Post on 18-Mar-2020
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
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
more difficult to control than electrical
drives ?
NO
3
Differences electric and fluid power drives (1/3)
Electric drives
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
Differences electric and fluid power drives (2/3)
Hydraulic drives
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
Differences electric and fluid power drives (2/3)
Other architectures of hydraulic drives
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
Low bandwidth High bandwidth
LoadMechanic
Power
command
High bandwidth
Electric
Power
angular positiondesired
command
Load
Low bandwidthHigh bandwidth
Not user friendly
6
Differences electric and fluid power drives (3/3)
Pneumatic drives
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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 ?
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
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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)
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
Speed
Displacement
2 commands : 𝑞𝑚𝑃 𝑢𝑃,𝑃𝑃
𝑞𝑚𝑁 𝑢𝑁,𝑃𝑁
𝑢𝑁 = 𝜓−1 𝑞𝑚𝑁, 𝑃𝑁𝑢𝑃 = 𝜓−1 𝑞𝑚𝑃, 𝑃𝑝
𝑞𝑚𝑁
𝑃𝑁
inversion
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The AT transform (1/2)
2 different phenomena
o The differential pressurization :
o The symmetric pressurization :
Let us consider the following coordinate transformation:
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
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The AT transform (2/2)
Make the really interesting variables appear in the
equations
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
𝐹𝑝𝑛𝑒𝑢=S. 𝑃𝑃 − 𝑃𝑁 = S.Δ𝑝
𝑃𝑇 =𝑃𝑁 + 𝑃𝑃
2
11
The AT transform (2/2)
Make the really interesting variables appear in the
equations
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
Decoupling
Force
generation
from
Pressurization
12
The AT transform (2/2)
Make the really interesting variables appear in the
equations
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
Speed
Displacement
PT ~ Actuator Stiffness
Active flow
Pressurization flow
13
Experimental validation
Open-loop : variation on
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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]
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Experimental validation
Open-loop : variation on
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
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Laboratoire AmpèreUnité Mixte de Recherche CNRS
Génie Électrique, Électromagnétisme, Automatique, Microbiologie Environnementale et Applications
Applications of the AT Transform
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
• 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
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
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Energy saving (Y-PTopti control)
Control synthesis :
o qmA is imposed (y trajectory)
o minimize
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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 :
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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
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
natural behavior of the
actuator to come back to its
equilibrium point
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Time [s]
Sti
ffn
ess
[N/m
]
desired Kpneu
measured Kpneu
Close loop stiffness
• Stiffness (Y-K control)
Control synthesis : Backstepping
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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]
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Conclusion
Active flow
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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…
FPNI 2016, 26-28 oct. 2016, Florianopolis, Brazil
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