October 27, 2004
Control of Electro-Hydraulic Poppet Valves (EHPV)
PATRICK OPDENBOSCHGraduate Research AssistantManufacturing Research Center
Room 259
Ph. (404) 894 3256
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.
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
INTRODUCTION
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
October 27, 2004GEORGIA TECH
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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]]
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
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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
October 27, 2004GEORGIA TECH
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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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
NLPN
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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)
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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.
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
October 27, 2004GEORGIA TECH
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CURRENT TO Kv MAP
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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:
October 27, 2004GEORGIA TECH
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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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
Kv [(LPM)/sqrt(MPa)]dP [MPa]
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
Kv [(LPM)/sqrt(MPa)]dP [MPa]
Inpu
t [A
]
T = 40 C
SIMULATED INVERSE MAP ESTIMATION
TPKgi Vsol ,,
Forward flow
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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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
Pressure Differential [MPa]
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
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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
Pressure Differential [MPa]
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
Pressure Differential [MPa]
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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
0
0.5
1
1.5
2
0
20
40
60
80
100
120
0
0.5
1
1.5
2
2.5
Pressure Differential [MPa]
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
Pressure Differential [MPa]
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
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CONTROL APPROACHES
October 27, 2004GEORGIA TECH
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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
October 27, 2004GEORGIA TECH
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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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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
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FUTURE WORK
October 27, 2004GEORGIA TECH
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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
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
CONCLUSIONS
October 27, 2004GEORGIA TECH
G.W.W. School of Mechanical Engineering
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