A Park - like transform for fluid power systems...

1

Laboratoire AmpèreUnité Mixte de Recherche CNRS

Génie Électrique, Électromagnétisme, Automatique, Microbiologie Environnementale et Applications

A Park - like transform for fluid power systems :

application to pneumatic stiffness control

FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil

Prof. Eric Bideaux, INSA Lyon, Ampère Lab, France

2

Context & problematics

Modeling and control of Fluid Power systems is usually

considered as a difficult task :

o multiphysic : mechanics, fluid dynamics,

thermodynamics, electrical eng., …

o highly non linear behavior


more difficult to control than electrical

drives ?

NO

3

Differences electric and fluid power drives (1/3)

Electric drives


Electric

Power

angular position

Load

desired

command

o lot of sensors (current, voltage)

o complex control algorithm embedded

(large computation capacity)

o but everything is included !!!

o high reflected inertia

o complex friction phenomena

o can be considered part of the

load (disturbance)

The whole package is on-the-shelves !!!

User friendly

High bandwidth Low bandwidth

4


Hydraulic drives


Hydraulic

PowerLoad

command

o ~ no sensor (mech/elec feedback)

o each design is different

o safety component have to be added

o low inertia

o nearly a integrator

Help yourself !!!!

Not user friendly

Low bandwidth High bandwidth

5


Other architectures of hydraulic drives


Low bandwidth High bandwidth

LoadMechanic

Power

command

High bandwidth

Electric

Power

angular positiondesired

command

Load

Low bandwidthHigh bandwidth

Not user friendly

6


Pneumatic drives


High bandwidth Low bandwidth

o ~ no sensor (mech/elec feedback)

o low efficiency

o each design is different

o safety component to be added

o low inertia

o low pressure dynamic

Help yourself !!!!

Not user friendly

Pneumatic

PowerLoad

command

7

Why electrical drive are so user-friendly ?


User-friendly control

Sim

pli

city

of

contr

ol

Servo/Prop. Hydraulic Act.

EHA/ displacement pump

EHA/ variable speed

Electric MA

Servo Pneumatic Act.

The intelligence

is in the box

Plug & Play

Nearly no computation

capacity embedded

Not Plug & Play

8

How to make the control easier ?

The physical variables are not always the best for control

purposes :

o On mechanical side

o On fluid side (pneumatic)


Speed

Displacement

2 commands : 𝑞𝑚𝑃 𝑢𝑃,𝑃𝑃

𝑞𝑚𝑁 𝑢𝑁,𝑃𝑁

𝑢𝑁 = 𝜓−1 𝑞𝑚𝑁, 𝑃𝑁𝑢𝑃 = 𝜓−1 𝑞𝑚𝑃, 𝑃𝑝

𝑞𝑚𝑁

𝑃𝑁

inversion

9

The AT transform (1/2)

2 different phenomena

o The differential pressurization :

o The symmetric pressurization :

Let us consider the following coordinate transformation:


do not modify the force

Force

with (*)

𝑞𝑚𝑃

𝑞𝑚𝑁 𝑞𝑚𝐴 = active flow𝑞𝑚𝑇 = pressurization flow

* Note : this transformation can easily be

extended to non-symmetric cylinder

10


Make the really interesting variables appear in the

equations


𝐹𝑝𝑛𝑒𝑢=S. 𝑃𝑃 − 𝑃𝑁 = S.Δ𝑝

𝑃𝑇 =𝑃𝑁 + 𝑃𝑃

2

11



equations


Decoupling

Force

generation

from

Pressurization

12



equations


Speed

Displacement

PT ~ Actuator Stiffness

Active flow

Pressurization flow

13

Experimental validation

Open-loop : variation on


𝑞𝑚𝐴 = 0

𝑞𝑚𝑇

𝒒𝒎𝑻variation of 4 bars

variation of 0.7 bars

Time [s]

Time [s]

Mea

np

ress

ure

PT

[bar

]P

ress

ure

dif

fere

nceD

P [

bar

]

Vir

tual

flo

w r

ates

[g

/s]

14

Experimental validation

Open-loop : variation on


𝑞𝑚𝐴

𝑞𝑚𝑇 = 0

𝒒𝒎𝑨

variation < 0.05 bar

variation max of 0.8 bars

Time [s]

Time [s]

Mea

np

ress

ure

PT

[bar

]P

ress

ure

dif

fere

nceD

P [

bar

]

Vir

tual

flo

w r

ates

[g

/s]

Time [s]

15

AT Transform vs. Park Transform

AT Transform

o change of variables for

control purpose:

o original flows of power

modulator change in :

virtual active flow qmA

virtual presurization flow qmT


Park Transform

o change of variables for

control purpose:

o original voltages of power

modulator change in :

virtual voltage Vd

virtual voltage Vq

Displacement and force generation

Force control Torque control

Actuator stiffness

Mean pressure control Magnetic flux control

16

Laboratoire AmpèreUnité Mixte de Recherche CNRS

Génie Électrique, Électromagnétisme, Automatique, Microbiologie Environnementale et Applications

Applications of the AT Transform


• Trajectory control (Y-PT control)

• Energy saving (Y-PTopti control)

• Displacement / Stiffness (Y-K control)

• Position oberver (at 0 speed)

• Mono-distributor

17

Application of the AT Transform

Active flow


Pressurization flow

𝑞𝑚𝐴 𝑞𝑚𝑇

Speed

Displacement

Pressure difference

Pressurization

control

(Y-PT control)

Energy saving

(Y-PTopti control)

Stiffness

(Y-K control)

Position oberver

(at 0 speed)

Mono-distributor

18

Trajectory control (Y-PT control)

Control synthesis : Backstepping


𝑞𝑚𝐴

𝑞𝑚𝑇

Time [s]

Time [s]

Mea

np

ress

ure

PT

[bar

]

Dis

pla

cem

ent

[mm

]V

irtu

al f

low

rat

es [

g/s

]

Time [s]

desired

trajectory yd desired

trajectory PTd

measured

trajectory PT

measured

trajectory y

Same results to what was

achieved with other control

techniques

19

Energy saving (Y-PTopti control)

Control synthesis :

o qmA is imposed (y trajectory)

o minimize


if

if

if

𝑞𝑚𝑇 = 𝑉0.𝑞𝑚𝑃

𝑉𝑃+𝑞𝑚𝑁

𝑉𝑁as

with 𝑞𝑚𝐴 = 𝑉0.𝑞𝑚𝑃

𝑉𝑃−𝑞𝑚𝑁

𝑉𝑁

If VN smaller than VP, less flow is required to produce qmA if qmN is used

If VP smaller than VN, less flow is required to produce qmA if qmP is used

Optimal control is

obtained for :

20

Stiffness (Y-K control)

Stiffness control:

o reject or not disturbances in open-loop (do not required fast

closed loop)

o variable compliance

Control synthesis :

o qmA is imposed (y trajectory)

o Actuator stiffness


natural behavior of the

actuator to come back to its

equilibrium point

21

Time [s]

Sti

ffn

ess

[N/m

]

desired Kpneu

measured Kpneu

Close loop stiffness

• Stiffness (Y-K control)

Control synthesis : Backstepping


Dis

pla

cem

ent

[mm

]

Time [s]

desired position yd

measured

displacement y𝑞𝑚𝐴

Time [s]

Vir

tual

flo

w r

ates

[g

/s]

Kpneu = 1,5.105 N/m

Kpneu = 2,5.105 N/m

Kpneu = 3,5.105 N/m

Time [s]

Lo

ad[N

]

Static error decreasing

with Kpneu at impact

Kpneu = 1,5.105 N/m

Kpneu = 2,5.105 N/m

Kpneu = 3,5.105 N/m

22

Position observer at standstill

Position observer at standstill (v=0) :

From pressure sensors only : Fpneu and PT can be calculated,

the full state can be obtained by differentiation:

Procedure

o change slightly qmT with qmA = 0


y, qmA, qmT

not known

estimated

system inputs

position

estimation error

theoritically Fpneu do not change (or < dry friction)

the piston do not move (v=0)

23Time [s]

Fo

rce

Fp

neu

[N/m

]

measured Kpneu

Position observer at standstill


Dis

pla

cem

ent

[mm

]

Time [s]

real position ym

estimated

position y

Time [s]

Lo

ad[N

]D

isp

lace

men

t[m

m]

der

ivat

ive

of

Fp

neu

[N/(

m.s

)]

Observer synthesis : Sliding mode

o 5 Hz Sinusoisal trajectory on PT

Time [s]

Time [s]

24

Conclusion

Active flow


Pressurization flow

𝑞𝑚𝐴 𝑞𝑚𝑇

Speed

Displacement

Pressure difference

Pressurization

control

(Y-PT control)

Energy saving

(Y-PTopti control)

Stiffness

(Y-K control)

Position oberver

(at standstill)

Mono-distributor

What else ?

25

Thanks a lot for your kind attention…


References : 1. Frédéric Abry, Xavier Brun, Sylvie Sesmat, Eric Bideaux. Non-linear position control of a pneumatic actuator

with closed-loop stiffness and damping tuning, ECC, Jul 2013, Zürich, Switzerland. pp.1089 - 1094, 2013

2. Frédéric Abry, Xavier Brun, Michaël Di Loreto, Sylvie Sesmat, Eric Bideaux. Piston position estimation for

an electro-pneumatic actuator at standstill, Control Engineering Practice, Elsevier, 2015, 41 (8), pp.176-185

A Park - like transform for fluid power systems...

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