What is I in PID? A (too) simple answer: it is the “Integral” component of Proportional-Integral-Derivative control.
First let’s start with a simple temperature control system. Now the natural thing to do would be to use “degrees” as the units for our process signal … but to keep things as simple as possible, let’s use “PERCENT of FULL SCALE” instead.
Let’s say that the controller’s SP (Setpoint – or “target”) has been set for something like 10% of full scale for a very long time.Let’s say that the controller has been regulating the CV (Control Variable – or controller “output”) at 25% for a very long time. Let’s say that the system’s PV (Process Variable – or “temperature”) has been accurately controlled at the desired target of 10% for a very long time.
You should already understand that every time the PID controller is executed, it calculates a value for E (Error – or “how far are we away from the target?”). In our example, the formula for this error calculation is “E=SP-PV”. Since E=10-10 then E=0% of full scale. This “0” error value is the PID controller’s way of knowing that WHATEVER the value going out to the CV, it’s PERFECT. In other words, we’re presently right on target,the PV is tracking the SP, so let’s keep everything right where we’ve got it ,“steady as she goes”.
Those are the conditions that we see at the left side of Figure 1 as shown below. So just to nail things down, we have a well-controlled system simmering along right on target.
Now, let’s do something really strange.
We’re going to do this just for EDUCATIONAL purposes only. We’re going to physically JAM the system’s output valve (the real-world field device) in its present (25%) position. Now at first glance you might think that this will really “mess things up” but it won’t in fact, as long as everything else (room temperature, gas pressure, etc.) stays the same , the system will
just keep on simmering along – right on target – think about it this way: we’ve already said that the CV has been running along at 25% for a very long time and even though we’ve physically jammed the valve at the 25% position, the system should stay right on target – just as long as nothing else changes and now the stage is set.
First we’ll begin with the “P” or “Proportional” setting. We’ll get to the “I” or “Integral” setting in due course.
The CV
starts out at position “A” on the graph. That’s the 25% setting
as soon as we reach position “B” on the graph, we suddenly increase the SP (the “target”) from its original setting of 10% to a new setting of 20%. The PID controller sees this change and it calculates a new Error based on this equation: “E=SP-PV”. Since E=20-10 then E=10% of full scale .
Now let’s say that our controller’s “P” or “Proportional” setting is currently a nice round value of 2.00.
The controller takes the E (10%) and multiplies that by the P setting (2.00) and then adds the result (20%) to the previous CV (25%). The result of this calculation (45%) becomes
the new value for the CV and that’s what we see happening at position “C” on the graph. Specifically, the controller’s proportional action has instantly stepped the CV from 25% to 45% in an effort to drive the PV up to the new target value.
Now notice the little blue “yardsticks” on the graph. Notice that one of these “yardsticks” is used to measure the sudden increase in the SP. This “yardstick” is 10% of full scale.
Now notice that it takes two “yardsticks” to measure the 20% jump in the CV between position “B” and position “C”. Just for discussion, if our controller’s P setting happened to be 1.00 instead of 2.00, then the increase in the CV from point “B” would only have been half as much. Specifically, it would have gone up one 10% “yardstick” rather than two. Since the PID’s proportional action is discussed in another paper, we won’t go into any more detail about it here.
Now we’re ready to tackle the “I” or “Integral” setting …
Remember that the system’s control valve has been physically jammed in the 25% position, it cannot possibly move, so even though the PID controller really and truly sends out a new value of 45% to the output valve, the valve (the field device) stays in the 25% position.That means that the PV is going to keep right on tracking along at its 10% value. You can see that happening on the graph. Specifically, the PV line stays completely horizontal. Even though the CV (the value in the PLC’s memory) does indeed go up. So now the Proportional action has done as much as it can to drive the PV toward the target but since we’ve jammed the valve, the PV doesn’t change. So the PID starts using the Integral action to try to increase the PV and that’s the “ramping” action that you see taking place in the CV after its initial jump up to position “C”.
Now let’s look at the CV as it takes off from position “C”
For discussion purposes, I’ve given you two possible paths for the CV :
let’s take the first one which leads up to position “D” – this is the path that the CV would take if the controller’s “I” setting was 2.00. That setting would literally mean “2.00 minutes per repeat”. In other words, it would take 2.00 minutes for the Integral action to REPEAT the Proportional action and that is what the two “yardsticks” are showing at position “D”.
let’s look at the CV again as it takes off from position “C” but this time we’ll take the second path : the one which leads up to position “E”. This is the path that the CV would take if the controller’s “I” setting was 4.00. That setting would literally mean “4.00 minutes per repeat”. In other words, with this setting it would take 4.00 minutes for the Integral action to REPEAT the Proportional action and that is what the two “yardsticks” are showing at position “E”. Specifically, the Integral action caused the CV to increase the same 20% (two “yardsticks”)
BUT : notice that it took twice as long (4 minutes rather than 2 minutes) to make the SAME amount of increase. So one thing that we’ve just learned is that for LESS Integral ACTION,
we need to use a HIGHER Integral SETTING. Specifically, a BIGGER NUMBER gives us LESS ACTION, conversely, for MORE Integral ACTION, we need to use a LOWER Integral SETTING.
Specifically, a SMALLER NUMBER gives us MORE ACTION …
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