1. Industrial Control
Behzad Samadi
Department of Electrical Engineering
Amirkabir University of Technology
Winter 2009
Tehran, Iran
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2. Liquid Level Systems
Electrical Analogy
Type of System Electrical Liquid Level
T-Variable i, current q, volumetric flow
A-Variable v, voltage h, head
Dissipator resistor orifice
Storage (A-Type) capacitor liquid tank
Storage (T-Type) inductor long pipe
Unidirectional diode check valve
Flow regimes are divided into laminar flow and turbulent flow.
[Ogata, 1997]
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3. Dissipator
Laminar flow: Rl = H
Q
[Ogata, 1997]
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4. Dissipator
Laminar flow: Rl = H
Q
Turbulent flow:
Q =K
√
H
Rt =
dQ
dH
=
2H
Q
[Ogata, 1997]
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5. Simple Liquid Tank
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6. Simple Liquid Tank
Capacitance:
C
dh
dt
=qi − qo
C =cross sectional area of the tank
[Ogata, 1997]
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7. Simple Liquid Tank
Capacitance:
C
dh
dt
=qi − qo
C =cross sectional area of the tank
Dynamic equation:
C
dh
dt
=qi −
h
R
RC
dh
dt
+ h =Rqi
[Ogata, 1997]
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8. Connected Tanks
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9. Connected Tanks
h1 − h2
R1
=q1
C1
dh1
dt
= q − q1
h2
R2
= q2
C2
dh2
dt
= q1 − q2
[Ogata, 1997]
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10. Ogata, K. (1997).
Modern Control Engineering.
Prentice Hall, 3 edition.
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