# How proportional action is produced in a pneumatic controller

## Homework Statement

(a) With the aid of a sketch explain how proportional action is produced
in a pneumatic controller whose output is 0.2 to 1.0 bar. Assume that
the controller is direct acting.

(b) Show, mathematically, that the output is dependent on the difference
between the measured and desired values.

(c) With the aid of a well annotated sketch describe the construction and
operation of a P + I + D controller having a pneumatic output.

## Homework Equations

none that I can think of

## The Attempt at a Solution

(a) I believe I have to produce this as the first part of the question. As my lessons are pretty poor this is all I can gather from the content.

(b) There is nothing that I can see in my notes for this. The tutor is as helpful as the notes also.

(c) I think this is what they are after, but again my lessons don't shed much light on this.

I just need pointed in the right direction and I should be good to be honest.

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## Answers and Replies

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jim hardy
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Try about page 17 here

http://www.instrumentationrepair.com/Documents/Manuals/Bailey/Instruments/P92-1-1.pdf

i'd download and print a copy because it takes some mental gymnastics to wrap your brain around that mechanical marvel.
The Bailey AD is a general purpose analog computer with two balance beams instead of just one as you have drawn,
but the principles of force balance and displacement balance are your basic thought tools.

Try about page 17 here

http://www.instrumentationrepair.com/Documents/Manuals/Bailey/Instruments/P92-1-1.pdf

i'd download and print a copy because it takes some mental gymnastics to wrap your brain around that mechanical marvel.
The Bailey AD is a general purpose analog computer with two balance beams instead of just one as you have drawn,
but the principles of force balance and displacement balance are your basic thought tools.
Thats great. Thanks for the information.

Now I have to derive an equation for Po relating to measure and desired pressures for b).
Any pointers?

jim hardy
Gold Member
2019 Award
Dearly Missed
Now I have to derive an equation for Po relating to measure and desired pressures for b).
Any pointers?

well as i said force balance and displacement balance are your thought tools.

Consider forces F acting on the beam, and their distances from the pivot..

assume all bellows have same area.
Equilibrium is when beam is balanced exactly horizontal, as shown
consider that a minute displacement from there, less than 0.001" changes nozzle pressure hence output pressure from minimum to maximum.
and for analysis imagine it takes zero movement from equilibrium to change output pressure over full range
so the nozzle is your "null" analogous to summing junction of an operational amplifier circuit.

In my opinion the spring on right end is mis-named it should be called Bias rather than Proportioning.

Since all bellows have same area, force exerted by any of them is proportional to pressure and we dont have to write area into the force balance equations.
Force up on left end of beam equals (Pmeasured - Pdesired),
and force up on right end of beam equals (Poutput - Fbias spring)

The beam is in equilibrium when sum of torques is zero
(Pmeasured - Pdesired) X D1 = (Poutput - Fbias spring) X D2
Solve for Poutput.
(You might want to set Fbias spring = 0 for starters.)

That should give you the idea what they're up to in the "How It Operates" chapter of that Bailey instruction leaflet.

It's the mechanical analogue to an operational amplifier circuit.
D1 and D2 are analogous to input and feedback resistors
and that 0.001" displacement i mentioned is analogous to open loop gain.
The AD relay has a pressure booster with gain around 20 placed between nozzle and output to increase its "open loop gain" .ie reducing the mechanical displacement necessary to achieve full output pressure swing..

Learn this stuff .
Maintaining a null has been the basis of automatic controls since well before computers.

old jm

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jim hardy
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2019 Award
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Answer to C is in that Bailey manual.

Answer to C is in that Bailey manual.
Hey Jim

Thanks for the info, someone at work is very good at PID controllers also. The above solutions are correct.

I will mark this as solved now.

Thanks again

jim hardy