Tension Control 101
An overview of tension measurement and closedloop PID tension control
with some lighthearted examples.
What is web tension?
In the materials processing industry, words like “stress” and “strain”
take on a different meaning from our typical, everyday usage of these terms.
I suppose there is a similarity in that they both are associated with the
effects produced by extending up to and beyond limits (strain). Stress
is the resulting condition of a solid structure (or person) being placed
under pressure or strain; and tension is a state that can result from strain
and stress. This article attempts to explain in simple terms some of the
mechanics of tension control in the industrial sense.
“Tension control” as applied to materials processing, refers to the
dynamic control of the tension produced by a web (or filament) being pulled,
usually through a machine’s processing zone, at a precise magnitude. This
is accomplished by either pulling at one end (in a rewind or intermediate
zone) and/or increasing the drag at the other end (the unwind zone); the
tension changing in response to a comparison between a measured and a desired
setting.
To investigate the basics of a tension control system, let’s look at
a primitive case where we have two ordinary spring scales supporting a
roller in a processing zone of interest. The web rides over the roller
in such a manner that the tension applied to the web is transferred to
the roller. In the case of measuring tension in an unwind zone, a person
could be stationed at this zone, reading the scales (a scaleman) and a
second person (a brakeman), at the unwind stand, could control a brake
to increase or decrease the drag on the web.
The scaleman would determine the desired reading on the scales (i.e.
20 lb., 51kg, or 12 stones) in his head, based on his experience with this
web material, and as the readings went up and down, he would holler to
the brakeman to either increase or decrease the braking force to keep the
scale readings at the set point. The scaleman and scale would be acting
as a tension measurement system and the brakeman and brake would be the
tensioning device.
If Benjamin Franklin needed web control on his press, this might have
been the method that he would have chosen. However this is not the 18th
century, but almost the 21st. Our choices and methods have changed quite
a bit since then. In our present world, we have replaced the scaleman and
the brakeman with an electronic control system.
Tension Transducers
Today the scales have been replaced with what we call tension transducers
(often, incorrectly, referred to as “load cells”). Transducers are
basically tension sensors composed of precisely designed beams that support
tiny strain gages. Strain gages are electrical resistors that change their
resistance as they are stretched. They act much like a piece of tubing
carrying water through it. If you stretched the tubing, the water has a
longer and narrower path to travel and therefore a greater resistance.
The further the gages are stretched, the higher the resistance. Of course,
we are talking about minute stretching in the vicinity of thousandths or
millionths of an inch for each inch of strain gage length.
Residing inside the transducer housing, the transducer beam compresses
and stretches as weight is applied, and the more weight the greater the
compressing and stretching. If the strain gages are bonded (glued) to the
beam in these compression and stretching areas, then a resistance change
is measured that is in relation to the amount of beam compression and stretching.
The magnitude of the resistance change is in direct proportion to the magnitude
of the weight applied to the beam.
If we place transducers at each end of an idler roll and suspend the
roll (in a machine frame), we have a replacement for the spring scale in
the scaleman/brakeman example. If we subtract out the initial weight of
the roller, the transducers can measure the added force placed upon the
roller from the web. Now that we have a method of determining the amount
of force exerted by the web upon the roller, we have to do something with
it. This leads us to a device mysteriously called a PID controller.
The Measurement Part Of A Modern Tension Controller
In our primitive system, where we had a scaleman who watched the scales
and directed the brakeman to adjust torque on the unwind brake, we have
an analogy to today’s electronic systems. Electronic control systems, however,
can provide far greater performance than a manual system could. An electronic
controller contains a circuit that looks at both the desired tension value
and the actual tension value.
The desired value is set with a potentiometer (appropriately enough
called a setpot) by the user. Then as the web machine runs, tension
on the roller of interest is measured by the transducers. But before the
measured tension is compared to the setpoint value, it must be electronically
adjusted to match the reference scale of the setpoint. After all, we should
only compare apples with apples.
Before this scaling adjustment is made, the measured tension has the
roll weight subtracted from it, so as only to count the tension contribution
from the web, not the roll. The output signal corresponding to actual tension
is then amplified to coincide with the magnitude of the desired tension
setpoint. We call the first step of subtracting the roll weight “zeroing”,
while the scaling procedure is called “calibrating”. These are two very
important aspects of any electronic measurement system.
P + I + D: The Corrective Actions of a Tension Controller
Proportional Action: the P of PID
Once the roll weight and transducers have been zeroed and calibrated, we
can compare the electrical signal of the actual web tension to our desired
tension setpoint. The result of this comparison is an error signal.
Because web processes are dynamic systems, with actual tension changing
from moment to moment, except for the moments when actual tension is exactly
equal to setpoint tension, actual tension usually will be less than or
greater than our desired tension. The aim of our controller circuitry is
to produce a correction signal that is sent to the tensioning mechanism.
This is where the gain circuitry of the controller comes into play.
The gain is simply like a multiplier which increases the error signal to
a value that can be used as our correction signal. The gain circuitry acts
to produce a correction signal (either increasing or decreasing tension)
that is proportional in magnitude to the original error signal.
As the error signal changes, the resulting correction signal changes by
the same factor. This proportional change of the correction signal is the
P of PID.
Determining the correct amount of gain to apply depends on how much
deviation from setpoint one expects from the process. Large deviations
produce a large error signal and therefore require less gain. Smaller deviations
produce smaller error signals and therefore require more gain in order
to produce a significant correction signal.
Derivative Action: the D of PID
As you may have experienced, the tighter the tolerance in which you try
to control something, the harder it is to hold. Imagine an automobile cruise
control set to a speed difference of +/ 0.1 miles per hour. It would constantly
be turning off and on, and overshooting the set speed. The same effect
would happen with tension control without the I and the D of PID.
In a real, dynamic tension control system, there are many actions, reactions
and changes that are occurring continuously and have to be dealt with as
the web moves through its process. A mass (rolls, rollers, web, motor armature,
etc.) has to be accelerated and decelerated in response to system changes
and constant modifications to the drive system are needed as a roll or
spool builds up or down. Sir Isaac Newton summed up a dynamic system’s
behavior in his laws on motion. As of yet, those laws have not been repealed,
only slightly amended.
Let’s first address the acceleration dilemma. Newton states that an
object at rest wants to stay at rest unless acted upon by an outside force.
The web and its associated paraphernalia are at rest and want to stay that
way. In our primitive system, let’s assume there is slack web and no tension
to start. As the web is started, the scaleman would be watching the Tension
as it builds up. Not being very responsive, he would wait to signal the
brakeman until the desired tension is reached. Too late!!
The brakeman, also not too swift, applies the brake a little late and
a little hard. As Newton stated, you can not stop all that mass on a dime.
Guess what? We overshoot our tension. Next the signalman tells the brakeman
to relax the brakes because we have overshot the desired tension. The brakeman
overreacts, and, if we include a little of Newton's law, we fall well below
the desired tension. To compensate, he overapplies the brake. The two
men keep repeating this over and over again until maybe they finally reach
the correct tension. At this point it seems like they may be out of the
woods. But alas, things can change, requiring corrections. If the scaleman
and the brakeman do not have their act together, they must repeat their
actions with the tension fluctuating all over the place.
Our two control men could have accomplished this far task far better
by using a little more intelligence and anticipation. We would come to
a nice steady tension If the scaleman had notified the brakeman when the
tension was within say ten percent of the desired tension. The brakeman
could have slowly applied the brake, increasing it as the tension reached
the desired value, and held it there. This is like you driving a car and
seeing a stop light; hopefully you apply the brake before reaching the
light, not waiting until you reach the light. Believe it or not, we have
just described the idea behind the derivative action of a control
system.
The derivative circuit of a PID controller monitors the tension, looking
for any changes. It is only interested in changes and not the steady stuff.
The correction signal output by this circuit changes as long as the magnitude
of error between the setpoint tension and actual tension changes; the output
signal is proportional to any change that the circuit measures. When there
is no change the output is zero, thus contributing nothing for a steady
state condition of the web (which very seldom exists).
When a machine starts, the web in the process has to go from zero speed
to its final speed. The tension builds up, and a corresponding correction
signal from our derivative circuit is applied. The added derivative signal
makes the tension signal look larger then it really is, thus causing more
brake to be applied before reaching the desired tension. This is what we
want.
As the tension approaches the desired value and the brakes are gradually
applied, the rate of change in tension decreases, thereby lowering the
derivative output being added on. The actual tension will approach the
desired tension at an increasingly slower rate until the two meet. At this
point the derivative signal will be zero because the actual and desired
tension values match.
We could say that the derivative circuit reads the rate of tension
change and outputs a correction signal corresponding to that rate. The
circuit seems to anticipate and respond early to the trend it is monitoring.
This is different from the proportional circuit which is only reacting
to the absolute error signal at any given moment in time.
It’s a full time job for the derivative circuit, always keeping a keen
vigilance, ready to pop into action at the slightest hint of a tension
change. It automatically adjusts for tension deviations in either direction.
Integral Action: the I of PID
Let’s move on to a totally new analogy just for a change. Integral action
is probably something we could use when we are in a shower (in addition
to soap, of course). When trying to regulate the water temperature, do
you ever overreact? When the water’s too hot do you turn the knob back
only to find that you went too far. Back and forth it goes, until you finally
reach a point where you’re somewhat satisfied.
Is the delayed result of your action due to the water temperature responding
too slowly to the control? Or, all things being relative, are you turning
the control too fast for the temperature to keep up with the change? The
answer is that both ways of looking at the problem are correct. Each perspective
just requires a different approach to solving the problem. We want better
control of our water temperature, right? The first perspective describes
the problem from the approach that makes derivative action look like the
solution. The second perspective makes integral action look like a better
approach. Fortunately a PID controller does both. Its working both ends
of the problem at once.
Let’s go back to the tension controller. Like the derivative circuit,
the integrator circuit also reads tension error trend. But instead of providing
an early output signal to improve tension response in direct reaction to
the trend, the integrator gives a correction output that acts to smooth
or, in effect, slow the rate of controller output so that the tensioning
mechanism will not overreact. It’s like the person in the shower turning
the knob more slowly so that the temperature change can keep up with the
control change. This is just another way of adding stability to our system.
By combining both the earlyresponding derivative action and the smoothingoutput
integral action we can gain an acceptable level of dynamic response and
stability.
In the case of most PID controllers, the P,I, and D components are all
combined to produce one output signal. The effect from each action is
adjusted during system setup and tuning, and varies depending upon the
system parameters. You’ll notice on SteadyWeb controllers that we refer
to the three components as “gain”, “stability”, and “response”. These
terms are more descriptive and useful than Proportional, Integral, and
Derivative.
