Industrial Control Systems - Hydraulic Systems

Industrial Control
Behzad Samadi
Department of Electrical Engineering
Amirkabir University of Technology
Winter 2010
Tehran, Iran
Behzad Samadi (Amirkabir University) Industrial Control 1 / 17

Hydraulic Systems
Electrical Analogy
Type of System Electrical Hydraulic
T-Variable i, current q, volumetric ﬂow
A-Variable v, voltage p, pressure
Dissipator resistor oriﬁce
Storage (A-Type) capacitor storage tank
Storage (T-Type) inductor long pipe
Unidirectional diode check valve

Hydraulic Systems
Electrical Analogy
Type of System Electrical Hydraulic
T-Variable i, current q, volumetric flow
A-Variable v, voltage p, pressure
Dissipator resistor orifice
Storage (A-Type) capacitor storage tank
Storage (T-Type) inductor long pipe
Unidirectional diode check valve
The fluid is assumed to be incompressible.
[Macia and Thaler, 2004, Ljung and Glad, 1994]

Hydraulic Dissipator
d’Arcy’s Law
For a thin tube:
p = Rf q

Hydraulic Dissipator
d’Arcy’s Law
For a thin tube:
p = Rf q
For a sudden change in area, such as an oriﬁce or valve:
p = ℋq2
sgn(q)
ℋ is a constant.
[Ljung and Glad, 1994]

Hydraulic Capacitor

Hydraulic Capacitor
p =
mg
A
=
𝜌g
A
V =
𝜌g
A
∫ t
0
q(𝜏)d𝜏
p =pressure at the bottom of the tank
V =volume of the ﬂuid in tank
A =cross section area of the tank
𝜌 =density of the ﬂuid

Hydraulic Capacitor
p =
mg
A
=
𝜌g
A
V =
𝜌g
A
∫ t
0
q(𝜏)d𝜏
p =pressure at the bottom of the tank
V =volume of the ﬂuid in tank
A =cross section area of the tank
𝜌 =density of the ﬂuid
Hydraulic Capacitor
Cf = A
𝜌g

Hydraulic Inductor

Hydraulic Inductor
F =ma = (𝜌lA)
dv
dt
p =
F
A
= 𝜌l
dv
dt
q =Av

Hydraulic Inductor
F =ma = (𝜌lA)
dv
dt
p =
F
A
= 𝜌l
dv
dt
q =Av
⇒ p =𝜌
l
A
dq
dt
= Lf
dq
dt

Hydraulic Inductor
F =ma = (𝜌lA)
dv
dt
p =
F
A
= 𝜌l
dv
dt
q =Av
⇒ p =𝜌
l
A
dq
dt
= Lf
dq
dt
Hydraulic Inductor
Lf = 𝜌 l
A

Hydraulic Junction
∑
i Qi = 0 (KCL)

Hydraulic Junction
∑
i Qi = 0 (KCL) p4 = p1 + p2 + p3 (KVL)

Hydraulic Transformer

Hydraulic Transformer
p1Q1 =p2Q2
p1 =𝛼p2
Q1 =
1
𝛼
Q2
𝛼 =
A2
A1

Hydraulic Servomechanism

xm: maximum displacement

x = xm ⇒
{
Pa = Ps
Pb = P0 = 0

x = xm ⇒
{
Pa = Ps
Pb = P0 = 0
x = −xm ⇒
{
Pa = P0 = 0
Pb = Ps

x = xm ⇒
{
Pa = Ps
Pb = P0 = 0
x = −xm ⇒
{
Pa = P0 = 0
Pb = Ps
Pa = 1
2( x
xm
+ 1)Ps

x = xm ⇒
{
Pa = Ps
Pb = P0 = 0
x = −xm ⇒
{
Pa = P0 = 0
Pb = Ps
Pa = 1
2( x
xm
+ 1)Ps
Pb = 1
2(− x
xm
+ 1)Ps

x = xm ⇒
{
Pa = Ps
Pb = P0 = 0
x = −xm ⇒
{
Pa = P0 = 0
Pb = Ps
Pa = 1
2( x
xm
+ 1)Ps
Pb = 1
2(− x
xm
+ 1)Ps
Pa − P1 = Rqq

x = xm ⇒
{
Pa = Ps
Pb = P0 = 0
x = −xm ⇒
{
Pa = P0 = 0
Pb = Ps
Pa = 1
2( x
xm
+ 1)Ps
Pb = 1
2(− x
xm
+ 1)Ps
Pa − P1 = Rqq
Pb − P2 = Rqq

x = xm ⇒
{
Pa = Ps
Pb = P0 = 0
x = −xm ⇒
{
Pa = P0 = 0
Pb = Ps
Pa = 1
2( x
xm
+ 1)Ps
Pb = 1
2(− x
xm
+ 1)Ps
Pa − P1 = Rqq
Pb − P2 = Rqq
q = A˙y

M¨y + B ˙y + Ky = A(P1 − P2)

M¨y + B ˙y + Ky = A(P1 − P2)
P1 + P2 = Ps ⇒ P2 = Ps − P1

M¨y + B ˙y + Ky = A(P1 − P2)
P1 + P2 = Ps ⇒ P2 = Ps − P1
P1 = Pa − Rqq = 1
2( x
xm
+ 1)Ps − RqA˙y

M¨y + B ˙y + Ky = A(P1 − P2)
P1 + P2 = Ps ⇒ P2 = Ps − P1
P1 = Pa − Rqq = 1
2( x
xm
+ 1)Ps − RqA˙y
M¨y + B ˙y + Ky =A(P1 − P2)
=A(2P1 − Ps)
=A((
x
xm
+ 1)Ps − 2RqA˙y − Ps)

Mÿ + B ˙y + Ky = A(P1 − P2)
P1 + P2 = Ps ⇒ P2 = Ps − P1
P1 = Pa − Rqq = 1
2( x
xm
+ 1)Ps − RqA˙y
Mÿ + B ˙y + Ky =A(P1 − P2)
=A(2P1 − Ps)
=A((
x
xm
+ 1)Ps − 2RqA˙y − Ps)
Mÿ + (B + 2RqA2
)˙y + Ky = APs
x
xm

Mÿ + B ˙y + Ky = A(P1 − P2)
P1 + P2 = Ps ⇒ P2 = Ps − P1
P1 = Pa − Rqq = 1
2( x
xm
+ 1)Ps − RqA˙y
Mÿ + B ˙y + Ky =A(P1 − P2)
=A(2P1 − Ps)
=A((
x
xm
+ 1)Ps − 2RqA˙y − Ps)
Mÿ + (B + 2RqA2
)˙y + Ky = APs
x
xm
Y (s)
X(s)
=
APs
xm
Ms2 + (B + 2RqA2)s + K

Hydraulic Integrator
If M = K = B = 0 then
Y (s)
X(s)
=
APs
2xmRg A2
1
s
[Ogata, 1997]

Hydraulic Integrator
If M = K = B = 0 then
Y (s)
X(s)
=
APs
2xmRg A2
1
s
Hydraulic integrator
[Ogata, 1997]

Hydraulic Proportional Controller

Hydraulic Proportional Controller
Y (s)
E(s)
=
bK
(a + b)s + aK
≃
b
a
[Ogata, 1997]

Hydraulic Damper

Hydraulic Damper
A(P1 − P2) = ky

Hydraulic Damper
A(P1 − P2) = ky
q = P1−P2
R

Hydraulic Damper
A(P1 − P2) = ky
q = P1−P2
R
qdt = A𝜌(dx − dy)

Hydraulic Damper
A(P1 − P2) = ky
q = P1−P2
R
qdt = A𝜌(dx − dy)
Y (s)
X(s)
=
1
1 + 1
Ts
[Ogata, 1997]

Hydraulic Proportional Integrator Controller

Y (s)
X(s) = K
s

Y (s)
X(s) = K
s
Z(s)
Y (s) = 1
1+ 1
Ts

Y (s)
X(s) = K
s
Z(s)
Y (s) = 1
1+ 1
Ts
Y (s)
E(s)
≃
b
a
(
1 +
1
Ts
)
[Ogata, 1997]

Hydraulic Proportional Derivative Controller

Y (s)
X(s) = K
s

Y (s)
X(s) = K
s
k(y − z) = A(P1 − P2)

Y (s)
X(s) = K
s
k(y − z) = A(P1 − P2)
Z(s)
Y (s) = 1
Ts+1

Y (s)
X(s) = K
s
k(y − z) = A(P1 − P2)
Z(s)
Y (s) = 1
Ts+1
Y (s)
E(s)
≃
b
a
(1 + Ts)
[Ogata, 1997]

Comparison
Electrical Hydraulic Pneumatic
Energy source Usually from outside
supplier
Electric motor or diesel
driven
Electric motor or diesel
driven
Energy storage Limited (batteries) Limited (accumulator) Good (reservoir)
Distribution system Excellent, with minimal
loss
Limited, basically a lo-
cal facility
Good, can be treated as
a plantwide service
Energy cost Lowest Medium Highest
Rotary actuators AC and DC motors.
Good control on DC
motors. AC motors
cheap
Low speed. Good con-
trol. Can be stalled.
Wide speed range. Ac-
curate speed control
diﬃcult
Linear actuators Short motion via
solenoid. Otherwise via
mechanical conversion
Cylinders. Very high
force
Cylinders. Medium
force
Points to note Danger from electric
shock
Leakage dangerous and
unsightly. Fire hazard
Noise
[Parr, 1999]

Analogy Summary
[Macia and Thaler, 2004]

Ljung, L. and Glad, T. (1994).
Modeling of Dynamic Systems.
Prentice Hall PTR, 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.

Industrial Control Systems - Hydraulic Systems

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Industrial Control Systems - Hydraulic Systems