## Pneumatic PID controller

A while ago I wrote an article about proportional-integral-derivative (PID) controllers, where I talked about the idea behind them. You’ll often find them in programmable logic controllers (PLC), using electronic elements such as capacitors and inductors. And if you studied PID controllers in school, they usually presented you with electrical wave signals. But how would a PID controller work using pneumatic systems instead of electronic?

Like the 4-to-20 milliamp range for the electronic control system, the pneumatic system has a range, 3 to 15 pounds per square inch (psi). It achieves this range by using a flapper-nozzle system. If you want to know more about that, then check out our #WishIKnew on it here.

Again, just like in the electronic controller, the pneumatic PID controller can go proportional only (P), proportional-derivative (PD), proportional-integral (PI), or proportional-integral-derivative (PID).  Let’s look at each element.

### Proportional

The proportional element of a pneumatic PID controller applies a direct change to the output value after reading the error between your set point (SP) and your process variable (PV). Take a look at this image to see what I mean.

Here you have two pressures applied to the right end of the lever. The difference between these two pressures represents the error of our system. An increase in the PV would shift the right side up, causing the baffle to come closer to the nozzle. This change increases the pressure in the feedback bellows, which will return the flapper to (or very close to) its original position.

Note that the change in the PV directly influences the output pressure. An increase in the PV generates an increase in the output. If we wanted to reverse the action, then we swap the pressure inputs for the bellows on the right.

Now you might wonder, “How do I change the gain in this system?” To do that, you’ll have to alter parts of your system, like changing the bellows or moving the fulcrum.

##### Auto and manual modes

Automatic mode means the SP and PV determine the output, and manual mode has an operator setting the output. This picture will show you the whole mechanism.

To change from auto to manual, the operator needs to check the balance indicator. Before switching, you should see zero pressure difference between the output bellows and the output regulator. At that point, the operator can change the transfer valve to manual mode. Then the output will no longer respond to changes in the PV or SP.

To switch back to auto, the operator repeats the process, switching the transfer valve back when the system sits at zero. Now the controller will once again respond to changes in PV and SP.

### Derivative

Now let’s have a look at the derivative element of the system. To add a derivative action to your controller, you need to set a restriction valve between the nozzle tube and the output bellows. This will cause the bellows to change its pressure more slowly, as shown here.

With this valve added, if a sudden change occurs in the PV or SP, the output pressure must saturate first before the output bellows can equalize the pressure with the output signal tube. Therefore, you’ll see a spike in the output pressure with this step change in the input.

In a ramp change on the PV or SP, the output signal will shift in direct proportion. However, you’ll see an offset to the output pressure, to keep air flowing through the output bellows to balance the changing signal. So the derivative action shifts the output pressure more than a proportional element would for a ramp input.

Okay, let’s move on to the integral action now.

### Integral

For this element, you’ll have to add not only another restriction valve but also another bellows, called the reset bellows. It should oppose the output feedback bellows, as you can see here.

This setup might seem counterintuitive at first. However, this valve creates a delay on the filling of the reset bellows. Thus, the system works similarly to the resistor–capacitor (RC) circuit on an electronic controller.

As the reset bellows slowly fills with the output pressure, the change in pressure on the lever forces the output bellows to stay ahead of the reset bellows by constantly filling. Got it? No? Okay, let’s see how it works in practice.

##### The practice

Take a look at this image. We simplified the system to just the integral components.

Here, we have an SP of 4 psi, and the PV reads 7 psi, giving us a 3 psi error. Let’s assume that the fulcrum location gives us a gain of 1. The error causes the mechanism to instantly respond with a 3-psi output pressure to the feedback bellows. Let’s also completely close the reset valve. With the reset valve closed and no pressure in the reset bellows, the system works like a simple proportional-only controller.

Now let’s open the reset valve a bit. As the reset bellows fills, it pushes down the left side of the lever. This force makes the baffle move closer to the nozzle, increasing the pressure in the output line. The regular output bellows has no restriction valve to slow its filling. Therefore, it immediately applies upward force on the lever with the rising output pressure. With this increase of the output pressure, the reset bellows has an even greater “final” pressure to achieve, which makes it continue filling.

##### The result

Okay, but why do we want these two opposing forces? One of these forces happens instantly, and the other has a delay due to its valve. This delay forces the output bellows to always stay three psi ahead of the reset bellows to maintain balance. This creates a constant pressure difference of 3 psi across the reset valve, resulting in constant flow into the reset bellows.

Eventually, this will cause the output pressure to saturate at maximum. However, until then the mechanism exhibits integral control response to the constant error between PV and SP.

The bigger the difference between the SP and the PV, the more the pressure will drop across the restriction valve. The faster the reset bellows fills, the faster the output pressure changes. Once again, we can see that pneumatic and electronic controllers function very similarly, where the magnitude of the error determines the velocity of the output signal.

Any questions? If so, then you know where to find us!

Recommended articles