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29.11Pneumatic PID controllers

A pneumatic controller receives a process variable (PV) signal as a variable air pressure, compares that signal against a desired setpoint (SP) value, and then mechanically generates another air pressure signal as the output, driving a final control element.

Throughout this section I will make reference to a pneumatic controller mechanism of my own design. This mechanism does not directly correspond to any particular manufacturer or model of pneumatic controller, but shares characteristics common to many. This design is shown here for the purpose of illustrating the development of P, I, and D control actions in as simple a context as possible.

29.11. PNEUMATIC PID CONTROLLERS

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29.11.1Proportional control action

Many pneumatic PID controllers use the force-balance principle. One or more input signals (in the form of pneumatic pressures) exert a force on a beam by acting through diaphragms, bellows, and/or bourdon tubes, which is then counter-acted by the force exerted on the same beam by an output air pressure acting through a diaphragm, bellows, or bourdon tube. The self-balancing mechanical system “tries” to keep the beam motionless through an exact balancing of forces, the beam’s position precisely detected by a nozzle/ba e mechanism:

Setpoint signal

(3-15 PSI)

Pneumatic proportional controller

These short diagonal lines represent a fixed anchor point

Baffle

Nozzle

Lever

Fulcrum

Spring

(pulls down on lever)

Output

(to control valve)

Orifice

Process variable signal

(3-15 PSI)

Air supply

The action of this particular controller is direct, since an increase in process variable signal (pressure) results in an increase in output signal (pressure). Increasing process variable (PV) pressure attempts to push the right-hand end of the beam up, causing the ba e to approach the nozzle. This blockage of the nozzle causes the nozzle’s pneumatic backpressure to increase, thus increasing the amount of force applied by the output feedback bellows on the left-hand end of the beam and returning the flapper (very nearly) to its original position. If we wished to reverse the controller’s action, all we would need to do is swap the pneumatic signal connections between the input bellows, so that the PV pressure was applied to the upper bellows and the SP pressure to the lower bellows.

Any factor influencing the ratio of input pressure(s) to output pressure may be exploited as a gain (proportional band) adjustment in this mechanism. Changing bellows area (either both the PV and SP bellows equally, or the output bellows by itself) would influence this ratio, as would a change in output bellows position (such that it pressed against the beam at some di erence distance

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from the fulcrum point). Moving the fulcrum left or right is also an option for gain control, and in fact is usually the most convenient to engineer.

In this illustration the fulcrum is shown moved to two di erent positions, to e ect a change in gain:

SP

High gain

(small proportional band)

SP

Low gain

(large proportional band)

Output	Output
PV	PV
Air supply	Air supply

Moving the fulcrum closer to the output bellows places that bellows at a mechanical disadvantage for generating torque (leverage) on the beam. This means any given change in input (PV or SP) force is more di cult for the output bellows to counterbalance. The output pressure, therefore, must change to a greater degree in order for this force-balance mechanism to achieve balance. A greater change in output pressure for a given change in input pressure is the definition of a gain increase.

Conversely, moving the fulcrum farther away from the output bellows increases that bellows’ mechanical advantage. This additional leverage makes it easier for the output bellows to counteract changes in input force, resulting in less output pressure change required to balance any given input pressure change. A lesser change in output pressure for a given change in input pressure is characteristic of a gain decrease.

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Some pneumatic controllers employ the motion-balance principle instead of the force-balance principle in their operation. In contrast to a force-balance system where opposing forces cancel each other to restrain motion of the mechanism, a motion-balance system freely moves as the signal pressures traverse their working ranges. A simple motion-balance proportional controller design appears here:

Setpoint signal

(3-15 PSI)

Pneumatic proportional

controller (motion-balance)

Lever

Output

(to control valve)

Process

variable signal

Orifice

(3-15 PSI)

Air supply

As the process variable signal increases, the right-hand end of the lever is forced up. This motion draws the lever away from the nozzle, resulting in decreased nozzle backpressure. The decreased backpressure causes the output bellows to collapse17, moving the left-hand end of the lever down and returning the nozzle/lever gap to (approximately) where it was before the PV signal change. This behavior identifies this controller as reverse-acting. If direct action were desired, all we would need to do is swap the process variable and setpoint input pressure connections.

Unlike the force-balance controller mechanism where the lever is maintained in an essentially stationary position by equal and opposite forces, the lever in this motion-balance system is free to tilt. In fact, tilting is precisely how a (nearly) constant nozzle gap is maintained: as one end of the lever moves (either up or down), the other end moves in the opposite direction to keep the nozzle/lever gap constant in the middle.

17Being a motion-balance mechanism, these bellows must act as spring elements in order to produce consistent pressure/motion behavior. Some pneumatic controllers employ coil springs inside the brass bellows assembly to provide the necessary “sti ness” and repeatability.

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The gain of such a mechanism may be changed by moving the position of the nozzle along the lever’s length. However, it must be understood that this position change will have the opposite e ect on gain compared with the fulcrum position change described for the force-balance mechanism. Here in the motion-balance system, it is the relative travel of each bellows that matters for gain, not the relative leverage (torque):

SP

Low gain

(large proportional band)

Lever

SP

High gain

(small proportional band)

Lever

Output

Output

PV

PV

Air supply

Air supply

With the nozzle positioned closer to the output bellows, that bellows need not stretch or collapse as much in order to maintain the nozzle gap constant even with a large motion at the input (righthand) end of the lever. The output pressure in this case will change only slightly for large changes in PV or SP pressures: characteristic of a low gain.

Moving the nozzle closer to the input (PV and SP) bellows gives those bellows more influence over the nozzle/lever gap. The output bellows must expand and contract quite a bit more than the input bellows in order to maintain a constant nozzle gap for any motion at the input side. This requires a greater change in output pressure for a given change in input pressure: the definition of increased gain.