control of electro-hydraulic poppet valves (ehpv)

October 27, 2004

Control of Electro-Hydraulic Poppet Valves (EHPV)

PATRICK OPDENBOSCHGraduate Research AssistantManufacturing Research Center

Room 259

Ph. (404) 894 3256

[email protected]

Georgia Institute of TechnologyGeorge W. Woodruff School of Mechanical Engineering

Sponsored by: HUSCO International and the Fluid Power Motion Control Center

October 27, 2004GEORGIA TECH

G.W.W. School of Mechanical Engineering

AGENDA

INTRODUCTION.

NLPN.

CURRENT TO Kv MAP.

CONTROL APPROACH.

FUTURE WORK.

CONCLUSIONS.



INTRODUCTION



APPLICATIONS:

Pressure & Flow Control

Construction machinery Robotics/manufacturing Automotive industry (active suspension)

EHPV FEATURES: Proportional flow area control Bidirectional Capability “Zero” leakage Low Hysteresis 12 Volt,1.5 Amp max (per solenoid)

ADVANTAGES OVER SPOOL VALVES: EHPV’s offer excellent sealing capabilities Less faulting High resistance to contamination High flow to poppet displacement ratios, Low cost and low maintenance, Applicable to a variety of control functions.

PressureCompensating

Spring

Armature

Coil

ModulatingSpring

ArmatureBias

Spring

Pilot Seat

Sensing Piston

Main Poppet

Pilot

Side Port

Nose Port

US PATENT # 6,745,992 & 6,328,275



EMPLOYMENT OF POPPET VALVES IN ACTUATOR MOTION CONTROL

US PATENT # 5,878,647

METERING MODES:Standard metering extendLow side regeneration extend Low side regeneration retract High side regeneration Standard float Wheatstone bridge assembly view

4 EHPV on wheatstone bridge arrangement

AA

AB

PA

PB

KvA

KvB

PS

PR

QA

QB

EQvEQB PKQA

2vB

32va

vBvAvEQ

KRK

KKK

RBAsEQ PPPPRP BA AAR

[[33]]

[[55bb]]

[[55aa]]

[[11]] [[11]]

[[22]] [[33]] [[44]]

[[44]]

[[55]]55]]

[[55cc]] [[11]] RReesseerrvvooiirr TTaannkk [[22]] PPuummpp [[33]] EEHHPPVV™™ ssuuppppllyy [[44]] EEHHPPVV rreettuurrnn [[55]] AAccttuuaattoorr [[55aa]] LLoowweerr ccaavviittyy [[55bb]] UUppppeerr ccaavviittyy [[55cc]] PPiissttoonn [[66]] CCoonnttrroolllleerr HHyyddrraauulliicc OOiill SSuuppppllyy HHyyddrraauulliicc OOiill RReettuurrnn PPWWMM SSiiggnnaall PPrreessssuurree SSiiggnnaall

[[66]]



Hierarchical control: System controller, pressure controller, function controller

Calculate desired speed,

Calculate equivalent KvEQ

Determine Individual Kv

US PATENT # 6,732,512 & 6,718,759 Calculate desired flow, QA B

Read port pressures, Ps PR PA PB

KvB

KvA

Determine input current to EHPV isol=f(Kv,P,T)

HIERARCHICAL CONTROL



0 5 10 15 20 25 300

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000Unit3 - Dist. Casting: Kv Correction Results

Delta Pressure [MPa]

Kv

[lph/

sqrt

(MP

a)]

Kv uncorrectedKv correctedKv Ideal

INPUT-OUTPUT MAP: Currently obtained through extensive offline

calibration Different valves (sizes) require different maps

(specifically tailored) Offline map might not accurately reflect valve

behavior after considerable continuous operation

PROBLEMS: EHPV transients might not be as

desired Open loop sensitivity to disturbances Flow forces on the main poppet and

the pilot harm the hydro-mechanical compensation especially at high P

Effects are different between forward and reverse flow

Flow conductance coefficient Kv as a function of input current and pressure differential

LOCAL (LOWER LEVEL) CONTROL



INPUT-OUTPUT MAP PROPOSED SOLUTIONS: Online learning of the input-output map through

suitable training criterion. Compatibility of adaptive look-up table with existing

industrial trends Improve mapping that more accurately reflects valve

behavior after considerable continuous operation Development of robust observer for the online

estimation of the KV.

OBJECTIVES: Implementation of feedback control with the aid of

soft sensor technology and online training algorithms Improve transient behavior Make the valve more intelligent and self contained

IMPROVED LOCAL CONTROL



NLPN



1

N

2

x 1

x 2

x n

y 1

y m

W ij v i

NODAL LINK PERCEPTRON NETWORK (NLPN)

TN

iii Wxwxfy

1

Basis functions are chosen so that1=1

The set B={i} is a linearly independent set i.e. if

N

iii xwxf

1

The idea is to choose wi and i so that

More details found at: Sadegh, N. (1998) “A multilayer nodal link perceptron network with least squares training algorithm,” Int. J. Control, Vol.70, No. 3, 385-404.

MAIN FEATURE Approximates nonlinear functions using a number of local adjustable functions.

NLPN structure

The NLPN is a three-layer perceptron network whose input is related to the output by:

N

iiiw

1

0 then 0iw for i =1 … N

For some > 0, it is true that

j

iij

1

2sup



DELTA RULE

kkTk

Tkkk

kkP

ePWW

1

1kk

Tk

kTkkk

kkP

PPPP

1

1kkk Wye

TRAINING Once a basis function structure is chosen, train the network to learn the “weights”.

Tkkkkk ecWW 1 kkkk Wye

LEAST SQUARES

HOW IT WORKS (1D EX) Triangular basis function structure is chosen Weights are computed using least squares

32 xxfFunction to be approximated:x

1 2 3

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.5

3

3.5

4

4.5

5

5.5

6

6.5

7

x

f(x)



COMMON BASIS FUNCTIONS

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Gaussian Basis Function

x

f(x)

sigma=0.1sigma=0.2sigma=0.5sigma=5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Hyperbolic Basis Function

x

f(x)

k=0.1k=1k=2k=5k=10

2

2

2

21

2

2

2

21

2

2

2exp

else0

if2

exp2

exp1

if2

exp2

exp1

Bx

CxBBCBC

BxABABA

xf

else0

if1

if

CxBBCBx

BxAABAx

xf

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Triagular Basis Function

x

f(x)

A B C A B CA B C

else0

iftanhtanh

iftanhtanh

CxBBCxC

BxAABAx

xf

TriangularGaussian Hyperbolic

For multidimensional input space:

n

jj

ij xj

1

xi

23

211

1

2

13,1 xxx

jj

ij

j

xFor example,

So that at most 2n components of are nonzero.



02.0,,2

2500

12121

iii xxwxxf

0

12

34

5

0

1

2

3

4

5-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

X1

X2

Y

01

23

4

5

0

1

2

3

4

5-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

X1

X2

Y

22211121 3.05.2exp6.0sin3.05.2expsin, xxxxxxxxfy

Actual Map NLPN approximation Approximation Error

COMMON APPLICATIONS

Offline curve fitting

Filtering

0 1 2 3 4 5 6 7 8 9 10-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time [sec]

Sig

nal

DataNLPN

System identification

Selmic, R. R., Lewis, F. L., (2000) “Identification of Nonlinear Systems Using RBF Neural Networks: Application to Multimodel Failure Detection,” Proceedings of the IEEE Conference on Decision and Control, v 4, 2001, p 3128-3133

Sanner, R. M., J. E. Slotine, (1991) “Stable Adaptive Control and Recursive Identification Using Radial Gaussian Networks,” Proceedings of the IEEE Conference on Decision and Control, v 3, 1991, p 2116-2123.

Sadegh, N., (1993), “A Perceptron Network for Functional Identification and Control of Nonlinear Systems,” IEEE trans. N. Networks, Vol. 4, No. 6, 982-988



CURRENT TO Kv MAP



APPLICATION TO CONTROL OF EHPV

Initially proposed control scheme:

P

Kv_DES

Adaptive Look-up table

PID _

+

Kv_EST Soft Sensor

xmeas

Kv_ACT +

+

isol

NLPN

VKPGi , EHPV

Feedback adaptive control scheme

Testing of NLPN map learning:

CITGO Anti-Wear Hydraulic Oil 32

Viscosity and Density Data(SI Units)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50

Temperature [C]

Vis

cosi

ty

840

850

860

870

880

890

900

0 10 20 30 40 50

Den

sity

[1000*m2/s] [N•s/m2] [kg/m3]

TBAT exp

DTCT

CITGO A/W Hydraulic Oil 32:

Viscosity:

Density:

A = 5.68x10-9 [Ns/m2]

B = 4827.6 [1/K]

C = 1056.1 [kg/m3]

B = -0.647 [kg/m3K]

Oil Properties:



At constant temperature

At constant opening

0

12

34

5

0

0.5

1

1.50

20

40

60

80

100

120

dP [MPa]

Constant Temperature (T = 30 C)

Input [A]

Kv

[(LP

M)/

sqrt

(MP

a)]

0

12

34

5

5

10

15

20

250

10

20

30

40

50

60

70

80

dP [MPa]

Constant Input (i = 1.2 A)

Temperature [C]

Kv

[(LP

M)/

sqrt

(MP

a)]

SIMULATED STEADY STATE EHPV Kv

TPifK solV ,,

Forward flow

P

QKV



020

4060

80100

0

1

2

3

4

50

0.2

0.4

0.6

0.8

1

1.2

1.4

Kv [(LPM)/sqrt(MPa)]dP [MPa]

Inpu

t [A

]

T = 20 C

020

4060

80100

0

1

2

3

4

50

0.2

0.4

0.6

0.8

1

1.2

1.4


Inpu

t [A

]

T = 30 C

020

4060

80100

0

1

2

3

4

50

0.2

0.4

0.6

0.8

1

1.2

1.4


Inpu

t [A

]

T = 40 C

SIMULATED INVERSE MAP ESTIMATION

TPKgi Vsol ,,

Forward flow



Hydraulic circuit employed at the HIL

Hardware-In-the Loop (HIL) Simulator

EHPV mounted on the HIL. Quick connections for forward and reverse flow

EXPERIMENTAL ESTIMATION

Steady state data was obtained from the Hydraulic circuit employed at the Hardware-In-the-Loop (HIL) Simulator



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

10

20

30

40

50

60

70

80

90

100

Pressure Differential [MPa]

Kv

[LP

M/s

qrt(

MP

a)]

EHPV Forward Flow Conductance Coefficient Measurement

1.5044 1.3565 1.2074 1.0584 1.4308 1.2818 1.13260.98395

0 0.2 0.4 0.6 0.8 1 1.2 1.40

20

40

60

80

100

120


Kv

[LP

M/s

qrt(

MP

a)]

EHPV Reverse Flow Conductance Coefficient Measurement

1.5071.35871.20911.05941.43331.2838 1.1340.9845

EXPERIMENTAL MEASUREMENT OF STEADY STATE FLOW CONDUCTANCE

COEFFICIENT Kv.

Forward Kv as a function of Pressure differential and input current

Reverse Kv as a function of Pressure differential and input current

Forward:

Side to nose

Reverse:

Nose to side



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0

0.5

1

1.5

2-40

-20

0

20

40

60

80

100

120


Forward Kv - Measured and Learned

Input Current [Amps]

Kv

[LP

M/s

qrt(

MP

a)]

0 20 40 60 80 100 1200

10

20

30

40

50

60

70

80

90

100

Measurement index

Kv

[LP

M/s

qrt(

MP

a)]

NLPN Learning

MeasuredNLPN

0

0.5

1

1.5

2

0

20

40

60

80

100

120

-1

0

1

2

3


Forward isol - Measured and Learned

Kv [LPM/sqrt(MPa)]

Inpu

t C

urre

nt [

Am

ps]

0 50 100 1500

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Measurement index

curr

ent

[A]

NLPN Learning

MeasuredNLPN

FORWARD Kv AND isol MAP LEARNING

Kv map

isol map

Kv

ma

p le

arn

ing

i sol m

ap

lea

rnin

g



0

0.5

1

1.5

2

0

20

40

60

80

100

120

0

0.5

1

1.5

2

2.5


Reverse isol - Measured and Learned

Kv [LPM/sqrt(MPa)]

Inpu

t C

urre

nt [

Am

ps]

0 20 40 60 80 100 1200

20

40

60

80

100

120

Measurement index

Kv

[LP

M/s

qrt(

MP

a)]

NLPN Learning

MeasuredNLPN

0 50 100 1500

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Measurement index

curr

ent

[A]

NLPN Learning

MeasuredNLPN

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0

0.5

1

1.5

2-40

-20

0

20

40

60

80

100

120

140


Reverse Kv - Measured and Learned

Input Current [Amps]

Kv

[LP

M/s

qrt(

MP

a)]

Kv

ma

p le

arn

ing

i sol m

ap

lea

rnin

g

Kv map

isol map

REVERSE Kv AND isol MAP LEARNING



CONTROL APPROACHES



EHPV NONLINEAR MAP

kBkAkk

solkkBkAkkk

TPPXhK

iTPPXfX

,,,

,,,,

v

1

Nonlinearities arise from

State constraints

Nonlinear flow models

Bidirectional mode

Model switching

Electromagnetic nonlinearities

PRELIMINAR STEP: BLOCK-INPUT FORM

kkk uxfx ,1

kkmk uxFx ,

kn

k ux ,

kmkmkkn

k uuuux ..., 21

Trivial example: kkk BuAxx 1 Tkmkmk

mk

mmk uuuBAABBxAx ...... 21

1

Tkkkk uuABBxAx 12

2 For m=2:

Let a system be described by:

Then, it can be transformed to a system such that:

Response is dominated by second order dynamics



TRACKING CONTROL

Let the nonlinear Function representing the behavior of the EHPV be expressed in block-input form by:

where,

kkBkAkkk uTPPXFX ,,,,2

ksol

ksolk i

iu

,

1,

Then linearizing about,

kd

kBkAkkd uTPPXS ,,,,*

yields,

kd

kkd

kkd

k

Skk

dk

Skk uuXXouu

u

FXX

X

FSFX

,**

*2

Assumptions:

2*

kdXSF1. The system is strongly controllable: there is a unique input so that

2. The controllability matrix Q has full rank for all inputs and states.

kd

kkkd

kkkkk uueouuQeJe ,**2

**

** ,,LetSk

k

Skkk

dkk u

FQ

X

FJXXe



Proposed control law:

where, lW Tkk ˆ̂

Upon substitution into the error equation,

Assumption:

tTnN

BNk

dkt

OlWzW

zuQzt

thatsuchexiststherethen

thatsuchbeand0Letting ,*

kd

kkk uQe *2

ˆ

kkkkk eJQu ̂*1*

(NLPN learning)

lWlWe Tk

Tkk

~ˆ2

WWW kk ˆ~

This result combined with the training law is used to study the stability of the closed loop system.

kBkAkkd

kd TPPXXl ,,,, 2



ESTIMATION TASK

The control law requires the knowledge of the Jacobian Jk* and the input matrix Qk

*:

kkkkk eJQu ̂*1*

Furthermore, the control law requires the knowledge of the desired states dXk

kk XTK VFor the desired states dXk

To obtain an estimate of the of the Jacobian Jk* and the input matrix Qk

*:

111112 ,

kkkkkk

Rkkk

Rkkk uuXXouu

u

FXX

X

FXX

11 ,,,, kkBkAkk uTPPXR

kkkkkkk uXouQXJX ,112

Rkk

Rkkkkkkkk u

FQ

X

FJuuuXXX

1111 ,,,Let



Procedure:

kd

kkd

kkk uuXXOJJ 111* ,

kd

kkd

kkk uuXXOQQ 111* ,

The Jacobian Jk* and the input matrix Qk

* can be approximated by

Applying the stack operator and the Kronecker product

kkkkkkk uXouQXJX ,112

)(BSACABCS

BSASBAST

T

k

Tk

knknkQS

JSuIXIX

1

12

or

k

kkkk u

XQJX 112

Looking for

AvBu

XQJX A

k

kkkk

minmin 112



221

vc

vvABAA

Tkkkk

kk

MODIFIED BROYDEN METHOD

CONTROL SIMULATION USING EHPV MATHEMATICAL MODEL

isol

ides

z

1

z

1

z

1

z

1

z

1

Saturation

Q.

Pp.

Vsol.

y p_dot.

y p.

y mp_dot.

y mp.

PC.

Ph.

Q_AB.

Q_CB.

Q_CA.

Flux.

Fsol.

Q_AP.

Q_BP.

Q_PC.

Q_PH.

SCOPES

Reshape

Reshape

Reshape

Reshape

Reshape1

Reshape

Qk

MatrixMultiply

MatrixMultiply

MatrixMultiply

MatrixMultiply

Product

[f]

[icont]

[isol]

[Kvd]

[error]

[Q]

[Q]

[u]

[J]

[Kvd]

[Kv]

[Kvd]

[Kv]

[u]

[J] [Q]

[Q]

[J]

[PB]

[Q]

[Q]

[J]

[J]

[f]

[Q]

[icont]

[PA]

[PB]

[error]

[icont]

[isol]

[Kvd]

[error]

[error]

[isol]

[PA]

Kv d

error

f

NLPN

Q

PA

PB

Kv

Kv CALCULATION1

Kv

Jk

MATLABFunction

INVERSE.1MATLABFunction

INVERSE..

MATLABFunction

INVERSE.

MATLABFunction

INVERSE

[Kv]

[ak]

[bk]

[Xk]

-1

[ak]

[bk]

[bk]

[Xk] Xk

Jk

Qk

Extraction

ERROR

PA

PB

isol

Q

Pp

Vsol

y p_dot

y p

y mp_dot

y mp

PC

Ph

Q_AB

Q_CB

Q_CA

Flux

Fsol

Q_AP

Q_BP

Q_PC

Q_PH

EHCV

1

-0.1

4.861

6.075

0.6117

0.09592

0.3822

0.8963

Demux

Demux

Demux

Demux

Demux

Demux

g(k)

d(k)

B(k)d = B.g

BROYDEN R1(modified)

(DSG)DISCRETE

SIGNALGENERATOR

SIMULINK model

TESTING:

0 0.5 1 1.5 2 2.5 30

20

40

60

80

100

120

Time [sec]

Kv

[LP

M/s

qrt(

MP

a)]

ActualDesired

Simulation Results



FUTURE WORK



TASKS TO BE ACCOMPLISHED:

Debug algorithms

Investigation of other possible algorithms for matrix estimation

Tune up and testing of NLPN controller and matrix estimators in the Hardware-In-the Loop simulator

Investigate robustness

Development of nonlinear Kv observer

Research possible online calibration methods.

Explore position control accuracy



CONCLUSIONS



RESEARCH OBJECTIVE Investigation and development of an advanced control methodology

for the EHPV using online training and soft sensing technology.

NLPN

Development of nonlinear mapping tool. Design with flexibility in basis functions Approximation of f: Rn Rm

CURRENT TO Kv MAPPING

Simulation of direct and inverse mappings Simulation of steady state mapping including temperature effects Experimental application for forward and reverse flow conditions on

both direct and inverse mappings

CONTROL APPROACH Development of NLPN controller Matrix estimation through modified Broyden method

control of electro-hydraulic poppet valves (ehpv)

Documents

requiredgeorgia techg

control approach

contamination high flow

disturbances flow forces

variety of control functions

smart float function

spool valves

metering modes