Transcript Auto-Calibration and Control Applied to Electro-Hydraulic Valves

Auto-Calibration and Control Applied to
Electro-Hydraulic Valves
A Ph.D. Thesis Proposal
Presented to the Faculty of the
George Woodruff School of Mechanical Engineering
at the Georgia Institute of Technology
By
PATRICK OPDENBOSCH
Committee Members:
Nader Sadegh (Co-Chair, ME)
Wayne Book (Co-Chair, ME)
Chris Paredis (ME)
Bonnie Heck (ECE)
Roger Yang (HUSCO Intl.)
November 29, 2005
PRESENTATION OUTLINE
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November 29, 2005
INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
REVIEW OF MOST RELEVANT WORK
PROPOSED RESEARCH
PRELIMINARY WORK
EXPECTED CONTRIBUTIONS
CONCLUSION
2
INTRODUCTION
 CURRENT APPROACH
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Electronic control
Use of solenoid Valves
Energy efficient operation
New electrohydraulic
valves
 Conventional hydraulic
spool valves are being
replaced by assemblies of
4 independent valves for
metering control
High
Pressure
Low
Pressure
Spool Valve
Spool piece
Spool motion
Piston
November 29, 2005
Piston motion
3
INTRODUCTION
 CURRENT APPROACH
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Electronic control
Use of solenoid Valves
Energy efficient operation
New electrohydraulic
valves
 Conventional hydraulic
spool valves are being
replaced by assemblies of
4 independent valves for
metering control
Low
Valve motion
Pressure
High
Pressure
November 29, 2005
Piston motion
4
INTRODUCTION
 ADVANTAGES
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Independent control
More degrees of freedom
More efficient operation
Simple circuit
Ease in maintenance
Distributed system
No need to customize
Valve motion
Low
Pressure
High
Pressure
November 29, 2005
Piston motion
5
INTRODUCTION
 METERING MODES
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Standard Extend
Standard Retract
High Side Regeneration
Low Side Regeneration
Valve motion
 DISADVANTAGES
 Nonlinear system
 Complex control
Low
Pressure
High
Pressure
November 29, 2005
Piston motion
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INTRODUCTION
 Excellent sealing
 Less faulting
 High resistance to
contamination
 High flow to poppet
displacement ratios
 Low cost and low
maintenance
Coil Cap
Modulating
Spring
Input Current
Coil
Armature
Control
Chamber
Pressure
Compensating
Spring
U.S. Patents (6,328,275) & (6,745,992)
 POPPET ADVANTAGES
Adjustment
Screw
Pilot Pin
Armature
Bias Spring
Main Poppet
Forward
(Side) Flow
November 29, 2005
Reverse
(Nose) Flow
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INTRODUCTION
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Poppet type valve
Pilot driven
Solenoid activated
Internal pressure
compensation
Virtually ‘zero’ leakage
Bidirectional
Low hysteresis
Low gain initial metering
PWM current input
November 29, 2005
Coil Cap
Modulating
Spring
Input Current
Coil
Armature
Control
Chamber
Pressure
Compensating
Spring
U.S. Patents (6,328,275) & (6,745,992)
 Electro-Hydraulic Poppet
Valve (EHPV)
Adjustment
Screw
Pilot Pin
Armature
Bias Spring
Main Poppet
Forward
(Side) Flow
Reverse
(Nose) Flow
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INTRODUCTION
 VALVE CHARACTERIZATION
Flow Conductance Kv
Kv
Q Q  K P1  P2   K P
2
V
2
V
P1
P2
or
Q  K V P1  P2 sgn P1  P2 
November 29, 2005
Q
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INTRODUCTION
EHPV Forward Flow Conductance Coefficient Measurement
100
1.5044
1.3565
1.2074
1.0584
1.4308
1.2818
1.1326
0.98395
90
 FORWARD MAPPING
80
Kv [LPM/sqrt(MPa)]
70
60
50
40
30
20
10
Side to nose
0
0
0.2
0.4
0.6
0.8
1
Pressure Differential [MPa]
1.2
1.4
1.6
1.8
Forward Kv at different input currents [A]
 REVERSE MAPPING
EHPV Reverse Flow Conductance Coefficient Measurement
120
1.507
1.3587
1.2091
1.0594
1.4333
1.2838
1.134
0.9845
100
Kv [LPM/sqrt(MPa)]
80
60
40
20
Nose to side
0
0
0.2
0.4
0.6
0.8
Pressure Differential [MPa]
1
1.2
1.4
Reverse Kv at different input currents [A]
November 29, 2005
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INTRODUCTION
 MOTIVATION
 Need to control valve’s KV
 Currently done by inversion
of the steady-state
input/output characteristics
 Requires individual offline
calibration
 CHALLENGES
 Online learning of steady
state and transient
characteristics
 Online estimation of
individual Kv.
 ADVANTAGES
 No individual offline
calibration
 Design need not be perfect
and ‘sufficiently fast’
 Maintenance scheduling
can be implemented from
monitoring and detecting
the deviations from the
normal pattern of behavior.
November 29, 2005
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PRESENTATION OUTLINE
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November 29, 2005
INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
REVIEW OF MOST RELEVANT WORK
PROPOSED RESEARCH
PRELIMINARY WORK
EXPECTED CONTRIBUTIONS
CONCLUSION
12
PROBLEM STATEMENT
 PURPOSE
 Develop a general theoretical framework for auto-calibration
and control of general nonlinear systems. It is intended to
explore the feasibility of the online learning of the system’s
characteristics while improving its transient and steady state
performance without requiring much a priori knowledge of
such system.
 APPLICATION
 This framework is applied to a hydraulic system composed of
electro-hydraulic valves in an effort to study the applicability
of having a self-calibrated system.
November 29, 2005
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PRESENTATION OUTLINE
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November 29, 2005
INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
REVIEW OF MOST RELEVANT WORK
PROPOSED RESEARCH
PRELIMINARY WORK
EXPECTED CONTRIBUTIONS
CONCLUSION
15
OBJECTIVES
THEORETICAL
 Development of a general
formulation for control of
nonlinear systems with
parametric uncertainty and
time-varying characteristics
 Development of a formulation
for auto-calibration of
nonlinear systems
 Study of learning dynamics
online along with fault
diagnosis
 Improve Kv control of EHPV’s
November 29, 2005
 EXPERIMENTAL
 Analysis and validation on
the effectiveness of the
proposed method
 Study of the accuracy of the
auto-calibration and
possible drift problems
 Development of
computationally efficient
algorithms
 Development of a nonlinear
observer for state estimation
for unmeasurable states
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PRESENTATION OUTLINE
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November 29, 2005
INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
REVIEW OF MOST RELEVANT WORK
PROPOSED RESEARCH
PRELIMINARY WORK
EXPECTED CONTRIBUTIONS
CONCLUSION
17
RELEVANT WORK REVIEW
Sadegh (1995)
 The plant is linearized about a desired trajectory
 A Nodal Link Perceptron Network (NLPN) is employed in the
feedforward loop and trained with feedback state error
 The control scheme needs the plant Jacobian and controllability
matrices – obtained offline
 Approximations of the Jacobian and controllability matrices can
be used without loosing closed loop stability.
November 29, 2005
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RELEVANT WORK REVIEW
Sadegh (1998)
x1
x2
1
2
Wij

y1
N
y  f x   wii x  W T Φ
i 1
x3
xn
N

ym
N
f x    wii x   
i 1
 Nodal Link Perceptron Network (NLPN)
 Functional approximation is achieved by the scaling of basis
functions
 The class of basis functions are to be selected as well as their
‘weights’ are to be trained so that the functional approximation
error is within prescribed bounds
November 29, 2005
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RELEVANT WORK REVIEW
 O'hara (1990), Book
(1998)
 Concept of “Inferred Flow
Feedback”
 Requires a priori
knowledge of the flow
characteristics of the valve
via offline calibration
Squematic Diagram for Programmable Valve
November 29, 2005
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RELEVANT WORK REVIEW
 Garimella and Yao (2002)
 Velocity observer based on
cylinder cap and rod side
pressures
 Adaptive robust techniques
 Parametric uncertainty for
bulk modulus, load mass,
friction, and load force
 Nonlinear model based
 Discontinuous projection
mapping
 Adaptation is used when
PE conditions are satisfied
November 29, 2005
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RELEVANT WORK REVIEW
 Liu and Yao (2005)
 Modeling of valve’s flow
mapping
 Online approach without
removal from overall
system
 Combination of model
based approach,
identification, and NN
approximation
 Comparison among
automated modeling,
offline calibration, and
manufacturer’s calibration
November 29, 2005
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PRESENTATION OUTLINE
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November 29, 2005
INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
REVIEW OF MOST RELEVANT WORK
PROPOSED RESEARCH
PRELIMINARY WORK
EXPECTED CONTRIBUTIONS
CONCLUSION
27
PROPOSED RESEARCH
 AUTO-CALIBRATION AND CONTROL
x k 1  f x k , u k , ω k 
y k  gx k , v k 
 k = 0,1,2… (discrete-time index)
 0 ≤ ui ≤ iUMAX, i = {1,2,…,m}
x k  n
u k  m
ω k  m
yk p
vk   p
 Set of admissible states
  x  n : x  r, r  0, 
 Set of admissible inputs
U  u  n : z  Fx, u, x, z   
November 29, 2005
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PROPOSED RESEARCH
 AUTO-CALIBRATION AND CONTROL
x k 1  f x k , u k , ω k 
y k  gx k , v k 
 k = 0,1,2… (discrete-time index)
 0 ≤ ui ≤ iUMAX, i = {1,2,…,m}
x k  n
u k  m
ω k  m
yk p
vk   p
The control purpose is to learn the input sequence {uk} that
forces the states of the system xk to follow a desired state
trajectory dxk as k→∞
PROPOSED: Adaptive approach without requiring detailed
knowledge about the system’s model
November 29, 2005
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PROPOSED RESEARCH
 SQUARE NONLINEAR SYSTEM
x k    Fx k , u k 
y k  Hx k , u k 
x k  n
u k  n
y k  n
 ASSUMPTIONS
 The system is strongly controllable:
 x, z   , a unique u  nsuch that Fx, u  z
 The system is strongly observable:
 u U , H x1 , u  H x2 , u  x1  x2
 The functions F and H are continuously differentiable
November 29, 2005
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PROPOSED RESEARCH
 SQUARE NONLINEAR SYSTEM
x k    Fx k , u k 
y k  Hx k , u k 
 CONTROL DESIGN
 Tracking Error:
 Error Dynamics:
ek 
 F

 x k


d
xk ,d uk
x k  n
u k  n
y k  n
ek  xk d xk


e   F
 k  u k



d
xk ,d uk

u  d u   oe , u  d u 
k
k
k
k
 k

ek   d J k e k  d Qk u k  d u k 
November 29, 2005
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PROPOSED RESEARCH
 SQUARE NONLINEAR SYSTEM
x k    Fx k , u k 
y k  Hx k , u k 
x k  n
u k  n
y k  n
 CONTROL DESIGN
 Error Dynamics:
ek   d J k e k  d Qk u k  d u k 
 Deadbeat Control Law:
u k  d u k  d Q k 1 d J k e k
November 29, 2005
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PROPOSED RESEARCH
 SQUARE NONLINEAR SYSTEM
x k    Fx k , u k 
y k  Hx k , u k 
x k  n
u k  n
y k  n
 CONTROL DESIGN
 Deadbeat Control Law:
u k  d u k  d Q k 1 d J k e k
 Proposed Control Law:
~ 1 ~
~
uk  uk  uk   Qk  J k  ek
November 29, 2005
uk    d x k 
~T d
~ W
 xk 
u
k
k Φ
34
PROPOSED RESEARCH
Nominal
inverse
mapping
~ ~
~
uk  Qk 1 J k  ek  uk  u
k
Inverse
Mapping
Correction
uk
NLPN
dx
xk
PLANT
k
Adaptive
Proportional
Feedback
November 29, 2005
Jacobian
Controllability
Estimation
36
PROPOSED RESEARCH
 ESTIMATION APPROACHES
ek   d J k e k  d Qk u k  d u k 
 Modified Broyden
B k  M k Vk
M k 1  M k
November 29, 2005

B

T


M
V
V
k
k
k
k
 2  VkT Vk
37
PROPOSED RESEARCH
 ESTIMATION APPROACHES
ek   d J k e k  d Qk u k  d u k 
 Recursive Least Squares
bk  mTk v k
Pk 1m k bk  mTk v k 1 
v k  v k 1 
k 1  mTk Pk 1m k
Pk 1m k mTk Pk 1
1 
 Pk 1 
Pk 
 k 1 
 k 1  mTk Pk 1m k



k   e k 1   e 1   
November 29, 2005
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PROPOSED RESEARCH
 APPLICATION
PS
Pump
 Kv Observer
  x
x
PA
QB-
M
QA+
PB 
T
KvB-
KvA+
PB
2


  

1
1 m AA3  AB  4  FL  f f 1 ,  2 
  
e
 2   

QA  QA  QL   2 AA  


 3 
VA 0  1 AA

  
e
 4  
QB   QB   QL   2 AB  
 VB 0  1 AB

QA  KVA sgn PS   3  PS   3
QB   KVB sgn  4  PR   4  PR
QB   K VB sgn PS   4  PS   4
QA  K VA sgn  3  PR   3  PR
QL  K L  3   4 
November 29, 2005
PA
KvP
KvB+
KvAPR
QB
KvT
QB+
QA-
QA
QL
Tank
FL
PB
PA
m
x
VB0
AB
AA
VA0
x
For each valve:
Z i ,k 1  f Z i ,k , ui ,k , t 
KVi ,k  hZ i ,k 
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PROPOSED RESEARCH
 APPLICATION
 Health Monitoring
November 29, 2005
8000
ORIGINAL CURVE
7000
TRUE CURVE
6000
5000
ERR2
4000
V
K [LPH/sqrtMPa]
 Failures: sensor fault,
wear of the mating parts,
contamination, break of a
component, or component
stiction
 Assess valve’s behavior
with respect to the
nominal behavior.
 Establish the criteria to
declare faulting on the
valves by studying the
deviations from the
nominal pattern.
3000
ERR1
2000
1000
0
-200
0
200
400
600
800
isol [mA]
1000
1200
1400
1600
Kv as a Function of Input Current: Deviations from Nominal
Patterns
40
PROPOSED RESEARCH
 THEORETICAL TASKS
 Work on the convergence
properties of the estimated
matrices
 Perform analysis about the
closed loop stability of the
overall system.
 Work on a nonlinear
observer for the valves’
flow conductances.
November 29, 2005
 EXPERIMENTAL TASKS
 Hydraulic testbed setup
 Sensor integration,
calibration, and filtering
design
 Data acquisition and
analysis
 Validation of theory
 Compare the performance
under learning to that of
fixed input/output mapping
41
PRESENTATION OUTLINE








November 29, 2005
INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
REVIEW OF MOST RELEVANT WORK
PROPOSED RESEARCH
PRELIMINARY WORK
EXPECTED CONTRIBUTIONS
CONCLUSION
42
PRELIMINARY WORK
Implemented Nominal Mapping
 NONLINEAR 1ST ORDER
DISCRETE TIME
SYSTEM
Desired State
xk
Nominal Input
0
0.9
1.8
2.7
3.6
4.5
5
6
8
xk 1  uk 0.21  0.1567 xk0.45   0.93 xk
uk
0
0.5
5.5
6.8
8.2
13.9
14.0
15.0
16.0
80
70
60
Control Input
uk  0.5
 0
uk   
uk  0.5 uk  0.5
d
50
40
30
20
10
0
0
2
4
6
8
Desired State
u_nom
u_ss
Comparison: implemented and true steady state mapping
November 29, 2005
43
PRELIMINARY WORK
FIRST ORDER DISCRETE SYSTEM TRAJECTORY CONTROL SIMULATION
1-D T(u)
uk
ubar = gamma(xdk)
xdk
uk
[J]
Jk-1
[Q]
Qk-1
duk
[E]
xkLN
NL vs. LN
Linear Approx System
Ek
uk
uk
xdk
xk
xdk vs. xk
(CLOSED LOOP)
ek
(DSG)
DISCRETE
SIGNAL
GENERATOR
Nonlinear First Order
Discrete System
[J]
[Q]
Q
Q+delta
xk
Jk-1
[J]
uk
Qk-1
[Q]
1
u
Zero Rejector
ESTIMATION
[E]
-1
Closed Loop
[J]
J
[Q]
1-D T(u)
xkcl vs xdk vs xkol
uk
Q
November 29, 2005
(DSG)
DISCRETE
SIGNAL
GENERATOR.
ubar = gamma(xdk).
xk
Nonlinear First Order
Discrete System.
Open Loop
44
PRELIMINARY WORK
5
Close-loop
Desired
Open-loop
4.5
4
3.5
xk
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
Time [sec]
Closed-loop and open-loop performance
November 29, 2005
45
PRELIMINARY WORK
2
1.8
J
Q
1.6
Estimated Value
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
Time [sec]
Estimated Jacobian and Controllability
November 29, 2005
46
PRELIMINARY WORK
 Single EHPV learning
control being investigated
at Georgia Tech
 Controller employs
Neural Network in the
feedforward loop with
adaptive proportional
feedback
 Satisfactory results for
single EHPV used for
pressure control
November 29, 2005
48
PRELIMINARY WORK
Georgia Institute of Technology
EHPV TECHNOLOGY PROJECT
George W. Woodruff School of Mechanical Engineering
Atlanta, GA 30332
ROBOT-EHPV CONTROL
[NLPN_RLS/RLS-NOMD APPROACH]
Target Scope
Id: 2
dP
Kv
ek
1
error
T
Kvd
GENERATOR
1
Filter
Kvd
Kv d
1
Vsol
J
Saturation
dP
isol
x
Date: April 6, 2005
1
Pp
Kv
1
T
1
Isol
Target Scope
Id: 1
1
Vsol
Vsol
Developed by: Patrick Opdenbosch
1
dP
Pp
x+noise
x
Sampling Rate: 1kHz
1
1
Kva
Q
Qtot
x
1
CONTROLLER
Target Scope
Id: 3
Qnet
Qtot
Kv k
1
Qnet
EHPV
Vsol
Vsolk
Kv k
x+noise
x
J
Kv a
J
1
J
Q
1
Q
Vsolk
Filter
CONST. ESTIMATION
November 29, 2005
Q
Linear Approx System
49
PRELIMINARY WORK
Flow
Flow
Conductance
Conductance
[LPM/sqrt(MPa)]
[LPM/sqrt(MPa)]
 Initial test response, no NLPN learning
60
60
50
50
40
40
30
30
Kvd
Kv
Kvd
Kvappx
Kv
Kvappx
20
20
10
0
10
0
0.5
0.5
1
1
1.5
2
1.5 Time [sec] 2
Time [sec]
2.5
2.5
3
3
3.5
3.5
Flow Conductance
12.5
10
J [ ]J [ ]
1
0.95
10
7.5
J
0.95
0.9
J
Q
0.9
Q
7.5
5
5
2.5
0.85
0.85
0.8
0.8
0
0.5
1
1.5
2
2.5
3
0
0.5
1
1.5 Time [sec] 2
Time [sec]
2.5
3
2.5
0
3.5
0
3.5
Q [LPM/V-sqrt(MPa)]
Q [LPM/V-sqrt(MPa)]
12.5
1
Estimated Jacobian and Controllability
November 29, 2005
50
PRELIMINARY WORK
 EHPV response with NLPN learning
50
40
40
5
4
3
Kv
Kvd
Vsol
30
30
20
10
20
0.5
0.5
1
1
1.5
1.5
2
2
2.5
2.5[sec]
Time
Time [sec]
2
1
3
3
3.5
3.5
4
4
4.5
4.5
Flow Conductance
Temp
dP
J[]
Temperature [C]
50
1.02
45
1
40
0.98
35
0.96
30
0.94
25
0.92
20
0.90
0
7
6
J
Q
0.5
0.5
1
1
1.5
1.5
2
2
2.5
2.5[sec]
Time
Time [sec]
Input Voltage [V]
Kvd
Kv
Kvappx
80
60
70
60
50
0
100
0
10
9
8
3
3
3.5
3.5
4
4
4.5
4.5
0
5
5
1.8
0.75
1.5
0.625
1.2
0.5
0.9
0.375
0.6
0.25
0.3
0.125
0
05
5
Pressure Diff [MPa]
Q [LPM/V-sqrt(MPa)]
Kv [LPH/sqrt(MPa)]
Flow Conductance [LPM/sqrt(MPa)]
100
70
90
Estimated Jacobian and Controllability
November 29, 2005
51
PRESENTATION OUTLINE








November 29, 2005
INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
REVIEW OF MOST RELEVANT WORK
PROPOSED RESEARCH
PRELIMINARY WORK
EXPECTED CONTRIBUTIONS
CONCLUSION
53
EXPECTED CONTRIBUTIONS
 An alternative methodology for control system design of
nonlinear systems with time-varying characteristics and
parametric uncertainty.
 A method to estimate and learn the flow conductance of
the valve online.
 Guidelines to experimentally use this control
methodology and health monitoring efficiently in the area
of electro-hydraulic control.
November 29, 2005
54
PRESENTATION OUTLINE








November 29, 2005
INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
REVIEW OF MOST RELEVANT WORK
PROPOSED RESEARCH
PRELIMINARY WORK
EXPECTED CONTRIBUTIONS
CONCLUSION
55
CONCLUSIONS
 The proposed control methodology combines adaptive
proportional feedback control with online corrected
feedforward compensation
 The input/output mapping of the system can be easily
extracted via a functional approximator on the
feedforward compensation
 Extensive knowledge about the dynamics of the system
are not needed a priori for satisfactory performance
 The proposed method is to be employed in a
Wheatstone bridge arrangement of novel ElectroHydraulic Poppet Valves seeking a self-calibrated
system
November 29, 2005
56