Industrial Control Systems - Hydraulic Systems

Industrial Control

Behzad Samadi

Department of Electrical EngineeringAmirkabir University of Technology

Winter 2010Tehran, Iran

Behzad Samadi (Amirkabir University) Industrial Control 1 / 17

Hydraulic Systems

Electrical Analogy

Type of System Electrical HydraulicT-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 Systems

Electrical Analogy

Type of System Electrical HydraulicT-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

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 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.



Hydraulic Capacitor

p =mg

A=

�g

AV =

�g

A

∫ t

0q(�)d�

p =pressure at the bottom of the tank

V =volume of the fluid in tank

A =cross section area of the tank

� =density of the fluid

Hydraulic Capacitor

Cf = A�g



Hydraulic Capacitor

p =mg

A=

�g

AV =

�g

A

∫ t

0q(�)d�





Hydraulic Capacitor

Cf = A�g



Hydraulic Capacitor

p =mg

A=

�g

AV =

�g

A

∫ t

0q(�)d�





Hydraulic Capacitor

Cf = A�g



Hydraulic Inductor

F =ma = (�lA)dv

dt

p =F

A= �l

dv

dtq =Av

⇒ p =�l

A

dq

dt= Lf

dq

dt

Hydraulic Inductor

Lf = � lA



Hydraulic Inductor

F =ma = (�lA)dv

dt

p =F

A= �l

dv

dtq =Av

⇒ p =�l

A

dq

dt= Lf

dq

dt

Hydraulic Inductor

Lf = � lA



Hydraulic Inductor

F =ma = (�lA)dv

dt

p =F

A= �l

dv

dtq =Av

⇒ p =�l

A

dq

dt= Lf

dq

dt

Hydraulic Inductor

Lf = � lA



Hydraulic Inductor

F =ma = (�lA)dv

dt

p =F

A= �l

dv

dtq =Av

⇒ p =�l

A

dq

dt= Lf

dq

dt

Hydraulic Inductor

Lf = � lA



Hydraulic Junction

∑i Qi = 0 (KCL)

p4 = p1 + p2 + p3 (KVL)



Hydraulic Junction

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



Hydraulic Transformer

p1Q1 =p2Q2

p1 =�p2

Q1 =1

�Q2

� =A2

A1



Hydraulic Transformer

p1Q1 =p2Q2

p1 =�p2

Q1 =1

�Q2

� =A2

A1



Hydraulic Servomechanism



xm: maximum displacement

x = xm ⇒{

Pa = Ps

Pb = P0 = 0

x = −xm ⇒{

Pa = P0 = 0Pb = Ps

Pa = 12 ( x

xm+ 1)Ps

Pb = 12 (− x

xm+ 1)Ps

Pa − P1 = Rqq

Pb − P2 = Rqq

q = Ay




x = xm ⇒{

Pa = Ps

Pb = P0 = 0

x = −xm ⇒{

Pa = P0 = 0Pb = Ps

Pa = 12 ( x

xm+ 1)Ps

Pb = 12 (− x

xm+ 1)Ps

Pa − P1 = Rqq

Pb − P2 = Rqq

q = Ay




x = xm ⇒{

Pa = Ps

Pb = P0 = 0

x = −xm ⇒{

Pa = P0 = 0Pb = Ps

Pa = 12 ( x

xm+ 1)Ps

Pb = 12 (− x

xm+ 1)Ps

Pa − P1 = Rqq

Pb − P2 = Rqq

q = Ay




x = xm ⇒{

Pa = Ps

Pb = P0 = 0

x = −xm ⇒{

Pa = P0 = 0Pb = Ps

Pa = 12 ( x

xm+ 1)Ps

Pb = 12 (− x

xm+ 1)Ps

Pa − P1 = Rqq

Pb − P2 = Rqq

q = Ay




x = xm ⇒{

Pa = Ps

Pb = P0 = 0

x = −xm ⇒{

Pa = P0 = 0Pb = Ps

Pa = 12 ( x

xm+ 1)Ps

Pb = 12 (− x

xm+ 1)Ps

Pa − P1 = Rqq

Pb − P2 = Rqq

q = Ay




x = xm ⇒{

Pa = Ps

Pb = P0 = 0

x = −xm ⇒{

Pa = P0 = 0Pb = Ps

Pa = 12 ( x

xm+ 1)Ps

Pb = 12 (− x

xm+ 1)Ps

Pa − P1 = Rqq

Pb − P2 = Rqq

q = Ay




x = xm ⇒{

Pa = Ps

Pb = P0 = 0

x = −xm ⇒{

Pa = P0 = 0Pb = Ps

Pa = 12 ( x

xm+ 1)Ps

Pb = 12 (− x

xm+ 1)Ps

Pa − P1 = Rqq

Pb − P2 = Rqq

q = Ay




x = xm ⇒{

Pa = Ps

Pb = P0 = 0

x = −xm ⇒{

Pa = P0 = 0Pb = Ps

Pa = 12 ( x

xm+ 1)Ps

Pb = 12 (− x

xm+ 1)Ps

Pa − P1 = Rqq

Pb − P2 = Rqq

q = Ay



My + By + Ky = A(P1 − P2)

P1 + P2 = Ps ⇒ P2 = Ps − P1

P1 = Pa − Rqq = 12 ( x

xm+ 1)Ps − RqAy

My + By + Ky =A(P1 − P2)

=A(2P1 − Ps)

=A((x

xm+ 1)Ps − 2RqAy − Ps)

My + (B + 2RqA2)y + Ky = APs

x

xm

Y (s)

X (s)=

APsxm

Ms2 + (B + 2RqA2)s + K



My + By + Ky = A(P1 − P2)

P1 + P2 = Ps ⇒ P2 = Ps − P1

P1 = Pa − Rqq = 12 ( x

xm+ 1)Ps − RqAy

My + By + Ky =A(P1 − P2)

=A(2P1 − Ps)

=A((x



x

xm

Y (s)

X (s)=

APsxm

Ms2 + (B + 2RqA2)s + K



My + By + Ky = A(P1 − P2)

P1 + P2 = Ps ⇒ P2 = Ps − P1

P1 = Pa − Rqq = 12 ( x

xm+ 1)Ps − RqAy

My + By + Ky =A(P1 − P2)

=A(2P1 − Ps)

=A((x



x

xm

Y (s)

X (s)=

APsxm

Ms2 + (B + 2RqA2)s + K



My + By + Ky = A(P1 − P2)

P1 + P2 = Ps ⇒ P2 = Ps − P1

P1 = Pa − Rqq = 12 ( x

xm+ 1)Ps − RqAy

My + By + Ky =A(P1 − P2)

=A(2P1 − Ps)

=A((x



x

xm

Y (s)

X (s)=

APsxm

Ms2 + (B + 2RqA2)s + K



My + By + Ky = A(P1 − P2)

P1 + P2 = Ps ⇒ P2 = Ps − P1

P1 = Pa − Rqq = 12 ( x

xm+ 1)Ps − RqAy

My + By + Ky =A(P1 − P2)

=A(2P1 − Ps)

=A((x



x

xm

Y (s)

X (s)=

APsxm

Ms2 + (B + 2RqA2)s + K



My + By + Ky = A(P1 − P2)

P1 + P2 = Ps ⇒ P2 = Ps − P1

P1 = Pa − Rqq = 12 ( x

xm+ 1)Ps − RqAy

My + By + Ky =A(P1 − P2)

=A(2P1 − Ps)

=A((x



x

xm

Y (s)

X (s)=

APsxm

Ms2 + (B + 2RqA2)s + K



My + By + Ky = A(P1 − P2)

P1 + P2 = Ps ⇒ P2 = Ps − P1

P1 = Pa − Rqq = 12 ( x

xm+ 1)Ps − RqAy

My + By + Ky =A(P1 − P2)

=A(2P1 − Ps)

=A((x



x

xm

Y (s)

X (s)=

APsxm

Ms2 + (B + 2RqA2)s + K


Hydraulic Integrator

If M = K = B = 0 then

Y (s)

X (s)=

APs

2xmRgA2

1

s

Hydraulic integrator

[Ogata, 1997]Behzad Samadi (Amirkabir University) Industrial Control 11 / 17

Hydraulic Integrator

If M = K = B = 0 then

Y (s)

X (s)=

APs

2xmRgA2

1

s

Hydraulic integrator

[Ogata, 1997]Behzad Samadi (Amirkabir University) Industrial Control 11 / 17

Hydraulic Proportional Controller

Y (s)

E (s)=

bK

(a + b)s + aK≃ b

a

[Ogata, 1997]


Hydraulic Proportional Controller

Y (s)

E (s)=

bK

(a + b)s + aK≃ b

a

[Ogata, 1997]


Hydraulic Damper

A(P1 − P2) = ky

q = P1−P2R

qdt = A�(dx − dy)

Y (s)

X (s)=

1

1 + 1Ts

[Ogata, 1997]


Hydraulic Damper

A(P1 − P2) = ky

q = P1−P2R


Y (s)

X (s)=

1

1 + 1Ts

[Ogata, 1997]


Hydraulic Damper

A(P1 − P2) = ky

q = P1−P2R


Y (s)

X (s)=

1

1 + 1Ts

[Ogata, 1997]


Hydraulic Damper

A(P1 − P2) = ky

q = P1−P2R


Y (s)

X (s)=

1

1 + 1Ts

[Ogata, 1997]


Hydraulic Damper

A(P1 − P2) = ky

q = P1−P2R


Y (s)

X (s)=

1

1 + 1Ts

[Ogata, 1997]


Hydraulic Damper

A(P1 − P2) = ky

q = P1−P2R


Y (s)

X (s)=

1

1 + 1Ts

[Ogata, 1997]


Hydraulic Proportional Integrator Controller

Y (s)X (s) = K

s

Z(s)Y (s) = 1

1+ 1Ts

Y (s)

E (s)≃ b

a

(1 +

1

Ts

)[Ogata, 1997]



Y (s)X (s) = K

s

Z(s)Y (s) = 1

1+ 1Ts Y (s)

E (s)≃ b

a

(1 +

1

Ts

)[Ogata, 1997]



Y (s)X (s) = K

s

Z(s)Y (s) = 1

1+ 1Ts

Y (s)

E (s)≃ b

a

(1 +

1

Ts

)[Ogata, 1997]



Y (s)X (s) = K

s

Z(s)Y (s) = 1

1+ 1Ts

Y (s)

E (s)≃ b

a

(1 +

1

Ts

)[Ogata, 1997]



Y (s)X (s) = K

s

Z(s)Y (s) = 1

1+ 1Ts Y (s)

E (s)≃ b

a

(1 +

1

Ts

)[Ogata, 1997]


Hydraulic Proportional Derivative Controller

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]



Y (s)X (s) = K

s

k(y − z) = A(P1 − P2)Z(s)Y (s) = 1

Ts+1Y (s)

E (s)≃ b

a(1 + Ts)

[Ogata, 1997]



Y (s)X (s) = K

s

k(y − z) = A(P1 − P2)

Z(s)Y (s) = 1

Ts+1Y (s)

E (s)≃ b

a(1 + Ts)

[Ogata, 1997]



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]



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]



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]



Y (s)X (s) = K

s

k(y − z) = A(P1 − P2)Z(s)Y (s) = 1

Ts+1Y (s)

E (s)≃ b

a(1 + Ts)

[Ogata, 1997]


Comparison

Electrical Hydraulic PneumaticEnergy source Usually from outside

supplierElectric motor or dieseldriven

Electric motor or dieseldriven

Energy storage Limited (batteries) Limited (accumulator) Good (reservoir)

Distribution system Excellent, with minimalloss

Limited, basically a lo-cal facility

Good, can be treated asa plantwide service

Energy cost Lowest Medium Highest

Rotary actuators AC and DC motors.Good control on DCmotors. AC motorscheap

Low speed. Good con-trol. Can be stalled.

Wide speed range. Ac-curate speed controldifficult

Linear actuators Short motion viasolenoid. Otherwise viamechanical conversion

Cylinders. Very highforce

Cylinders. Mediumforce

Points to note Danger from electricshock

Leakage dangerous andunsightly. 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.


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Industrial Control Systems - Hydraulic Systems

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