# Get your ducts in a row

## Readers of CONTROL respond with comments, suggestions and a solution to the problem: What can we do to get six identical air flows from our air plennum splitting system?

**PROBLEM:**

**we have an air plenum splitting system**that consists of six identically sized round pipe ducts with the same valve in each pipe. We simply cannot control the airflow so that the same flowrate moves through each splitter. What should we be doing, with either hardware or software, to get six identical air flows?

*-- from August 2004 CONTROL*

**SOLUTIONS:**

**Match the Master**

This is a relatively simple problem. Even if all the ducts are not the same, the motor/inverter drive/fan equipment would be the same, except that each duct would have a flowmeter sensor on the pipe output for feedback to the drive of that pipe. An external master controller would set the required flow for the first pipe. Each drive would be connected to use the flowmeter sensor on the master pipe output as a setpoint to all the drives. The flow level of the master pipe would then be matched by the other five pipe systems.

*John Malinowski, Baldor Electric Co.*

**Overcontrol Syndrome**

Sounds like the ever-present overcontrol syndrome. Assuming these valves are control valves, I can understand why the flows are not equal and the valves are probably constantly oscillating. A different view might be to simplify the system by putting a variable speed control on the blower and installing dampers instead of the control valves.

*Paul Sparks, Dow Reichhold*

**A Trick Question**This is a trick question. If it is constant volume, get a balance contractor! If variable, they could get fancy and place flow measuring stations in each duct, go to a controller, and modulate the dampers.

*Jeff Miller, ABB Drives*

Submitted by Rick Rys of r2controls: www.r2controls.com

Q: Is the source of the air provided from a blower?

A: Assume yes.

Q: The Flow into the plenum is variable?

A: Assume the flow varies with a typical centrifugal blower performance curve.

(i.e. max pressure at zero flow and the blower is fairly close to the plenum).

Q: The plenum is pressure controlled?

A: Assume not, plenum pressure floats on the blower output pressure.

Q: The ducts are independent?

A: Let's assume each duct is essentially a pipe resistance to atmosphere.

Q: What are the fluid dynamics?

A: Lets' assume that the clean dry air is near atmospheric pressure (and temperature), say 1 PSIG in the plenum if all 6 valves are shut, dropping to 0.2 PSIG if all 6 valves are wide open. With the valves full open the pressure loss in the valves is nil and the 0.2 PSIG is due to duct pressure drop.

Q: Are there any upsets? Let’s assume that we can get some upsets in the downstream pressure on each of the 6 ductsâ€¦

A: maybe a spike of 0.1 PSIG from time to time.

Q: What is the process control objective?

A: The process objective is to allow equal flow in all 6 ducts up to the blower capacity, with the possibility to regulate the flow in a roughly 5:1 turndown.

Q: What kind of valves?

A: Simple low cost butterfly valves, with pneumatic actuator, but no positioner.

We can compute the relative gain to understand and to quantify the interaction:

Î»i,j Is the relative gain (dimensionless). Where c is the "Controlled Variable" (Flow in a duct), m is the "Manipulated Variable" (Flow Valve) and Î» is the relative gain. i is the instance of the controlled variable and j is the instance of the manipulated variable. mother=constant means that all other manipulated variables are held constant during the evaluation of the derivative (numerator). cother=constant means that all other controlled variables are perfectly regulated at their setpoint (when evaluating the denominator). Here we consider regulating the Flow in Duct 1 with the valve in duct 1 and thus would compute the gain Î»1,1.

Î»i,j > 1.0 reduced control effectiveness

Î»i,j < 1.0 interaction will extend the loop period and raises gain

The relative gain can be computed by plant test or by using a process model. Î»1,1 is slightly greater than 1.0 for the problem as described. Here is why: The numerator is âˆ†Flow/âˆ†Valve with the remaining 5 valves held constant. The numerator is slightly more than the denominator which is âˆ†Flow/âˆ†Valve with the remaining 5 other controllers regulating flow. Lets say we evaluate the relative gain at a typical operating condition with FV1 = 50% and increasing to 55%.

This movement will increase the flow thus the derivative is a positive number. In the numerator the plenum pressure will drop somewhat reducing the flow to the other 5 ducts. In the denominator the flow will drop less as the other 5 controllers will further reduce the plenum pressure in order to keep their flow at setpoint, thereby reducing the control effectiveness of the first controller. From the perspective of FC1 there is a reduced loop gain when FC2...FC6 controllers are in Automatic.

Of course we made huge assumptions here and we could be way off base. It could be that some other interacting control loop is causing the plenum pressure to oscillate and we really need to be looking at that loop. Or it could be tuning problems, valve problems, or process problems. We also do not know specifically how good the control needs to be. Some loops oscillate their whole life and still are acceptable.

We assumed 6 simple single control loops without any known installation or application problems. The simplicity of 6 single loop controllers is appealing, and it may be quite possible to simply retune them. Adaptive tuning might be helpful for initial tuning if the remaining 5 controllers are in manual mode, but as we can see from the RGA analysis putting the other 5 controllers in AUTO will impact the loop gain and thus the optimal tuning. Tuning features might not be available depending on PID software or availability of third party tuning packages. The controller tuning will be especially important here and care should be taken to insure the tuning is stable at all loads and that an oscillation in one control loop will not excite the other loops into a 6-piece orchestra of oscillations.

The multivariable approach would surely handle the interaction problem, but just how do you make a step test with FV1 while keeping FC2....FC6 in tight control. It would seem that you almost need to fix the control problem before you can do the step tests that will lead to fixing the control problem. This is a common issue when planning the step tests. The way we have assumed the problem, it does not look like we have the hardware or software to jump into the multivariable controller solution. Additionally, what happens if the multivariable controller is out of service? Say one flowmeter or valve is failed, can the controller continue to work with the remaining 5 loops? Or is there a fallback scheme? Our potentially false assumptions could mean that our multivariable control solution is off base. Based on our assumptions a multivariable controller structure with 6 CV's (FT1...FT6), 6 MV's (FV1...FV6) and possibly 1 FF (Plenum Pressure) would seem the most likely structure. Decoupling is inherent in the multivariable solution assuming a good feedforward model is captured in the step testing.

Of course cost, operator training, and support over the life of the plant may need to be factored in. 6 simple loops appears to be the easiest to understand and support if it can be made to work.

In that line of thinking, a few other things that could help are: to characterize those butterfly valves so that the controller output is roughly linear to the flow through the valve (this applies to either multivariable or PID control). If we have a Plenum pressure measurement, we could implement feedforward compensation (in the PID) so that when the plenum pressure falls, the valves all open appropriately, even before the flow measurement responds. This would decouple the system. In some PID algorithms, connecting the feedforward calculation into the "BIAS" will allow for smooth Auto/Manual transitions making the feedforward easier for the operator to manage. Many single loop controllers could accommodate this addition with relatively minor wiring and software configuration changes. There are a number of ways to decouple the PID controllers, implicitly by simple tuning or explicitly by wiring feedforward signals or by decoupling.

If the interaction is via the plenum pressure, why not put in a pressure controller to keep the pressure constant. It may manipulate the blower, but could add hardware and increase energy consumption a bit. If the pressure controller is fast compared to upsets or the 6 flow controllers, it would surely end the interaction problem.

This little "what if" anaysis shows a few of the approaches that might be considered.

Keeping the solution simple, but effective, is the real goal.

*Bill Brown, Control Engineer*

**Algorithm Required**This sounds like a good application for a most-open-valve flow splitting algorithm. This approach requires a master valve position controller and an airflow controller for each of the valves.

*Will Lloyd, Lloyd Engineering, PLC*

**Verify Capacity First**First you must verify that there is enough capacity for the plenum, both in pressure and volume. Control will require some pressure drop. If there is extra pressure available, simple orifices could balance the flow. If more sophisticated control is required, flowmeters can be installed. For simple, even distribution with only minor downstream pressure changes, orifices with significant pressure drop could provide good distribution. If this is not available, increasing the source (for instance, faster fan speed) is often more practical than adding flow controls.

*Bob Hershey, NGK Ceramics USA*

In addition, a very well though-out solution to this problem appears as aIn addition, a very well though-out solution to this problem appears as a

**WEB ONLY BONUS**!Submitted by Rick Rys of r2controls: www.r2controls.com

**APPROACH TO PROBLEM:**

**1) Process Understanding:**

The process is not described in detail so let's make some assumptions:Q: Is the source of the air provided from a blower?

A: Assume yes.

Q: The Flow into the plenum is variable?

A: Assume the flow varies with a typical centrifugal blower performance curve.

(i.e. max pressure at zero flow and the blower is fairly close to the plenum).

Q: The plenum is pressure controlled?

A: Assume not, plenum pressure floats on the blower output pressure.

Q: The ducts are independent?

A: Let's assume each duct is essentially a pipe resistance to atmosphere.

Q: What are the fluid dynamics?

A: Lets' assume that the clean dry air is near atmospheric pressure (and temperature), say 1 PSIG in the plenum if all 6 valves are shut, dropping to 0.2 PSIG if all 6 valves are wide open. With the valves full open the pressure loss in the valves is nil and the 0.2 PSIG is due to duct pressure drop.

Q: Are there any upsets? Let’s assume that we can get some upsets in the downstream pressure on each of the 6 ductsâ€¦

A: maybe a spike of 0.1 PSIG from time to time.

Q: What is the process control objective?

A: The process objective is to allow equal flow in all 6 ducts up to the blower capacity, with the possibility to regulate the flow in a roughly 5:1 turndown.

Q: What kind of valves?

A: Simple low cost butterfly valves, with pneumatic actuator, but no positioner.

**Summary:**This is a process with interaction, in that increasing the flow in 1 duct will reduce the plenum pressure and steal flow from the remaining ducts. If the existing control system is 6 single loop flow controllers, the interaction could easily result in all 6 controllers oscillating. All 6 loops have the same dynamics and will have the same natural period so an oscillation in one loop will tend to excite the remaining 5 loops. So let’s focus on solving the interaction problem.**2) Determining Interaction:**

In 1966 Edgar Bristol wrote a key paper on the measurement of interaction where he introduced "Relative Gain". Shinskey and others utilized this extensively to determine interaction and develop control approaches that deal with interaction. Multivariable controllers like: DMC+, DOT Products, PCL Connoisseur, and related technologies are particularly good at dealing with such interactions and use some related mathematics to achieve multivariable control of interacting processes.We can compute the relative gain to understand and to quantify the interaction:

Î»i,j Is the relative gain (dimensionless). Where c is the "Controlled Variable" (Flow in a duct), m is the "Manipulated Variable" (Flow Valve) and Î» is the relative gain. i is the instance of the controlled variable and j is the instance of the manipulated variable. mother=constant means that all other manipulated variables are held constant during the evaluation of the derivative (numerator). cother=constant means that all other controlled variables are perfectly regulated at their setpoint (when evaluating the denominator). Here we consider regulating the Flow in Duct 1 with the valve in duct 1 and thus would compute the gain Î»1,1.

**The interpretation is:**

Î»i,j = 1.0 no interaction with other loopsÎ»i,j > 1.0 reduced control effectiveness

Î»i,j < 1.0 interaction will extend the loop period and raises gain

The relative gain can be computed by plant test or by using a process model. Î»1,1 is slightly greater than 1.0 for the problem as described. Here is why: The numerator is âˆ†Flow/âˆ†Valve with the remaining 5 valves held constant. The numerator is slightly more than the denominator which is âˆ†Flow/âˆ†Valve with the remaining 5 other controllers regulating flow. Lets say we evaluate the relative gain at a typical operating condition with FV1 = 50% and increasing to 55%.

This movement will increase the flow thus the derivative is a positive number. In the numerator the plenum pressure will drop somewhat reducing the flow to the other 5 ducts. In the denominator the flow will drop less as the other 5 controllers will further reduce the plenum pressure in order to keep their flow at setpoint, thereby reducing the control effectiveness of the first controller. From the perspective of FC1 there is a reduced loop gain when FC2...FC6 controllers are in Automatic.

**THE SOLUTION:**

Of course we made huge assumptions here and we could be way off base. It could be that some other interacting control loop is causing the plenum pressure to oscillate and we really need to be looking at that loop. Or it could be tuning problems, valve problems, or process problems. We also do not know specifically how good the control needs to be. Some loops oscillate their whole life and still are acceptable.

We assumed 6 simple single control loops without any known installation or application problems. The simplicity of 6 single loop controllers is appealing, and it may be quite possible to simply retune them. Adaptive tuning might be helpful for initial tuning if the remaining 5 controllers are in manual mode, but as we can see from the RGA analysis putting the other 5 controllers in AUTO will impact the loop gain and thus the optimal tuning. Tuning features might not be available depending on PID software or availability of third party tuning packages. The controller tuning will be especially important here and care should be taken to insure the tuning is stable at all loads and that an oscillation in one control loop will not excite the other loops into a 6-piece orchestra of oscillations.

The multivariable approach would surely handle the interaction problem, but just how do you make a step test with FV1 while keeping FC2....FC6 in tight control. It would seem that you almost need to fix the control problem before you can do the step tests that will lead to fixing the control problem. This is a common issue when planning the step tests. The way we have assumed the problem, it does not look like we have the hardware or software to jump into the multivariable controller solution. Additionally, what happens if the multivariable controller is out of service? Say one flowmeter or valve is failed, can the controller continue to work with the remaining 5 loops? Or is there a fallback scheme? Our potentially false assumptions could mean that our multivariable control solution is off base. Based on our assumptions a multivariable controller structure with 6 CV's (FT1...FT6), 6 MV's (FV1...FV6) and possibly 1 FF (Plenum Pressure) would seem the most likely structure. Decoupling is inherent in the multivariable solution assuming a good feedforward model is captured in the step testing.

Of course cost, operator training, and support over the life of the plant may need to be factored in. 6 simple loops appears to be the easiest to understand and support if it can be made to work.

In that line of thinking, a few other things that could help are: to characterize those butterfly valves so that the controller output is roughly linear to the flow through the valve (this applies to either multivariable or PID control). If we have a Plenum pressure measurement, we could implement feedforward compensation (in the PID) so that when the plenum pressure falls, the valves all open appropriately, even before the flow measurement responds. This would decouple the system. In some PID algorithms, connecting the feedforward calculation into the "BIAS" will allow for smooth Auto/Manual transitions making the feedforward easier for the operator to manage. Many single loop controllers could accommodate this addition with relatively minor wiring and software configuration changes. There are a number of ways to decouple the PID controllers, implicitly by simple tuning or explicitly by wiring feedforward signals or by decoupling.

If the interaction is via the plenum pressure, why not put in a pressure controller to keep the pressure constant. It may manipulate the blower, but could add hardware and increase energy consumption a bit. If the pressure controller is fast compared to upsets or the 6 flow controllers, it would surely end the interaction problem.

This little "what if" anaysis shows a few of the approaches that might be considered.

Keeping the solution simple, but effective, is the real goal.

DECEMBER'S PROBLEM:

DECEMBER'S PROBLEM:

W |

**e can’t believe our vortex shedding flowmeter**! We are having issues with the believability of our current vortex shedding flowmeter used in NH3 service when compared to a mass flowmeter. The vortex shedder has been compensated with square-root P/T compensation. The flow valve is in manual, the line pressure is constant, with dropping temperature only. But the reading from the vortex shedding flowmeter decreased and the mass flow increased. Looking at trend data, the NH3 vaporizer pressure dipped. Because the vortex meter uses the calculation: (volume)=M(mass)/D(density), where D is inversely affected by temperature, we have come to the conclusion that the vortex meter is not compensating for increased M that the vaporizer is pushing into the line. How would I compensate for this in a formula?*Please send us your comments, suggestions or solutions to this problem. Solutions will be published in our December issue, but we need your responses by November 20 to meet our editorial deadlines. If you have a solution to this problem or a problem of your own that you would like to pose to your colleagues, mail, fax or email it to *CONTROL*, 555 W. Pierce Road, Itasca, IL. 60143. Tel.: 630-467-1300; fax: 630-467-1124;* wboyes@putman.net.

**Insert and Orifice**

Determine the individual flows by inserting an orifice, one at a time in each channel and measure. Calculate an orifice size for each duct that will provide constant flow at constant air pressure. If the flows are not constant, this simple solution will not work, and flow control and actuated dampers will be called for.

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