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