The document discusses liquid level control systems and their electrical analogies. It describes how flow regimes are divided into laminar and turbulent flow. Equations are presented for the resistance of a dissipator and capacitance of a simple liquid tank. Dynamic equations are shown for a simple tank and connected tanks system. The document references Ogata's Modern Control Engineering as the source for the information.

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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