topic #15 · 2017. 3. 16. · d.n. manik 25 2 2 11 12 1 b s s w w ww ªº§· «»¨¸ ¬¼©¹ 2 1...
TRANSCRIPT
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ME 779 Control Systems
Hydraulic Controllers
Topic #15
Reference textbook:
Control Systems, Dhanesh N. Manik,Cengage Publishing, 2012
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Control Systems: Hydraulic Controllers
Learning Objectives
• Dashpot- derivative action- integral action
• Proportional and integral controllers• Proportional and derivative controllers• Dashpots connected in series• Proportional, integral and derivative controllers
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DASHPOT
1 2P Pq
R
q: flow rate
P1, P2 pressures
R: resistance
Control Systems: Hydraulic Controllers
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DASHPOT: derivative action
1 2( )F A P P
1 2( )A P P kz
dy dz q
dt dt A
( )qdt A dy dz
Control Systems: Hydraulic Controllers
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DASHPOT: derivative action
2
dy dz kz
dt dt RA
2
( )
( )
Z s s
kY ss
RA
2RA
k
( )
( ) 1
Z s
sY s s
The output has to be integrated to be compared with the input and hence the derivative action of the dashpot (you can only compare apples with apples at the summing point)
Control Systems: Hydraulic Controllers
s
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DASHPOT- integral action
1 2( ) ( )k y z A P P
qdt A dz
1 2P Pq
R
Control Systems: Hydraulic Controllers
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DASHPOT- integral action
( ) 1
( ) 1
Z s
Y s s
2RA
k
The output has to be differentiated to be comparedwith the input and hence the integral action of the dashpot (you can only compare apples with applesat the summing point)
Control Systems: Hydraulic Controllers
s
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Hydraulic proportional plus
integral controller
Control Systems: Hydraulic Controllers
Derivative action in the feedback loop
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Hydraulic proportional plusintegral controller
Control Systems: Hydraulic Controllers
1
s
s
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( ) ( ) ( )
( )1 1
( ) ( 1) ( )( 1)
b K b K
Y s a b s a b s
Ka s KaX s
a b s s a b s
Control Systems: Hydraulic Controllers
Hydraulic proportional plusintegral controller
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( ) ( 1) 11
( )
Y s b s b
X s a s a s
Control Systems: Hydraulic Controllers
Hydraulic proportional plusintegral controller
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Hydraulic proportional plus derivative controller
Control Systems: Hydraulic Controllers
Integral action in the feedback loop
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Control Systems: Hydraulic Controllers
Hydraulic proportional plus derivative controller
1
1s
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( ) ( )
( )1
( ) ( 1)
b K
Y s a b s
KaX s
a b s s
( )
1( )
Y s bs
X s a
Control Systems: Hydraulic Controllers
Hydraulic proportional plus derivative controller
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Hydraulic proportional-integral-derivative controller
Control Systems: Hydraulic Controllers
Derivative Integral
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Dashpots connected in series
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
Derivative Integral
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1 1 2( )k z A P P
1 21
1
P Pq
R
1 1 1k z AR q2 1 2 3 4( ) ( ) ( )k y u A P P A P P
1 ( )q dt A du dz
1
du dzq A
dt dt
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
Dashpots connected in series
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3 42
2
P Pq
R
1qdu dz
dt A dt
1
2
1
k zdu dz
dt R A dt
1
du z dz
dt dt
2q dt A du
2
duq A
dt
2
11
1
R A
k
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controllerDashpots connected in series
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3 4 3 42
2
2 2
( )P P A P Pqdu
dt A R A R A
3 4
2 2
( )A P Pdu
dt k
2 1 2 2( )du
k y u k z kdt
2
22
2
R A
k
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
Dashpots connected in series
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2 2 1 2 2
duk y k u k z k
dt
2 2 2 2 1( ) ( ) ( )k Y s U s k k s k Z s
1
( ) 1( )
Z sU s s
s
1
1
1( ) ( )
sU s Z s
s
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
Dashpots connected in series
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12 2 2 1
1
1( ) 1 ( )
sk Y s k s k Z s
s
1
2 11 2 1 2 1
2
( )
( )( ) 1
sZ s
Y s ks s s
k
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
Dashpots connected in series
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1 2
2 1
k
k
1
2
1 2 1 2
( )
( ) ( 2 ) 1
sZ s
Y s s s
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
Dashpots connected in series
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Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
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1
2
1 2 1 2
( ) ( )
( )1
( ) ( 2 ) 1
b K
Y s a b s
sKaX s
a b s s s
1
2
1 2 1 2
1( ) ( 2 ) 1
sKa
a b s s s
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
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D.N. Manik 25
22
1 1
2( ) 11
( )
Y s bs
X s a s
2
1
1
2
21
1
p
I
D
bK
a
bK
a
bK
a
( )
( )
Ip D
KY sK K s
X s s
Control Systems: Hydraulic Controllers
Hydraulic proportional-integral-derivative controller
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Control Systems: Hydraulic Controllers
Conclusion
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