Energy-Saving Control of Hydraulic Systems with Novel ...byao/Research/EH/EnergySavingEH.pdf · Energy-Saving Control of Hydraulic Systems with Novel Programmable Valves Principle

School of Mechanical Engineering, Purdue UniversitySchool of Mechanical Engineering, Purdue UniversitySchool of Mechanical Engineering, Purdue University

EnergyEnergy--Saving Control of Hydraulic Systems Saving Control of Hydraulic Systems with Novel Programmable Valveswith Novel Programmable Valves

Principle Investigator: Bin YaoResearch Assistant: Song Liu

School of Mechanical EngineeringPurdue University

West Lafayette, IN 47907, USA

OUTLINE

MotivationUniqueness of Proposed Programmable ValvesApplication to Boom Motion Control

Problem formulation and dynamic modelEnergy saving ARC controller design

Task Level: Valve Utilization (or Mode Selection)

Valve Level:ARC Pressure Controller Design for Off-Side ChamberARC Motion Controller Design for Working-Side

Experiment ResultsConclusions


Motion Control with Conventional Valves

Meter-in and meter-out orifice areas are coupled in 4-way directional control valves

Cannot control all cylinder states (pressures of both chambers)

Deadband for PDC valves

Leakage for servo valves


Non-Conventional Valves

Two valves:

Patented by:

J. Ardema, 1996Uses two directional control valves to meter flows

Four valves

Used by both:

J. Ardema and D. Koehler, 1999R. Book and C. Goering, 1999

Uses four poppet valves to independently control meter-in and meter-out flows


Regeneration Valves

Regeneration Valve

Patented by:K. Garnjost, 1989.

Uses one additional valve to provide regenerative flow for energy saving but cannot control both chambers independently


Energy Saving Programmable Valves

Purdue Energy SavingProgrammable Valves

Developed by:Bin Yao, 2000

Take advantages of four valve configuration to control meter-in/meter-out flows independently for precise cylinder positioning

Using an additional valve to precisely control cross-port flow (or regenerative flow) for energy saving


Purdue Programmable Valves

Cylinder

Valve #2

Load

Valve #5

Valve #4

Valve #3

Valve #1

XL

Q2

Q1

P1

P2

PS PT

QV1

QV2

QV5

QV4

QV3


Motion Control of Hydraulic Arm


d 1

a 1

x0

z0

y0

q1

x1

y1

z1 α1=90 deg.

q2

x2

y2

z2

x3

y3

z3

-q3

Coordinate Systems of Hydraulic Arm


Dynamic Model

Boom Motion Dynamics

Cylinder Dynamics

),,()()()()( 2222112

2222 qqtTAPAP

q

xqgmqGqmJ L

gLceLc +−∂∂=+++

2 2 22 2 2 2 2 3 3 2 3 2 3 3 3 2 3 3 2 3

2 2 2 2 2 2 2 2 3 2 2 3 23 3 23 23

2 2 2 3 23

2 2 22 3 2 3 3

2 ( 2 ) 2 2

( ) ( ) ( )

( )

2

c b st st

c b b st st

g

e

J I m l x m l I m l l l l c m l x c m l y s

G q m gl c m gx c m gy s m g l c l c m g x c y s

l q l c l c

l l l l l c

= + + + + + + + −= + − + + + −

= +

= + +


122

11111 )(

Qqq

xAQxAP

e

xV LL

L +∂∂

−=+−=β

222

22222 )(

Qqq

xAQxAP

e

xV LL

L −∂∂

=−=β

Dynamic Model

Programmable Valve Flow Model

Valve Dynamics

3452

3121

vvv

vvv

QQQQ

QQQQ

−−=−−=

),(

),(

),(

),(

),(

5555

4444

3333

2222

1111

vvvv

vvvv

vvvv

vvvv

vvvv

xPfQ

xPfQ

xPfQ

xPfQ

xPfQ

∆=∆=∆=∆=∆=

1 1

2 1

3 1 2

4 2

5 2

v t

v s

v

v s

v t

P P P

P P P

P P P

P P P

P P P

∆ = −∆ = −∆ = −∆ = −∆ = −


2

2 2

( ) ( )

( ) ( ) 2vi v v

i v v v v

x s N s

v s D s s s

ωζ ω ω

= =+ +

Overall Strategies

The difficulties in the coordinated control of five cartridge valves for precision motion and pressure control are dealt with through a task level valve utilization (or mode selection) algorithm and local valve level ARC pressure and motion controllers.

The nonlinear model based adaptive robust control (ARC) design in our previous studies is used to deal with the common difficulties in the precision control of electro-hydraulic systems directly to synthesize the desired load flow that is needed for precise motion control

nonlinear dynamics, large parameter variations, uncertain nonlinearities, and the mismatched model uncertainties

Nonlinear adaptive robust pressure controller is developed to handle the pressure control of the off-side chamber for energy saving purpose


Task Level Valve Utilization

Objective: Let Q1d and Q2d be the desired control flows to the two chambers of the cylinder that are needed to provide certain load pressure profile for motion tracking while maintaining the lowest possible cylinder chamber pressures to reduce the flow losses for energy saving. The task level of the controller determines how the five valves of the proposed programmable valve should be used in order to provide the required control flows Q1d and Q2d

Difficulties: Non-unique due to the added flexibility of independently controlling each of the five cartridge valves

Working Mode Selection:The paper uses seven modes, of which the first five are for motion tracking control and the last two for regulation control.


Desired-Force-Based Mode Selection

Extend Resistive Mode (T1)

Desired Velocity > 0Desired Control Force > 0

Uses valve #2 and valve #5Head-end (P1) for motion controlMaintain pressure of rod end (P2) as low as possible to have low working pressure for energy saving

Cylinder

Valve #2

Load

Valve #5

Valve #4

Valve #3

Valve #1

XL

Q 2

Q 1

P1

P2

PS PT

Q V2

Q V5

Extend Resistive-FLoad


Extend Overrunning Regeneration Mode (T2)

Desired Velocity > 0Desired Control Force < 0

Uses valve #2 and valve #3Rod-end (P2) for motion control through regeneration flow by valve #3 for significant energy savingMaintain head-end pressure (P1) as low as possible

Cylinder

Valve #2

Load

Valve #5

Valve #4

Valve #3

Valve #1

XL

Q 2

Q 1

P1

P2

PS PT

Q V2

ExtendOverrunning

FLoad

-QV3


ARC Pressure Controller Design(Head End as Off-side)

Cylinder Dynamics

Error Dynamics

Control Law

Adaptation Law

11 1 1 1L M Q

e

VP A x Q Qθ

β= − + + + ∆

1 1 1 1 1 1 1 11

1( ) ,p L M Q d p de A x Q Q P e P P

Vβ

θθ

= − + + + ∆ − = −

2111

1111

111

ˆˆ

MsppMs

QdLMa

MsMaM

QekQ

PVxAQ

QQQ

+−=

−+=

+=

θθβ

0

)~

(1

211

11211

1

≤

≤

−∆−−

Msp

pdQMsp

Qe

PQQV

e εθθ β

)(Prˆ

)(Prˆ

1

11

pQQ

pd

eoj

ePoj

Qγθ

γθ

θ

βθβ β

=

−=


ARC Motion Controller for Working SideDefine a switching-function-like quantity

Virtual Control Input (Desired Cylinder Force)

Adaptation Function

2 1 1 1 2 2 1 2 2 2 2 1 1, ,r d r dz z k z q q z q q q q k z= + = − = − = −

12 2 2 1 1 2 2 2 1 2 2 22 2

2

1 1( ) ( ) ( )L

r c g g rc e e

xz q q PA P A G q gl q gl T q

J q l l

θ θ θ ∂= − = − − + − + + − ∂

+−+−+

∂∂=

+=

)ˆ1ˆ(

ˆ)(

),ˆ,ˆ,,(

22221

12

2

2122

rge

ge

cc

LLda

LdsLdaLd

qgll

gll

JqG

x

qP

PPtqqP

θθθ

θθ

222

min11

21

zkx

qJP

PPP

L

cLds

LdsLdsLds

∂∂

−=

+=

θ 0

~~

22

2

2222

12

≤∂∂

≤

+−

∂∂

LdsL

TLds

L

c

Pq

xz

TPq

x

Jz εφθθ

T

ge

cLdaL

c

gll

GPq

x

J

z

+−

∂∂=

=

0,1,1

)(1

22

2

2222

φ

φωτ


ARC Motion Controller DesignDefine

where

Objective: find a virtual control law Q1Ld such that PL tracks the desired control function PLd

21 1 1

3 3 2 1 11 2 1 1

LL Ld M Ldc Ldu

A x A Az P P q Q Q P P

V q V Vθ ∂= − = + + − − ∂

2221

22112

12

212122

22

2

ˆ1ˆ)(

ˆˆ

ˆˆ

~~~1~(

1

ˆ

θθθ

θθ

θθθ

+−+

−−

∂∂

=

∂∂

+

+−−−

∂∂

−∂∂

=

∂∂

+∂∂

+∂∂

=

ge

ge

cL

c

Ldg

eL

L

c

LdLdu

LdLdLdLdc

gll

gll

GAPAPq

x

Jq

PTgl

lGcP

q

x

Jq

PP

t

Pq

q

Pq

q

PP

11 1

1L M

AQ Q

V=


ARC Motion Controller DesignControl Law

where

Adaptation Function

1 2 2 1 2 1 1 1 1 2

1 1 1 1 3 33min3

ˆ( , , , , , )

1 1,

ˆ

Ld Lda Lds Lds

Lda Lde Lds

Q q q P P t Q Q Q

Q Q Q k z

θ

θθ

= + +

= − = −

22 1

1 2 1 2 33 2 1 2

22 2

3 2 2 2

32

21

2 11 2

1 ˆ ˆ

1 1( )

L LLde Ldc

c

LdL LL c g

c c e

Ld

LLda

x A xQ z q P

J q V q

Px xz P G gl

J q q J q l

P

q

A xq Q

V q

ω θ θω

ωω

φ

∂ ∂= − −∂ ∂

∂∂ ∂− − + ∂ ∂ ∂ ∂= −

∂ ∂ − +

∂

3 3 3 3ˆ Pr ( ),oj zθθ τ τ ω φ= Γ =

0

ˆˆ

~~~

213

32

3132133

≤

≤

∂∂

−∂∂

−−+

Lds

LdLdTLLds

Qz

PT

q

PQQz εθ

θφθθθ


Overall Controller Structure

Valve UsageMode Selection

Adaptive Robust Pressure & Motion

Controllers Nonlinear Valve Flow Mappings

Inverse Valve Flow Mappings

NonlinearSystem Dynamics

DesiredTrajectory

Full State Feedback

Controller

Output

Controller

Plant

Experiment with Low-Speed/No-Load

Experiment Results

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

rad

Boom: ARC No Load Slow Trajectory

Desired AngBoom Ang

0 1 2 3 4 5 6 7 8 9−0.5

−0.250

0.250.5

rad/

s BM Ang Vel

0 1 2 3 4 5 6 7 8 90

2000400060008000

10000

Kpa P1 Pres

0 1 2 3 4 5 6 7 8 90

2000400060008000

10000

Kpa P2 Pres

0 1 2 3 4 5 6 7 8 9−0.1

−0.050

0.050.1

rad Error

0 1 2 3 4 5 6 7 8 90

200400600800

m2 *K

g/s3

time (s)

Energy Usage LS Energy Usage


Experiment with Higher Speed/No-Load

Experiment Results

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

rad

Boom: ARC No Load Fast Trajectory

Desired AngBoom Ang

0 1 2 3 4 5 6 7 8 9−0.5

−0.250

0.250.5

rad/

s BM Ang Vel

0 1 2 3 4 5 6 7 8 90

2000400060008000

10000

Kpa P1 Pres

0 1 2 3 4 5 6 7 8 90

2000400060008000

10000

Kpa P2 Pres

0 1 2 3 4 5 6 7 8 9−0.1

−0.050

0.050.1

rad Error

0 1 2 3 4 5 6 7 8 90

200400600800

m2 *K

g/s3

time (s)



Experiment with Low-Speed/50lb-Load

Experiment Results

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6ra

dBoom: ARC Loaded Slow Trajectory

Desired AngBoom Ang

0 1 2 3 4 5 6 7 8 9−0.5

−0.250

0.250.5

rad/

s BM Ang Vel

0 1 2 3 4 5 6 7 8 90

2000400060008000

10000

Kpa P1 Pres

0 1 2 3 4 5 6 7 8 90

2000400060008000

10000

Kpa P2 Pres

0 1 2 3 4 5 6 7 8 9−0.1

−0.050

0.050.1

rad Error

0 1 2 3 4 5 6 7 8 90

200400600800

m2 *K

g/s3

time (s)



Experiment with Higher-Speed/50lb-Load

Experiment Results

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6ra

dBoom: ARC Loaded Fast Trajectory

Desired AngBoom Ang

0 1 2 3 4 5 6 7 8 9−0.5

−0.250

0.250.5

rad/

s BM Ang Vel

0 1 2 3 4 5 6 7 8 90

2000400060008000

10000

Kpa P1 Pres

0 1 2 3 4 5 6 7 8 90

2000400060008000

10000

Kpa P2 Pres

0 1 2 3 4 5 6 7 8 9−0.1

−0.050

0.050.1

rad Error

0 1 2 3 4 5 6 7 8 90

200400600800

m2 *K

g/s3

time (s)



CONCLUSIONS

The utilization of the programmable valve and proper ARC motion and pressure controllers results in significant gains in reducing pump energy usage while achieving reasonable tracking performance

The significant gains in energy saving is realized through precise control of regenerative flows in maintaining working-side chamber pressure for motion tracking while keeping off-side chamber pressure at desired low level


ACKNOWLEDGEMENTSACKNOWLEDGEMENTSSponsors:

National Science FoundationCAREER Grant CMS-9734345

Purdue Electro-Hydraulic Research Center

Supported by

Caterpillar Inc. Valve Donations by:

Documents

Energy-Saving Control of Hydraulic Systems with Novel ...byao/Research/EH/EnergySavingEH.pdf · Energy-Saving Control of Hydraulic Systems with Novel Programmable Valves Principle