April 07, 2003
Presented by:
PATRICK OPDENBOSCH
HUSCO Electro-Hydraulic Poppet Valve
Project Review
George W. Woodruff School of Mechanical Engineering
AGENDA
1. Components2. Opening Sequence3. Related Work4. Mathematical Modeling5. Control Schemes6. Future Work7. Conclusions
Outlet
Input
Main Poppet
Main Spring
Solenoid CorePilot
Inlet
Control Chamber
Pilot Spring
1. COMPONENTS
Feed Line
2. OPENING SEQUENCE
2. OPENING SEQUENCE
2. OPENING SEQUENCE
Performance Limitations of a Class of Two-Stage Electro-hydraulic Flow Valves1
• Done by:
Rong Zhang.
Dr. Andrew Alleyne.
Eko Prasetiawan.
3. RELATED WORK
(1) Zhang, R.,Alleyne, A., and Prasetiawan, E., “Performance Limitations of a Class of Two-Stage
Electro-hydraulic Flow Valves”, International Journal of Fluid Power, April 2002.
Figure 3.1 Vickers EPV-16 Valvistor
.
• Valve Modeling:
States:Output:
Figure 3.2 Electro-proportional flow valve
(3.1)
(3.2)
(3.3)
• Jacobian Linearization and Model Reduction :
(3.4)
(3.5)
(3.6)
(3.7)
Assumptions:
Figure 3.4 Flow valve identification test setup
(3.8)
Figure 3.3 Simplified Second Order Model
Figure 3.5 Time domain experimental validationFigure 3.6 Root-locus of a Valvistor-controlled system
Main Results:• Pilot flow introduces open-loop zeros that limit the closed-loop bandwidth.• Pilot flow can be re-routed to tank trading performance by efficiency.• Open-loop zeros can be moved leftwards by altering valve parameters.
4. MATHEMATICAL MODELING• Flow Distribution:
Qa
Q2
Qb
Q1
Qp
uv
pamrs PPxDRQ 2
xm
Pa
Pp
Dr
Q2
(4.2) bamM PPxRQ 1
xm
Pb
Q1
(4.1)
bpmppp PPxxRQ
Qp
Pp
Pb
xm
xp
(4.3)
Pa
: Fluid densityV: Chamber volume: Equivalent length of pilot inside control volume: Bulk modulus
Q2
Qp
xmxo
am,1 xp
• Compressibility: pQQdt
d
2
ppmom xaxxa 1,
ppmm xaxa 1,
pQQ 2
pP
pmom
p QQxxa
P
21,
ppmmpppmom
p xaxaQQxaxxa
P
1,21,
small
small
small
(4.4)
(4.5)
(4.6)
(4.7)
(4.9)
(4.10)
(4.8)
• Second Order Systems:
Pilot Dynamics (from equilibrium state):
ve uK δ
pp xk δ
pp xb δ
ppaP
pxδ
ppvepppppp aPuKxkxbxm δδδδδ (4.11)
Main Poppet Dynamics (from equilibrium state):
absmpammmmmmm PPaPPaxkxbxm δδδδδδδ ,1, (4.12)
mxδ
mm xb δ
1,mpaP
smma aaP ,1,
smbaP ,
am,1 : Poppet’s Large areaam,s : Poppet’s Small area
mm xk δ
bbpmppbbaamMoutb
v
p
e
p
p
p
p
p
p
bbpmpppaamrsmm
m
absmam
m
m
m
m
m
m
p
p
p
m
m
PPXPXxXxRPPPPXxRYQ
Du
m
K
Xm
aX
m
bX
m
kX
PPXPXxXxRXPPPXxDRXxxa
m
PPaPaX
m
aX
m
bX
m
kX
x
x
P
x
x
X
X
X
X
X
3141
354
5
31431101,
,1,3
1,21
2
5
4
3
2
1
δ0
0
0
0
δ
δ
δ
δ
δ
p
p
p
m
m
p
p
m
p
p
p
m
m
x
x
P
x
x
x
P
x
x
x
P
x
x
δ
δ
δ
δ
δ
0
0
bbb
aaa
vvv
PPP
PPP
uuu
δ
δ
δ
(4.14)
(4.13)Letting: and
EHPV State Space Representation about Equilibrium Point
bb
mppmrs
bbmppaamrsmppbbaamMoutb
v
p
e
p
mppmrs
bbmppaamrs
p
p
p
p
p
p
m
absmamp
mppmrs
bbmppaamrs
m
m
m
m
m
m
p
p
m
m
PPXxXxRXxDR
PPXxXxRPPXxDRXxXxRPPPPXxRYQ
Du
m
K
PXxXxRXxDR
PPXxXxRPPXxDR
m
aX
m
bX
m
k
X
m
PPaPaP
XxXxRXxDR
PPXxXxRPPXxDR
m
aX
m
bX
m
k
X
x
x
x
x
X
X
X
X
214
221
2
214
221
2
141
214
221
2
214
221
2
54
5
,1,2
1422
12
214
221
21,
21
2
5
4
2
1
δ0
0
0
δ
δ
δ
δ
Reduced Order EHPV State Space Representation about Equilibrium Point
(4.16)
ppmom QQ
Pxxa
2
1,
(4.15)
From (4.10):
0Then, solving for X3 and substituting in (4.14):
5. CONTROL SCHEMES
• Jacobian Linearization
• Input-output Linearization
+BL CL
AL
Int
uDXCyuXhy
uBXAXuXfX
LL
LL
,
,
u y+
BL
Xhy
uXgXfX
Vy r
VXGXFX
• Jacobian Linearization:
bbppbbaaM
bbpp
bbp
mpp
paa
mrs
paas
PPPRPPPPR
PPPR
PPP
xxR
PPP
xDR
PPPR
4
3
2
1
22
XPPPR
PPP
xxRQ
u
m
KX
X
X
X
X
m
b
m
k
m
a
am
a
m
b
m
k
x
x
x
x
X
X
X
X
bbpp
bbp
mppb
v
p
e
p
p
p
p
p
p
m
m
m
m
m
m
m
p
p
m
m
δ02
0
0
0
0
0
δ
δ
δ
δ
δ
00
10000
0
00
00010
δ
δ
0
δ
δ
δ
δ
0
δ
δ
4
5
4
3
2
1
321,1
1,
5
4
2
1
(5.1)
(5.2)
(5.3)
Assumption: Incompressible fluid:
0 1 2 3 4 5 6 7 8 9 1037.5
37.6
37.7
37.8
37.9
38
38.1
38.2
38.3
38.4
Time [s]
Out
put
Flo
w [
gpm
]
Figure 5.1 Output flow for PWM input about nominal value.
Figure 5.2 Control diagram.
-1
-1
-1 K
AL
CL
L
AL
CLBL
F
KiR QbInt Int
Int
Dist
Integral Controller
Plant
Observer
• Input-Output Linearization (Model Reduction):
bbpmpppaamrsmm
m
absmam
m
m
m
m
m
m
p
m
m
PPXPXxxRXPPPXxDRXxxa
m
PPaPaX
m
aX
m
bX
m
kX
P
x
x
X
X
X
3131101,
,1,3
1,21
2
3
2
1
δ
δ
δ
W
Xxxa
PPXPR
mm
bbpp
101,
3
0
0
bbpmppbbaamMoutb PPXPXxWxRPPPPXxRYQ 311
(5.4)
(5.5)
Assumption: Pilot dynamics are fast and can be considered as the Input to the system (i.e. xp=W)
WxXx
PPXPR
PPPPXxRVpm
bbpp
bbaamM
1
3
1
VQb
(5.6)
(5.7)
Equation 5.7 gives a direct mapping between fictitious input V and output flow.
6. FUTURE WORK
• Complete control scheme for jacobian linearized system.
• Extend input-ouput linearization theory to full order system.
• Compare simulation results to experimental results.
• Perform system parameter identification (hardware)
• Determine control solutions to EHPV operational problems
7. CONCLUSIONS
• Review of valve components and opening sequence
• Determination of valve limitations:• Pilot flow introduces open-loop zeros• Re-route flow to tank (efficiency/performance)• Alter valve parameters
• Evaluation of 5th order EHPV mathematical model
• Control alternatives:• Jacobian linearized system• Input-Output linearization