1. The document discusses pneumatic systems and their analogy to electrical systems, with pneumatic variables like pressure and mass flow rate corresponding to electrical variables like voltage and current. 2. Components of pneumatic systems like orifices, air tanks, and pipes are described along with their analogous electrical components like resistors, capacitors, and inductors. 3. Models of common pneumatic devices are presented, including dissipators, capacitors, nozzles, flappers, relays, check valves, bellows, and proportional/PID controllers. Linear models are used around operating points since high pressure pneumatic systems are nonlinear.

1. Industrial Control
Behzad Samadi
Department of Electrical Engineering
Amirkabir University of Technology
Winter 2009
Tehran, Iran
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2. Pneumatic Systems
Electrical Analogy
Type of System Electrical Pneumatic
T-Variable i, current q, mass flow
A-Variable v, voltage p, pressure
Dissipator resistor orifice
Storage (A-Type) capacitor air tank
Storage (T-Type) inductor long pipe
Unidirectional diode check valve
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3. Pneumatic Systems
Electrical Analogy
Type of System Electrical Pneumatic
T-Variable i, current q, mass flow
A-Variable v, voltage p, pressure
Dissipator resistor orifice
Storage (A-Type) capacitor air tank
Storage (T-Type) inductor long pipe
Unidirectional diode check valve
High pressure pneumatic systems are very nonlinear due to the compression of
air.
In this course, low pressure pneumatic systems and linear models around the
operating point are considered.
[Macia and Thaler, 2004, Ljung and Glad, 1994]
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4. Pneumatic Dissipator
Hagen - Poiseuille Law
∆p =
8µL
πr4
q = Rf q
∆p = pressure drop
q = mass flow rate
µ = dynamics viscosity
L = length of the pipe
r = radius
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5. Pneumatic Dissipator
Hagen - Poiseuille Law
∆p =
8µL
πr4
q = Rf q
∆p = pressure drop
q = mass flow rate
µ = dynamics viscosity
L = length of the pipe
r = radius
Hagen (1839) - Poiseuille (1838-1840) Law corresponds to Ohm’s law for electrical
circuits (v = ρ L
Ai = Ri)
Describes slow viscous incompressible flow through a constant circular cross-section
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6. Pneumatic Dissipator
Computation of the value of the gas flow resistance may be quite
time consuming.
[Ogata, 1997]
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7. Pneumatic Dissipator
Computation of the value of the gas flow resistance may be quite
time consuming.
It can however be easily determined from the plot of ∆p versus q.
Rf =
d(∆p)
dq
[Ogata, 1997]
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8. Pneumatic Capacitor
q p
Capacitance
Cf =
dm
dp
Cf = capacitance
m = mass of gas inside the tank
p = gas pressure
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9. Pneumatic Capacitor
Ideal Gas Law
pV
T
= nR
p =gas pressure
V =volume of the gas
T =absolute temperature
n =number of moles of gas
R =universal gas constant
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10. Pneumatic Capacitor
Ideal Gas Law
pV
T
= nR
p =gas pressure
V =volume of the gas
T =absolute temperature
n =number of moles of gas
R =universal gas constant
m =nM =
pV
RT
M
M =molar mass
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11. Pneumatic Capacitor
Ideal Gas Law
pV
T
= nR
p =gas pressure
V =volume of the gas
T =absolute temperature
n =number of moles of gas
R =universal gas constant
m =nM =
pV
RT
M
M =molar mass
Pneumatic Capacitor
Cf =
dm
dp
=
V
R
M T
Isothermal change is assumed.
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12. Simple Air Tank
Air Tank
Compressed
Air
Orifice
p
in
p
out
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13. Simple Air Tank
Air Tank
Compressed
Air
Orifice
p
in
p
out
pin =Rf Cf
dpout
dt
+ pout
pin =input pressure
pout =air tank pressure
Rf =orifice resistance
Cf =air tank capacity
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14. Pneumatic Nozzle-flapper Amplifier
[Ogata, 1997]
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15. Pneumatic Relay
In this course, it is assumed that Pneumatic Relay is a linear gain.
[Love, 2007]
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16. Check Valve
Pneumatic diode
[Parr, 1999]
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17. Bellows
Bellows actuator
[Parr, 1999]
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18. Bellows
Bellows actuator
Bellows feedback
[Parr, 1999]
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19. Pneumatic Proportional Controller
[Ogata, 1997]
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20. Pneumatic Proportional Controller
pb = K1x
[Ogata, 1997]
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21. Pneumatic Proportional Controller
pb = K1x
pb = K2z
[Ogata, 1997]
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22. Pneumatic Proportional Controller
pb = K1x
pb = K2z
pc = K3z
[Ogata, 1997]
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23. Pneumatic Proportional Controller
pb = K1x
pb = K2z
pc = K3z
pc = K1K3
K2
x = Kx
[Ogata, 1997]
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24. Pneumatic Proportional Controller
pb = K1x
pb = K2z
pc = K3z
pc = K1K3
K2
x = Kx
x = b
a+b e − a
a+b y
[Ogata, 1997]
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25. Pneumatic Proportional Controller
pb = K1x
pb = K2z
pc = K3z
pc = K1K3
K2
x = Kx
x = b
a+b e − a
a+b y
Apc = Ksy
[Ogata, 1997]
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26. Pneumatic PD Controller
[Ogata, 1997]
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27. Pneumatic PI Controller
[Ogata, 1997]
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28. Pneumatic PID Controller
[Ogata, 1997]
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29. I/P Converter
[Parr, 1999]
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30. Ljung, L. and Glad, T. (1994).
Modeling of Dynamic Systems.
Prentice Hall PTR, 1 edition.
Love, J. (2007).
Process Automation Handbook: A Guide to Theory and Practice.
Springer, 1 edition.
Macia, N. F. and Thaler, G. J. (2004).
Modeling and Control of Dynamic Systems.
Delmar Learning.
Ogata, K. (1997).
Modern Control Engineering.
Prentice Hall, 3 edition.
Parr, A. (1999).
Hydraulics and Pneumatics: A Technicians and Engineers Guide.
Butterworth-Heinemann, 2 edition.
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