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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
Behzad Samadi (Amirkabir University) Industrial Control 2 / 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
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]
Behzad Samadi (Amirkabir University) Industrial Control 2 / 17
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
Behzad Samadi (Amirkabir University) Industrial Control 3 / 17
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 (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
Behzad Samadi (Amirkabir University) Industrial Control 3 / 17
Pneumatic Dissipator
Computation of the value of the gas flow resistance may be quitetime consuming.
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 4 / 17
Pneumatic Dissipator
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]
Behzad Samadi (Amirkabir University) Industrial Control 4 / 17
Pneumatic Capacitor
q p
Capacitance
Cf =dm
dp
Cf = capacitance
m = mass of gas inside the tank
p = gas pressure
Behzad Samadi (Amirkabir University) Industrial Control 5 / 17
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
Behzad Samadi (Amirkabir University) Industrial Control 6 / 17
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
RTM
M =molar mass
Behzad Samadi (Amirkabir University) Industrial Control 6 / 17
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
RTM
M =molar mass
Pneumatic Capacitor
Cf =dm
dp=
VR
MT
Isothermal change is assumed.
Behzad Samadi (Amirkabir University) Industrial Control 6 / 17
Simple Air Tank
Air Tank
CompressedAir
Orifice
pin
pout
Behzad Samadi (Amirkabir University) Industrial Control 7 / 17
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
Behzad Samadi (Amirkabir University) Industrial Control 7 / 17
Pneumatic Nozzle-flapper Amplifier
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 8 / 17
Pneumatic Relay
In this course, it is assumed that Pneumatic Relay is a linear gain.
[Love, 2007]
Behzad Samadi (Amirkabir University) Industrial Control 9 / 17
Check Valve
Pneumatic diode
[Parr, 1999]
Behzad Samadi (Amirkabir University) Industrial Control 10 / 17
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]
Behzad Samadi (Amirkabir University) Industrial Control 12 / 17
Pneumatic Proportional Controller
pb = K1x
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
Pneumatic Proportional Controller
pb = K1x
pb = K2z
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
Pneumatic Proportional Controller
pb = K1x
pb = K2z
pc = K3z
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
Pneumatic Proportional Controller
pb = K1x
pb = K2z
pc = K3z
pc = K1K3K2
x = Kx[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
Pneumatic Proportional Controller
pb = K1x
pb = K2z
pc = K3z
pc = K1K3K2
x = Kx
x = b
a+be −
a
a+by
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
Pneumatic Proportional Controller
pb = K1x
pb = K2z
pc = K3z
pc = K1K3K2
x = Kx
x = b
a+be −
a
a+by
Apc = Ksy
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
Pneumatic PD Controller
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 14 / 17
Pneumatic PI Controller
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 15 / 17
Pneumatic PID Controller
[Ogata, 1997]
Behzad Samadi (Amirkabir University) Industrial Control 16 / 17
I/P Converter
[Parr, 1999]
Behzad Samadi (Amirkabir University) Industrial Control 17 / 17
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.
Behzad Samadi (Amirkabir University) Industrial Control 17 / 17