Auto-Calibration and Control Applied to Electro-Hydraulic Valves

November 29, 2005

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 2

PRESENTATION OUTLINE

INTRODUCTION PROBLEM STATEMENT OBJECTIVES REVIEW OF MOST RELEVANT WORK PROPOSED RESEARCH PRELIMINARY WORK EXPECTED CONTRIBUTIONS CONCLUSION

November 29, 2005 3

INTRODUCTION

CURRENT APPROACH 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

Spool Valve

Spool piece

Piston

Low Pressure

High Pressure

Piston motion

Spool motion

November 29, 2005 4

INTRODUCTION

CURRENT APPROACH 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

Piston motion

Low Pressure

High Pressure

Valve motion

November 29, 2005 5

INTRODUCTION

ADVANTAGES Independent control More degrees of freedom More efficient operation Simple circuit Ease in maintenance Distributed system No need to customize

Piston motion

High Pressure

Valve motion

Low Pressure

November 29, 2005 6

INTRODUCTION

METERING MODES Standard Extend Standard Retract High Side Regeneration Low Side Regeneration

DISADVANTAGES Nonlinear system Complex control

Piston motion

High Pressure

Valve motion

Low Pressure

November 29, 2005 7

INTRODUCTION

POPPET ADVANTAGES Excellent sealing Less faulting High resistance to

contamination High flow to poppet

displacement ratios Low cost and low

maintenance

Pilot Pin

Main Poppet

Reverse (Nose) Flow

Forward (Side) Flow

ControlChamber

ModulatingSpring

Coil

Armature

ArmatureBias Spring

PressureCompensatingSpring

Coil CapAdjustmentScrew

Input Current

U.S

. P

ate

nts

(6

,32

8,2

75

) &

(6

,74

5,9

92

)

November 29, 2005 8

INTRODUCTION

Electro-Hydraulic Poppet Valve (EHPV) Poppet type valve Pilot driven Solenoid activated Internal pressure

compensation Virtually ‘zero’ leakage Bidirectional Low hysteresis Low gain initial metering PWM current input

Pilot Pin

Main Poppet

Reverse (Nose) Flow

Forward (Side) Flow

ControlChamber

ModulatingSpring

Coil

Armature

ArmatureBias Spring

PressureCompensatingSpring

Coil CapAdjustmentScrew

Input Current

U.S

. P

ate

nts

(6

,32

8,2

75

) &

(6

,74

5,9

92

)

November 29, 2005 9

INTRODUCTION

VALVE CHARACTERIZATION

Flow Conductance Kv

or

PKPPKQQ 2

V21

2

V

Kv

P2 P1

Q 2121V sgn PPPPKQ

November 29, 2005 10

INTRODUCTION

FORWARD MAPPING

REVERSE MAPPING

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

Forward Kv at different input currents [A]

Reverse Kv at different input currents [A]

Side to nose

Nose to side


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.





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.





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

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





RELEVANT WORK REVIEW

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.

Sadegh (1995)



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

1

x1

2

N

x2

x3

xn

y1

ym

Wij

ΦWxxy T

1

N

iiiwf

N

iiiwf

1

xx

Sadegh (1998)



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



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



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





PROPOSED RESEARCH

AUTO-CALIBRATION AND CONTROL

k = 0,1,2… (discrete-time index) 0 ≤ ui ≤ iUMAX, i = {1,2,…,m}

Set of admissible states

Set of admissible inputs

n

k x

kkk

kkkk

vxgy

ωuxfx

,

,,1

m

k um

k ω

p

k yp

k v

,0,: rrn xx

zxuxFzu ,,,:nU


PROPOSED RESEARCH

AUTO-CALIBRATION AND CONTROL

k = 0,1,2… (discrete-time index) 0 ≤ ui ≤ iUMAX, i = {1,2,…,m}

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

n

k x

kkk

kkkk

vxgy

ωuxfx

,

,,1

m

k um

k ω

p

k yp

k v


PROPOSED RESEARCH

SQUARE NONLINEAR SYSTEM

ASSUMPTIONS The system is strongly controllable:

The system is strongly observable:

The functions F and H are continuously differentiable

kkk

kkk

uxHy

uxFx

,

,

n

k xn

k un

k y

zuxFuzx ,thatsuchuniquea,, n

2121 ,,, xxuxuxu HHU


PROPOSED RESEARCH


CONTROL DESIGN Tracking Error: Error Dynamics:

kkk

kkk

uxHy

uxFx

,

,

n

k xn

k un

k y

k

d

kkk

d

k

k

k

k

k ok

dk

dk

dk

d

uueuuu

Fe

x

Fe

uxux

,,,

k

d

kk xxe

k

d

kk

d

kk

d

k uuQeJe


PROPOSED RESEARCH


CONTROL DESIGN Error Dynamics:

Deadbeat Control Law:

kkk

kkk

uxHy

uxFx

,

,

n

k xn

k un

k y

k

d

kk

d

kk

d

k uuQeJe

kk

d

k

d

k

d

k eJQuu 1


PROPOSED RESEARCH


CONTROL DESIGN Deadbeat Control Law:

Proposed Control Law:

kkk

kkk

uxHy

uxFx

,

,

n

k xn

k un

k y

kkkkkk eJQuuu ~~~ 1

kk

d

k

d

k

d

k eJQuu 1

k

d

k xu

k

dT

kk xΦWu~~


PROPOSED RESEARCHNominal inverse

mapping

Inverse Mapping

Correction

Adaptive Proportional Feedback

NLPN PLANT

Jacobian Controllability

Estimation

xk

dxk

uk

kkkkkk uueJQu ~~~ 1


PROPOSED RESEARCH

ESTIMATION APPROACHES

Modified Broyden

kkk VMB

k

d

kk

d

kk

d

k uuQeJe

kk

kkkkkk VV

VVMBMM

T2

T

1


PROPOSED RESEARCH

ESTIMATION APPROACHES

Recursive Least Squares

k

d

kk

d

kk

d

k uuQeJe

k

T

kkb vm

kk

T

kk

k

T

kkkkkk

b

mPm

vmmPvv

11

111

kk

T

kk

k

T

kkkk

k

k mPm

PmmPPP

11

111

1

1

11 ekek


PROPOSED RESEARCH

APPLICATION Kv Observer

TBA PPxx

BLBB

BB

e

ALAA

AA

e

fLBA

AQQQAV

AQQQAV

fFAAm

2

10

2

10

2143

2

4

3

2

1 ,1

43

33

44

44

33

sgn

sgn

sgn

sgn

LL

RRVAA

SSVBB

RRVBB

SSVAA

KQ

PPKQ

PPKQ

PPKQ

PPKQ

kikVi

kikiki

ZhK

tuZfZ

,,

,,1, ,,

For each valve:

FL

x

PA PB

QB-

x

PR

PS

PB PA

QA+

QL QA

QB+

QB

QA-

AA AB

KvB- KvA+

KvB+ KvA-

VA0 VB0

m

Pump

Tank

KvP

KvT

M


PROPOSED RESEARCH

APPLICATION Health Monitoring

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.

-200 0 200 400 600 800 1000 1200 1400 16000

1000

2000

3000

4000

5000

6000

7000

8000

isol [mA]

KV

[LP

H/s

qrtM

Pa] ERR2

ERR1

ORIGINAL CURVE

TRUE CURVE

Kv as a Function of Input Current: Deviations from Nominal Patterns


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.

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





PRELIMINARY WORK

NONLINEAR 1ST ORDER DISCRETE TIME SYSTEM

Desired State kd x Nominal Input ku

0 0 0.9 0.5 1.8 5.5 2.7 6.8 3.6 8.2 4.5 13.9 5 14.0 6 15.0 8 16.0

0

10

20

30

40

50

60

70

80

0 2 4 6 8

Desired State

Co

ntr

ol I

np

ut

u_nom u_ss

Comparison: implemented and true steady state mapping

Implemented Nominal Mapping

5.05.0

5.00

93.01567.021.0 45.0

1

kk

k

k

kkkk

uu

uu

xxux


PRELIMINARY WORK

xdkek

uk

FIRST ORDER DISCRETE SYSTEM TRAJ ECTORY CONTROL SIMULATION

Closed Loop

Open Loop

xkcl vs xdk vs xkol

xdk vs. xk(CLOSED LOOP)

uk

1-D T(u)

ubar = gamma(xdk).

1-D T(u)

ubar = gamma(xdk)

Q Q+delta

Zero Rejector

Q

[Q]

[J]

[E]

[Q]

[J]

[E]

[Q]

[Q]

[J]

[J]

uk xk

Nonlinear First OrderDiscrete System.

uk xk

Nonlinear First OrderDiscrete System

xdk

Ek

dukNL vs. LN

1

u

uk

Jk-1

Qk-1

xkLN

Linear Approx System

J

-1

xk

uk

Jk-1

Qk-1

ESTIMATION

(DSG)DISCRETE

SIGNALGENERATOR.

(DSG)DISCRETE

SIGNALGENERATOR


PRELIMINARY WORK

0 0.5 1 1.5 2 2.5 3 3.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time [sec]

xkClose-loopDesiredOpen-loop

Closed-loop and open-loop performance


PRELIMINARY WORK

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time [sec]

Estim

ate

d V

alu

e

JQ

Estimated Jacobian and Controllability


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


PRELIMINARY WORKGeorgia Institute of TechnologyGeorge W. Woodruff School of Mechanical Engineering

Atlanta, GA 30332

EHPV TECHNOLOGY PROJECTDeveloped by: Patrick Opdenbosch

Date: April 6, 2005ROBOT-EHPV CONTROL

[NLPN_RLS/RLS-NOMD APPROACH]

Sampling Rate: 1kHz

1

x

1

ek

1

dP

1

Vsol

1

T

Target ScopeId: 3

Target ScopeId: 2

Target ScopeId: 1

Saturation

1

Qtot1

Qnet

1

Q

1

Pp

Kv k

Vsolk

J

Q

Kv a

Linear Approx System

KvdGENERATOR

1

Kvd1

Kva

1

Kv

1

J

1

Isol

x+noise x

Filter

x+noise x

Filter

Vsol

dP

Kv

Pp

T

isol

x

Qtot

Qnet

EHPV

dP

error

Kv d

J

Q

Vsol

CONTROLLER

Kv k

Vsolk

Vsol

J

Q

CONST. ESTIMATION


PRELIMINARY WORK

0 0.5 1 1.5 2 2.5 3 3.510

20

30

40

50

60

Time [sec]

Flo

w C

ond

ucta

nce

[LP

M/s

qrt(

MP

a)]

KvdKvKvappx

0 0.5 1 1.5 2 2.5 3 3.50.8

0.85

0.9

0.95

1

J [

]

Time [sec]0 0.5 1 1.5 2 2.5 3 3.5

0

2.5

5

7.5

10

12.5

Q [

LPM

/V-s

qrt(

MP

a)]

J

Q

0 0.5 1 1.5 2 2.5 3 3.510

20

30

40

50

60

Time [sec]

Flo

w C

ondu

ctan

ce [

LPM

/sqr

t(M

Pa)

]

KvdKvKvappx

0 0.5 1 1.5 2 2.5 3 3.50.8

0.85

0.9

0.95

1

J [

]

Time [sec]0 0.5 1 1.5 2 2.5 3 3.5

0

2.5

5

7.5

10

12.5

Q [

LPM

/V-s

qrt(

MP

a)]

J

Q


Flow Conductance

Initial test response, no NLPN learning


PRELIMINARY WORK


Flow Conductance

EHPV response with NLPN learning

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

10

20

30

40

50

60

70

80

90

100

Kv

[LP

H/s

qrt(

MP

a)]

Time [sec]0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

1

2

3

4

5

6

7

8

9

10

Inpu

t V

olta

ge [

V]

KvKvdVsol

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 520

25

30

35

40

45

50

Tem

pera

ture

[C

]

Time [sec]0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.3

0.6

0.9

1.2

1.5

1.8

Pre

ssur

e D

iff [

MP

a]

Temp

dP

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510

20

30

40

50

60

70

Time [sec]

Flo

w C

ond

ucta

nce

[LP

M/s

qrt(

MP

a)]

KvdKvKvappx

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.9

0.92

0.94

0.96

0.98

1

1.02

J [

]

Time [sec]0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.125

0.25

0.375

0.5

0.625

0.75

Q [

LPM

/V-s

qrt(

MP

a)]

J

Q





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.





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 Electro-Hydraulic Poppet Valves seeking a self-calibrated system

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Auto-Calibration and Control Applied to Electro-Hydraulic Valves

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