Transcript Georgia Institute of Technology George W. Woodruff School

George W. Woodruff School of Mechanical Engineering
HUSCO
Electro-Hydraulic Poppet Valve
Project Review
Presented by:
PATRICK OPDENBOSCH
April 07, 2003
AGENDA
1.
2.
3.
4.
5.
6.
7.
Components
Opening Sequence
Related Work
Mathematical Modeling
Control Schemes
Future Work
Conclusions
1. COMPONENTS
Input
Pilot Spring
Pilot
Control Chamber
Feed Line
Solenoid Core
Main Spring
Main Poppet
Inlet
Outlet
2. OPENING SEQUENCE
2. OPENING SEQUENCE
2. OPENING SEQUENCE
3. RELATED WORK
Performance Limitations of a Class of Two-Stage
Electro-hydraulic Flow Valves1
• Done by:
Rong Zhang.
Dr. Andrew Alleyne.
Eko Prasetiawan.
Figure 3.1 Vickers EPV-16 Valvistor
(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.
• Valve Modeling:
.
States:
Output:
(3.1)
(3.2)
Figure 3.2 Electro-proportional flow valve
(3.3)
• Jacobian Linearization and Model Reduction :
Assumptions:
(3.4)
(3.5)
(3.6)
(3.7)
(3.8)
Figure 3.3 Simplified Second Order Model
Figure 3.4 Flow valve identification test setup
Figure 3.5 Time domain experimental validation
•
•
•
Figure 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:
uv
Q2
Qa
Qp
Q1
Qb
Pa
Dr
xm
Q1
Q2
Pb
xm
Pp
Pa
Q1  RM xm  Pa  Pb
Q2  Rs Dr  x m  Pa  Pp
(4.1)
xp
Pp
xm
Qp
Pb
Q p  R p x p  x m  Pp  Pb
(4.3)
(4.2)
• Compressibility:
am,1
xp
Q2
xm
xo
d  r
 r Q2  Q p 
dt
(4.4)
  r Q  Q 
r  r
2
p
(4.5)
  am,1 xo  xm   a p e  x p 
(4.6)
  a x  a x

m,1 m
p p
(4.7)
Qp
r 
r : Fluid density
V: Chamber volume
e : Equivalent length of pilot
inside control volume
b : Bulk modulus
Pp 
b
am,1 xo  xm   a p
r 
P
b p
(4.8)
e  x  Q
2
b
am,1 xo  xm 
 Qp  am,1 xm  a p x p 
p
small
small
Pp 
small
Q
2
 Qp 
(4.10)
(4.9)
• Second Order Systems:
Pilot Dynamics (from equilibrium state):
K e δuv
k pδxp
δx p
bp δx p
Pp a p
mpδxp  bpδx p  k pδx p  Keδuv  δPp a p
(4.11)
Main Poppet Dynamics (from equilibrium state):
kmδxm
Pp am,1
δxm
bmδxm
am,1 : Poppet’s Large area
am,s : Poppet’s Small area
Pa am,1  am,s 
Pb am,s
mmδxm  bmδxm  kmδxm  am,1 δPa  δPp   am,s δPb  δPa 
(4.12)
Letting:
 xm   xm  δxm 
 x    δx 
 m  0   m
 Pp    Pp   δPp 
     
 x p   x p   δx p 
 x p   0   δx p 
 
 
uv  uv  δuv
and
Pa  Pa  δPa
(4.13)
Pb  Pb  δPb
EHPV State Space Representation about Equilibrium Point
X2



  0 
a
a P  am ,s Pb  Pa 
k
b
 X 1  δx m  
 m X 1  m X 2  m ,1 X 3  m ,1 a
  
   δx  
mm
mm
mm
mm
  0 
X2   m  
b

Rs Dr  xm  X 1  Pa  Pa  Pp  X 3   R p x p  X 4  xm  X 1  Pp  X 3  Pb  Pb     0  δuv  D
 X 3   δPp   
 


      am ,1 x0  xm  X 1
  0 

δ
x
X
 4  p  
X5
  Ke 
 X   δxp  
k
b
a
 m 
p
p
p
 5  

X4 
X5 
X3

  p
m
m
m
p
p
p




Qb  Yout  RM  xm  X 1  Pa  Pa  Pb  Pb   R p x p  X 4  xm  X 1  Pp  X 3  Pb  Pb 
(4.14)
Reduced Order EHPV State Space Representation about
Equilibrium Point
From (4.10):
am,1 xo  xm Pp
b
 Q2  Qp 
(4.15)
0
Then, solving for X3 and substituting in (4.14):
X2


2
2
2
2

 am,1Pa  am,s Pb  Pa   0 
am,1  Rs Dr  xm  X 1  Pa  Pa   R p x p  X 4  xm  X 1  Pb  Pb 
bm
 X 1  δxm   km
  
 Pp  
2
2
   δx   m X 1  m X 2  m 
2
2
 0
m




R
D

x

X

R
x

X

x

X

m
m 
m
s
r
m
1
p p
4
m
1

X2   m    m
   0 δuv  D
X5
 X 4  δx p  
  Ke 
2
2
    
2
2


  








k
b
a
R
D

x

X
P


P

R
x

X

x

X
P


P

p
p
p  s
r
m
1
a
a
p p
4
m
1
b
b
 X 5  δxp 
 X4  X5  

P

  mp 

p
2
2
2
2
m
m
m




R
D

x

X

R
x

X

x

X

p
p
p 


s
r
m
1
p p
4
m
1

Qb  Yout  RM xm  X 1  Pa  Pa  Pb  Pb   R p x p  X 4  xm  X 1 
  Rs2 Dr  xm  X 1 2 Pa  Pa   R p2 x p  X 4  xm  X 1 2 Pb  Pb 




P


P
 b
b
2
2
2
2


Rs Dr  xm  X 1   R p x p  X 4  xm  X 1 



(4.16)
5. CONTROL SCHEMES
• Jacobian Linearization
X  f  X , u   X  AL X  BL u
y  h X , u 
u
BL
+
Int
 y  C L X  DL u
CL
+
AL
BL
• Input-output Linearization
X  f  X   g  X u
y  h X 
y r   V
X  F  X   G X V
y
• Jacobian Linearization:
Assumption: Incompressible fluid:
1
0
0
0 
 0
 0 
 δX 1  δxm   k m
am,1
bm
  δX 1   


0
0 
   δx  
δX   0 
δ
X
m
m
m
m
2
m
m
m

   
 2   0 
am,1
2
3
0  δX 3  
 0    0    1
 uv
      0


0
0
0
1  δX 4  0 
δX 4  δx p  
  Ke 
ap
kp
bp  
δX  δxp   0



0


δ
X
 5  
mp
mp
m p   5   m p 



R p x p  xm 

Qb   4 0
R p Pp  Pb  Pb 0 δX


2 Pp  Pb  Pb


(5.1)
(5.2)
1   Rs Pa  Pa  Pp
 R D  x 
s
r
m
 2  
 2 Pa  Pa  Pp

R p x p  xm  

2 Pp  Pb  Pb 
 3   R p Pp  Pb  Pb
 4  RM Pa  Pa  Pb  Pb  R p Pp  Pb  Pb
(5.3)
38.4
38.3
Output Flow [gpm]
38.2
38.1
38
37.9
37.8
37.7
37.6
37.5
0
1
2
3
4
5
Time [s]
6
7
8
9
Figure 5.1 Output flow for PWM input about nominal value.
10
Dist
F
R
Ki
Int
Plant
BL
Int
CL
Qb
AL
Integral Controller
L
Int
CL
-1
AL
-1
K
-1
Figure 5.2 Control diagram.
Observer
• Input-Output Linearization (Model Reduction):
Assumption: Pilot dynamics are fast and can be considered as the
Input to the system (i.e. xp=W)




X2
 X 1  δx m  

a m,1
a m,1Pa  a m, s Pb  Pa 
km
bm
  
 


X1 
X2 
X3 
 X 2   δxm   

mm
mm
mm
mm
 X 3  δPp  

 
  
b
Rs Dr  x m  X 1  Pa  Pa  Pp  X 3   R p x p  x m  X 1  Pp  X 3  Pb  Pb  
 a m,1 x0  x m  X 1 






0


W

0
  bR P  X  P  P  
p
p
3
b
b




a m,1  x 0  x m  X 1 
Qb  Yout  RM x m  X 1  Pa  Pa  Pb  Pb   R p x p  W  x m  X 1  Pp  X 3  Pb  Pb 

(5.4)
(5.5)
V  RM xm  X 1  Pa  Pa  Pb  Pb 
Rp
P
p
 X 3  Pb  Pb 
 xm  X 1  x p  W
Qb  V
Equation 5.7 gives a direct mapping between fictitious input V
and output flow.
(5.6)
(5.7)
6. FUTURE WORK
• Complete control scheme for jacobian linearized system.
• Extend input-ouput linearization theory to full order system.
• Perform system parameter identification (hardware)
• Compare simulation results to experimental results.
• 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