Industrial Control Systems - Pneumatic Systems

Industrial Control

Behzad Samadi

Department of Electrical EngineeringAmirkabir University of Technology

Winter 2009Tehran, Iran

Behzad Samadi (Amirkabir University) Industrial Control 1 / 17

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


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 ofair.In this course, low pressure pneumatic systems and linear models around theoperating point are considered.

[Macia and Thaler, 2004, Ljung and Glad, 1994]


Pneumatic Dissipator

Hagen - Poiseuille Law

∆p =8µL

πr4q = Rf q

∆p = pressure drop

q = mass flow rate

µ = dynamics viscosity

L = length of the pipe

r = radius



Hagen - Poiseuille Law

∆p =8µL

πr4q = 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 electricalcircuits (v = ρ

L

Ai = Ri)

Describes slow viscous incompressible flow through a constant circular cross-section



Computation of the value of the gas flow resistance may be quitetime consuming.

[Ogata, 1997]



Computation of the value of the gas flow resistance may be quitetime consuming.

It can however be easily determined from the plot of ∆p versus q.

Rf =d(∆p)

dq

[Ogata, 1997]


Pneumatic Capacitor

q p

Capacitance

Cf =dm

dp

Cf = capacitance

m = mass of gas inside the tank

p = gas pressure


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


Pneumatic Capacitor

Ideal Gas Law

pV

T= nR

p =gas pressure





m =nM =pV

RTM

M =molar mass


Pneumatic Capacitor

Ideal Gas Law

pV

T= nR

p =gas pressure





m =nM =pV

RTM

M =molar mass

Pneumatic Capacitor

Cf =dm

dp=

VR

MT

Isothermal change is assumed.


Simple Air Tank

Air Tank

CompressedAir

Orifice

pin

pout


Simple Air Tank

Air Tank

CompressedAir

Orifice

pin

pout

pin =Rf Cf

dpout

dt+ pout

pin =input pressure

pout =air tank pressure

Rf =orifice resistance

Cf =air tank capacity


Pneumatic Nozzle-flapper Amplifier

[Ogata, 1997]


Pneumatic Relay

In this course, it is assumed that Pneumatic Relay is a linear gain.

[Love, 2007]


Check Valve

Pneumatic diode

[Parr, 1999]


Bellows

Bellows actuator

[Parr, 1999]Behzad Samadi (Amirkabir University) Industrial Control 11 / 17

Bellows

Bellows actuator

Bellows feedback

[Parr, 1999]Behzad Samadi (Amirkabir University) Industrial Control 11 / 17

Pneumatic Proportional Controller

[Ogata, 1997]



pb = K1x

[Ogata, 1997]



pb = K1x

pb = K2z

[Ogata, 1997]



pb = K1x

pb = K2z

pc = K3z

[Ogata, 1997]



pb = K1x

pb = K2z

pc = K3z

pc = K1K3K2

x = Kx[Ogata, 1997]



pb = K1x

pb = K2z

pc = K3z

pc = K1K3K2

x = Kx

x = b

a+be −

a

a+by

[Ogata, 1997]



pb = K1x

pb = K2z

pc = K3z

pc = K1K3K2

x = Kx

x = b

a+be −

a

a+by

Apc = Ksy

[Ogata, 1997]


Pneumatic PD Controller

[Ogata, 1997]


Pneumatic PI Controller

[Ogata, 1997]


Pneumatic PID Controller

[Ogata, 1997]


I/P Converter

[Parr, 1999]


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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Industrial Control Systems - Pneumatic Systems

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