#### 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 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 over-applies 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 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 with-in 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 early-responding derivative action and the smoothing-output 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.