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1 August 2006

Mind Your Ps

Discovering the value of proportional-only level control leaves a legacy of possibilities

By Rod Corbett

I worked for more than 10 years in nuclear, oil, and pulp and paper combined before encountering a pneumatic controller. And when I started at the StoraEnso paper mill in Nova Scotia, I had to fully understand the requirements for control of basic loops if I was to make any progress in control. At first glance, available tools appeared simple, even primitive. But over time, I came to appreciate how elegant all these old fashioned control devices are. I developed a knack for using different types of pneumatic devices, realizing these 50-year-old control tools were still effective and the mathematical models involved in defining legacy control devices can import successfully into modern computer-based control systems.

Pneumatic controllers are actually practical, working analog computers. At the StoraEnso mill, we continually made discoveries to improve level control, and we realized using pneumatic controllers in process tanks could be successful in minimizing variability in attached process areas as long as we set them up as proportional only (P-only) controllers. However, we had to consider some important issues:

To avoid any overflow condition and to maximize inventory in intermediate tanks, we often changed the controller from the original P-only to the more modern proportional plus integral (PI). 

To maintain level at a set point, we changed the control scheme from the original P-only to PI. The smaller the tank was in relation to the process, the more likely a change to a PI controller. 

In cases where the tank level measurement was susceptible to quick process changes, the level control output would change quickly causing premature wear of valves, pumps, and other associated equipment.

On failure of a pneumatic P-only controller, the replacement was often a PI controller. To convert from a PI pneumatic controller to a P-only pneumatic controller, it was not enough to turn off the integral action. We also had to remove the integral bellows completely from the controller, a laborious procedure and not often worthwhile, particularly since a PI controller could hold set-point so well.

In cases where the final control element (pump/valve) was seriously non-linear or where continuing change in controller output did not result in more flow, level control would be a challenge. This was particularly bad with a PI level controller. 

In several cases, using a PI controller on level, coupled with the lack of anti-reset windup on the controller, made the level control worse than manual control. This resulted in the controller remaining in manual and eliminating the smoothing flow changes a tank would normally provide. 

Finally, there were cases where the process tank was too small and the process too dynamic. We needed to use sophisticated control schemes to successfully control the level. Often, imposed sophisticated solutions introduced process dynamics, which then required more solutions. In the end, the problem became controlling the controller, not the process.

An unusual application of P-only level control involves the secondary treatment sludge press level. The sludge press is a screw-type press, which depends on a head of sludge at the inlet to the screw. Prior to entering the chute, we pre-drained the sludge so it was the consistency of heavy porridge. Then we measured the feed chute level and used it as the demand signal, adding polymer in ratio to the demand flow. 

We configured the sludge level as a PI controller. The level controller cycled at +/- 40% at a high frequency. We converted the level controller to P-only. We couldn’t have done this if the level signal wasn’t first heavily filtered. We installed a first-order filter with a time constant of 1.5 minutes. The large filter time makes it possible for the level controller to ignore shocks to the level measurement as the drained sludge falls into the chute. The only hook in the project was being able to install such a large filter using the existing PLC. So we had to write a special algorithm to do the filtering. As soon as we converted the control to P-only, the sludge press performance improved, substantially reducing the amount of polymer required.

Proportional-only control curve 

No level loop is any more complicated than the simple flush toilet. The simplest mode of control for continuous processes is proportional only. The P-only controller takes an input, applies a gain to it, and generates an output. The curve for the simplest P-only controller looks like a straight line. (See “Toilet tank level control” figure.)

This equation describes the simple toilet tank float control where the float makes the measurement, and the gain is normally about 2, since the water comes on full force when the float is down to half the height of the tank.

Output = Gain × Input
y = mx + b; straight-line equation 
m = gain 
x = measurement (input)
b = 0

Actually, the gain is a function of the length of the float arm. The final control element is the inlet valve to the toilet tank. (See “Toilet tank level control (2)” figure.) The term proportional band (PB) accurately describes what happens with the toilet tank level control. The output (inlet water valve position) changes by 100% for a 50% movement of the measurement signal (float position), so the proportional band is 50% and the gain is 2 (1/PB×100). 

To give the controller some flexibility, you need a set-point. To control a set-point, the controller must be ready to respond to the difference between the desired set-point and the point at which the process is actually operating. The simplified equation becomes:

Output = Gain × Error
y = mx + b; straight-line equation
m = gain
x = error
b = 0
Error = Measurement - Set-Point

Re-examining the toilet tank control set-up, we can say the controller has a fixed set-point of 100%. (See the “Effect of changing set-point on P-only controller figure” and the “Effect of changing P band on P-only controller” figure.)

Off-set

All the texts explain how P-only controllers will control at an off-set from set-point, except at the system load for which the process was set up. For the toilet tank float controller, the system load is zero flow (i.e.: with the tank full, the float fully up, and the inlet valve fully closed). So what can you do about loads other than the design load?

Everyone has had an experience with the water running in the toilet, most often because the rubber valve did not completely reset after a flush. In this case, the float controls but never reaches its full height to shut off the inlet valve. (See “Toilet tank level control (2)” figure.) If the leak is substantial, the toilet tank level will stabilize at a value noticeably lower than full, and the inlet valve will pass a lot of water. The situation will be stable, although not good. This simple P-only controller is actually controlling a non-design load stably at an off-set, just like the text books predicted it would. So how do we force the control back to set-point? 

Adding bias

It is possible, even with a toilet continuously running, to force the tank to completely fill by bending the float arm upwards. This allows the inlet valve to stay more open at a lower position of the float. Forcing the output of the controller to go to a new position for the same process measurement is called adding a bias to the output of the controller. In short, the bias (sometimes called output bias) of a P-only controller is the output of the controller when there is no error (when the measurement equals set-point).

Mathematically, the controller equation becomes:

Output = Gain × (Meas – SP) + bias 

When the toilet is not continuously running, the bias = 0 and the level is at its set-point of 100%. To keep the level at its set-point when it is continuously running, the bias has to be greater than zero to force the valve to be open enough to allow enough make-up water in. The standard industrial single loop P-only pneumatic or electronic controller has a bias of 50%. When the system is operating at other than the design load, this P-only controller will control at an off-set, a condition no operator appreciates. So how can we make sure the controller controls at the set-point at least most of the time?

When a P-only controller that controls to set-point has to handle a load change, it will no longer control at set-point. If an operator wants to get things back to set-point without having to call a technician, he could apply an adjustment to the output and manipulate it until the set-point and measurement were equal. This had the effect of actually sliding the control curve either to the left or right. Because this action brought the measurement and set-point back into alignment, the controller reset back to its set-point. The adjusting device on the controller became the manual reset button. 

In one instance at the paper mill, we used smart bias to control thermal mechanical pulp (TMP) heat recovery feed. The demineralized (demin) water feed to the TMP boiler was cycling endlessly. The TMP heat recovery unit (reboiler feed) had three operational modes: no unit in operation, one unit in operation, and two units in operation. We couldn’t apply simple P-only control because of the huge changes in water demand and the small size of the vessel. Using data on the average demin water make-up flow for each of these conditions made it possible to calculate the required bias for a P-only controller for this application and to then have stable level control with a wide proportional band resulting in the elimination of the continuous swings in make-up flow.

We had to use a significant first-order filter on the clean steam production flow to avoid introducing cycling due to measurement noise. We coupled the existing heat recovery unit level control valve with an existing water flowmeter to create a make-up water flow control loop. The level controller output then became a remote set-point for the water flow controller. This allowed the linearization of the level control, which made for even better response. 

Automatic reset

To move from manual reset to automatic reset action, the control suppliers added integral modules to the control. The integral modules were designed to repeat the proportional action as many times as necessary over a period of time. Because an integral module had the effect of forcing the process back to its set-point, it has also been called reset. The time constant for this module was defined as the amount of time required to repeat the proportional action, such as minutes per repeat.

Because level is already an integrating process, it is almost anathema to apply an integrator to a level process. A sustained integral cycle will always ensue if you apply integration to a level loop. The only thing we could question is the magnitude and frequency of the cycle. A level controller that uses integral action will cycle. 

Without reset, a P-only controller will control with an off-set for any condition except for design load. Some users will add a very small amount of reset to slowly force the controller back to its set-point, but even a very small amount of reset will cause cycling.

For a level loop, the big issue is you can control either at set-point and have a cycle, or you forget about the set-point and have no cycle. The former is almost always no good. You can tolerate the latter if you explain to the operators the need to let the tank level float. 

It is possible to control the level in a tank accurately by using a PI controller. If the tank level controller has integral action, then the level control will be good and the make-up flow to the tank will tend to follow, and amplify in time any change in flow out of the tank. The question is do we really want to control the level accurately? 

In fact, in most cases the level in the tank does not matter as long as the tank does not overflow and the level doesn’t go too low. Letting the tank level float effectively uses the capacitance of the tank to smooth out flows or remove disturbances in flow. If you allow the tank level to float, the shape of the make-up flow trend will follow exactly the shape of the outlet flow, but the PB setting on the controller will attenuate it. Letting the level swing and thereby smoothing out either the flow-in or flow-out of the tank is averaging level control.

It is an axiom that you remove variability. You only relocate it. In the case of level control, the variability in the flow to or from a tank becomes the variability in the level of the tank when you apply averaging level control. Most of the time, variability in the level of a tank does not matter. In the “Averaging level control” figure, a typical tank level control with highlighted capacity figures has a time constant of 10 minutes (v/f). This  normally becomes a defining point in the need to react quickly to changes. In actual fact though, the real process changes you must respond to are in the neighborhood of roughly +/-10% of normal flow. This amounts to 100 lpm, which makes the effective tank time constant 10 times what you would normally calculate, or 100 minutes. Remember, the problem is level control, not concentration control. Therefore the tank is very large and has lots of capacity to absorb normal swings in flow. In fact, it will be quite effective in handling surges.

If the tank is running at its target level of 65% full, it could drop to 50% in 1.5 minutes if the inlet flow is completely cut off, or it could rise to 80% in 1.5 minutes if the outlet flow should drop to zero (pump failure, outlet valve fails shut).

But a more reasonable condition would be a normal flow change of say +/- 5%. Five percent of 1,000 lpm is 50 lpm. Were the 5% variation in flow to be sustained, it would now take 30 minutes to reach the 80% full mark (or 50% full mark) if starting from 65%. An uncorrected 5% variation increase flow would only raise the tank by 2.5% in five minutes. 

This is still an extreme case. With a  P-only controller, the inlet flow would slowly start to throttle as soon as there was any change in the level. So there is actually a great deal of time available to react to any change in level of normal magnitudes. The corollary to this is there is not much need to react to a change in level very quickly.

Even the definition of a process change can differ for level processes. Normal process signal filtering in the neighborhood of 0 to 10 seconds for flow and pressure measurement is not applicable to level measurement problems. Because level cannot change very quickly, what we can call process noise now encompasses variations that may be several seconds long, even tens of seconds, meaning a level transmitter filter can be very large if required.

About the Author

Rod Corbett was the superintendent of process control at StoraEnso Port Hawkesbury Ltd. in Port Hawkesbury, Nova Scotia, Canada, when the plant indefinitely closed. He will begin as manager of instrument and control systems at Renaissance Technology for Shell Oil Company’s Scotford site in Edmonton at the end of this month.