water at 70 0F. Design (maximum) flowrate of 150 gpm, operating flowrate of 110 gpm, and a minimum flowrate of 25 gpm. The pipe diameter is 3 inches. At 70 0F, water has a specific gravity of 1.0.

STEP #2: Define a maximum allowable pressure drop for the valve
When defining the allowable pressure drop across the valve, you should first investigate the pump. Remember that the system pressure drop is limited by the pump.
The usual rule of thumb is that a valve should be designed to use 10-15% of the total pressure drop or 10 psi, whichever is greater. For our system, 10% of the total pressure drop is 15 psi which is what we'll use as our allowable pressure drop when the valve is wide open (the pump in our system is easily capable of the

STEP #3: Calculate the valve characteristic

STEP #4: Preliminary valve selection
Don't make the mistake of trying to match a valve with your calculated Cv value. The Cv value should be used as a guide in the valve selection, not a hard and fast rule. Some other considerations are:

a. Never use a valve that is less than half the pipe size
b. Avoid using the lower 10% and upper 20% of the valve stroke. The valve is much easier to control in the 10-80% stroke range.
Before a valve can be selected, you have to decide what type of valve will be used. For our case, we'll assume we're using an equal percentage globe valve. The valve chart for this type of valve is shown below.

For our case, it appears the 2 inch valve will work well for our Cv value at about 80-85% of the stroke range. Notice that we're not trying to squeeze our Cv into the 1 1/2 valve which would need to be at 100% stroke to handle our
maximum flow. If this valve were used, two consequences would be experienced: the pressure drop would be a little higher than 15 psi at our design (max) flow and the valve would be difficult to control at maximum flow. Also, there would be no room for error with this valve, but the valve we've chosen will allow for flow surges beyond the 150 gpm.

STEP #5: Check the Cv and stroke percentage at the minimum flow

If the stroke percentage falls below 10% at our minimum flow, a smaller valve may have to be used in some cases. Judgement plays role in
many cases. For example, is your system more likely to operate closer to the maximum
flowrates more often than the minimum flowrates? Or is it more likely to operate near
the minimum flowrate for extended periods of time. It's difficult to find the perfect valve, but you should find one rates well most of the time.

Referring back to our valve chart, we see that a Cv of 6.5 would correspond to a stroke
percentage of around 35-40% which is certainly acceptable.

SELECTING A VALVE TYPE
When speaking of valves, it's easy to get lost in the terminology. Valve types are used to describe the mechanical characteristics and geometry (Ex/ gate, ball, globe valves). We'll use valve control to refer to how the valve travel or stroke (openness) relates to the flow:

1. Equal Percentage: equal increments of valve travel produce an equal percentage in flow change
2. Linear: valve travel is directly proportional to the valve stoke
3. Quick opening: large increase in flow with a small change in valve stroke
So how do you decide which valve control to use? Here are some rules of thumb for each one:

1. Equal Percentage (most commonly used valve control)
a. Used in processes where large changes in pressure drop are expected
b. Used in processes where a small percentage of the total pressure drop is
permitted by the valve
c. Used in temperature and pressure control loops
2. Linear
a. Used in liquid level or flow loops
b. Used in systems where the pressure drop across the valve is expected to remain fairly constant (ie. steady state systems)
3. Quick Opening
a. Used for frequent on-off service
b. Used for processes where "instantly" large flow is needed (ie. safety systems or cooling water systems)
Gate Valves
Best Suited Control: Quick Opening
Recommended Uses:

1. Fully open/closed, non-throttling
2. Infrequent operation
3. Minimal fluid trapping in line
Applications: Oil, gas, air, slurries, heavy liquids, steam, noncondensing gases, and corrosive liquids
1. High capacity 1. Poor control
2. Tight shutoff 2. Cavitate at low
3. Low cost pressure drops 3. Cannot be used for throttling
4. Little resistance to flow

Globe Valves
Best Suited Control: Linear and Equal percentage
Recommended Uses:

1. Throttling service/flow regulation
2. Frequent operation
Applications: Liquids, vapors, gases, corrosive substances, slurries
1. Efficient throttling 1. High pressure drop
2. Accurate flow control 2. More expensive
3. Available in multiple ports
Ball Valves

Best Suited Control:Quick opening, linear
Recommended Uses:

1. Fully open/closed, limited-throttling
2. Higher temperature fluids
Applications:Most liquids, high temperatures, slurries
1. Low cost 1. Poor throttling characteristics
2. High capacity 2. Prone to cavitation
3. Low leakage and maint.

4. Tight sealing with low torque

Butterfly Valves
BestSuitedControl: Linear, Equal percentage
Recommended Uses:
1. Fully open/closed or throttling services
2. Frequent operation
3. Minimal fluid trapping in line
Applications: Liquids, gases, slurries, liquids with suspended solids
1. Low cost and maint. 1. High torque required
2. High capacity for control 2. Prone to cavitation
3. Good flow control
4. Low pressure drop at lower flows
Other Valves

Another type of valve commonly used in conjunction with other valves is called a check valve. Check valves are designed to restrict the flow to one direction. If the flow reverses direction, the check valve closes. Relief valves are used to regulate the operating pressure of incompressible flow. Safety valves are used to release excess pressure in gases or compressible fluids.

Also this very interesting link to check out here :
https://instrumentationandcontroltoday.blogspot.com/2015/06/control-valves-basic-concepts.html

I am sure that it can help ! and sure that you school project will be well studied with the informations I share here !!

Controlsguy25.

#### Crogla

Crogla,

You will find here after some precious informations on the subject that you posted here:
Valve Sizing and Selection

What is Cv?

The definition of Cv factor is the number of G.P.M. that will pass through a valve with a
pressure drop of one (1) psi. A unit of measure for comparing valve flows.

STEP #1: Define the system

The system is pumping water from one tank to another through a piping system with a total
pressure drop of 150 psi. The fluid is water at 70 0F. Design (maximum) flowrate of 150 gpm, operating flowrate of 110 gpm, and a minimum flowrate of 25 gpm. The pipe diameter is 3 inches. At 70 0F, water has a specific gravity of 1.0.

STEP #2: Define a maximum allowable pressure drop for the valve
When defining the allowable pressure drop across the valve, you should first investigate the pump. Remember that the system pressure drop is limited by the pump.
The usual rule of thumb is that a valve should be designed to use 10-15% of the total pressure drop or 10 psi, whichever is greater. For our system, 10% of the total pressure drop is 15 psi which is what we'll use as our allowable pressure drop when the valve is wide open (the pump in our system is easily capable of the

STEP #3: Calculate the valve characteristic

STEP #4: Preliminary valve selection
Don't make the mistake of trying to match a valve with your calculated Cv value. The Cv value should be used as a guide in the valve selection, not a hard and fast rule. Some other considerations are:

a. Never use a valve that is less than half the pipe size
b. Avoid using the lower 10% and upper 20% of the valve stroke. The valve is much easier to control in the 10-80% stroke range.
Before a valve can be selected, you have to decide what type of valve will be used. For our case, we'll assume we're using an equal percentage globe valve. The valve chart for this type of valve is shown below.

For our case, it appears the 2 inch valve will work well for our Cv value at about 80-85% of the stroke range. Notice that we're not trying to squeeze our Cv into the 1 1/2 valve which would need to be at 100% stroke to handle our
maximum flow. If this valve were used, two consequences would be experienced: the pressure drop would be a little higher than 15 psi at our design (max) flow and the valve would be difficult to control at maximum flow. Also, there would be no room for error with this valve, but the valve we've chosen will allow for flow surges beyond the 150 gpm.

STEP #5: Check the Cv and stroke percentage at the minimum flow

If the stroke percentage falls below 10% at our minimum flow, a smaller valve may have to be used in some cases. Judgement plays role in
many cases. For example, is your system more likely to operate closer to the maximum
flowrates more often than the minimum flowrates? Or is it more likely to operate near
the minimum flowrate for extended periods of time. It's difficult to find the perfect valve, but you should find one rates well most of the time.

Referring back to our valve chart, we see that a Cv of 6.5 would correspond to a stroke
percentage of around 35-40% which is certainly acceptable.

SELECTING A VALVE TYPE
When speaking of valves, it's easy to get lost in the terminology. Valve types are used to describe the mechanical characteristics and geometry (Ex/ gate, ball, globe valves). We'll use valve control to refer to how the valve travel or stroke (openness) relates to the flow:

1. Equal Percentage: equal increments of valve travel produce an equal percentage in flow change
2. Linear: valve travel is directly proportional to the valve stoke
3. Quick opening: large increase in flow with a small change in valve stroke
So how do you decide which valve control to use? Here are some rules of thumb for each one:

1. Equal Percentage (most commonly used valve control)
a. Used in processes where large changes in pressure drop are expected
b. Used in processes where a small percentage of the total pressure drop is
permitted by the valve
c. Used in temperature and pressure control loops
2. Linear
a. Used in liquid level or flow loops
b. Used in systems where the pressure drop across the valve is expected to remain fairly constant (ie. steady state systems)
3. Quick Opening
a. Used for frequent on-off service
b. Used for processes where "instantly" large flow is needed (ie. safety systems or cooling water systems)
Gate Valves
Best Suited Control: Quick Opening
Recommended Uses:

1. Fully open/closed, non-throttling
2. Infrequent operation
3. Minimal fluid trapping in line
Applications: Oil, gas, air, slurries, heavy liquids, steam, noncondensing gases, and corrosive liquids
1. High capacity 1. Poor control
2. Tight shutoff 2. Cavitate at low
3. Low cost pressure drops 3. Cannot be used for throttling
4. Little resistance to flow

Globe Valves
Best Suited Control: Linear and Equal percentage
Recommended Uses:

1. Throttling service/flow regulation
2. Frequent operation
Applications: Liquids, vapors, gases, corrosive substances, slurries
1. Efficient throttling 1. High pressure drop
2. Accurate flow control 2. More expensive
3. Available in multiple ports
Ball Valves

Best Suited Control:Quick opening, linear
Recommended Uses:

1. Fully open/closed, limited-throttling
2. Higher temperature fluids
Applications:Most liquids, high temperatures, slurries
1. Low cost 1. Poor throttling characteristics
2. High capacity 2. Prone to cavitation
3. Low leakage and maint.

4. Tight sealing with low torque

Butterfly Valves
BestSuitedControl: Linear, Equal percentage
Recommended Uses:
1. Fully open/closed or throttling services
2. Frequent operation
3. Minimal fluid trapping in line
Applications: Liquids, gases, slurries, liquids with suspended solids
1. Low cost and maint. 1. High torque required
2. High capacity for control 2. Prone to cavitation
3. Good flow control
4. Low pressure drop at lower flows
Other Valves

Another type of valve commonly used in conjunction with other valves is called a check valve. Check valves are designed to restrict the flow to one direction. If the flow reverses direction, the check valve closes. Relief valves are used to regulate the operating pressure of incompressible flow. Safety valves are used to release excess pressure in gases or compressible fluids.

Also this very interesting link to check out here :
https://instrumentationandcontroltoday.blogspot.com/2015/06/control-valves-basic-concepts.html

I am sure that it can help ! and sure that you school project will be well studied with the informations I share here !!

Controlsguy25.
Thank you for such detailed descriptions and your work.

Main element of that system should be proportional solenoid valve and its control. So that is type of valve I must use. Valve should be controled by current as it is described where I was modeling system(equation for valve). Those type of valves have non-linear characteristic with dead-band at start and after that they are linear. So I need to model that let's say it like that.

#### ControlsGuy25

Thank you for such detailed descriptions and your work.

Main element of that system should be proportional solenoid valve and its control. So that is type of valve I must use. Valve should be controled by current as it is described where I was modeling system(equation for valve). Those type of valves have non-linear characteristic with dead-band at start and after that they are linear. So I need to model that let's say it like that.

I am glad that you can, at least have some datas, for modeling this system.

Do not hesitate ,to share with us your studies.

Controlsguy

#### Crogla

I am glad that you can, at least have some datas, for modeling this system.

Do not hesitate ,to share with us your studies.

Controlsguy
Let's say this is the valve in system.
https://www.boschrexroth.com/en/xc/...valves/proportional-flow-control-valves/3frez there are characteristics of it in pdf. And I modeled valve equation based on this https://fluidpower.pro/proportional-valve-calculation-1/ but instead of voltage ratio y/ymax I used valve openess which I get from PID regulator. Yesterday I connected my system with regulator and ran simulation and I got weird values for flow rate but besides that everything is working fine.

#### ControlsGuy25

Let's say this is the valve in system.
https://www.boschrexroth.com/en/xc/...valves/proportional-flow-control-valves/3frez there are characteristics of it in pdf. And I modeled valve equation based on this https://fluidpower.pro/proportional-valve-calculation-1/ but instead of voltage ratio y/ymax I used valve openess which I get from PID regulator. Yesterday I connected my system with regulator and ran simulation and I got weird values for flow rate but besides that everything is working fine.
Good choice !

I tried to download rexroth data sheet but seems that it gave a .jsp file nammed pdf §§§!!!
Can you share the pdf file here?
Also can you write us some notes on voltage ratio y/ymax ?
It would be also nice to see how it worked with a hmi or video view!

Thanks for the feedback,
Controlsguy 25

#### Crogla

Good choice !

I tried to download rexroth data sheet but seems that it gave a .jsp file nammed pdf §§§!!!
Can you share the pdf file here?
Also can you write us some notes on voltage ratio y/ymax ?
It would be also nice to see how it worked with a hmi or video view!

Thanks for the feedback,
Controlsguy 25

This was voltage ratio I was talking about and equation that I used to describe flow of proportional valve. In my model instead of that voltage ratio I use valve openness that I get from my PID regulator which then I scale from 0-100% to 0-1 and send back to model so it scales valve orifice which is in this case Aland. y/ymax would do same thing as for example ymax is 10V and y value is 5, you would get 0.5 or 50% opening of orifice.

https://www.boschrexroth.com/en/xc/...220&search_action=submit&edition_enum=re29220

I don't have PLC at home so I can't run simulation till monday.

#### ControlsGuy25

View attachment 249
This was voltage ratio I was talking about and equation that I used to describe flow of proportional valve. In my model instead of that voltage ratio I use valve openness that I get from my PID regulator which then I scale from 0-100% to 0-1 and send back to model so it scales valve orifice which is in this case Aland. y/ymax would do same thing as for example ymax is 10V and y value is 5, you would get 0.5 or 50% opening of orifice.

https://www.boschrexroth.com/en/xc/...220&search_action=submit&edition_enum=re29220