(sma) actuators - cecs - australian national university
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High Performance Force Control forShape Memory Alloy (SMA) Actuators
Dept. Information Engineering,The Australian National University
© 2006 R. Featherstone, Y. H. Teh
http://users.rsise.anu.edu.au/~roy/SMA
(reporting the work of Yee Harn Teh)
Roy Featherstone
© 2008 Roy Featherstone
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An alloy exhibiting the shape memory effect has thefollowing property:
The Shape Memory Effect
it can be deformed easily when cold, but returnsto its original shape when heated.
The shape recovery process is accompanied by largeforces, which can be harnessed to perform mechanicalwork.
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The Shape Memory Effect
The effect is caused by a transformation between twocrystal phases:
a martensite crystal phase, which is stable atlower temperatures.
Austenite crystals are cubic:
Martensite crystals are monoclinic: or
2.
1. an austenite crystal phase, which is stable athigher temperatures, and
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The Shape Memory Effect
hotcooling
cold
deformwarming
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The Shape Memory Effectm
arte
nsite
ratio
temperature
100%
0%
thermalhysteresis
Af
As
Ms
Mf
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SMA Actuators
but recover theiroriginal shapewhen heated
SMA wires areeasily stretchedwhen cool
antagonistic−pairactuator
forcesensors
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mechanically simple
easily miniaturized
large force outputs
high force−to−weight ratio
clean
silent
spark−free
cheap
inefficient
slow
hard to controlaccurately
a better controlsystem can fix these
SMA Actuators
Advantages Disadvantages
low strain
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Force Control System
left SMA
right SMA
powerlimit
powerlimit
anti−slack
anti−overload
map
Fcmd
Pmax,LPmax,R
Pcom
PLFL
FR
RL
RR
Fdiff
Fdiff
differentialforce
controller
++
+−
−+
−+
PR
Pdiff
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Force Control System
left SMA
right SMA
powerlimit
powerlimit
anti−slack
anti−overload
map
Fcmd
Pmax,LPmax,R
Pcom
PLFL
FR
RL
RR
Fdiff
Fdiff
differentialforce
controller
++
+−
−+
−+
PR
Pdiff
PL = Pcom + max(0,Pdiff )
PR = Pcom + max(0,−Pdiff )
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Differential Controller
left SMA
right SMA
powerlimit
powerlimit
anti−slack
anti−overload
map
Fcmd
Pmax,LPmax,R
Pcom
PLFL
FR
RL
RR
Fdiff
Fdiff
differentialforce
controller
++
+−
−+
−+
PR
Pdiff
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Differential Controller
Fcmd
Pmax,L Pmax,R
Fdiff
Pdiff−
+ Kp
−1
Td s minmax
+−
+++
+−
min
max
1Ti s
differential force controller
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Behaviour of the Plant
The small−signal AC response ofnickel−titanium SMA approximatesto a first−order low−pass filter. 7−8 dB
gain
phase
Gain varies with mean stressand strain in a 7−8 dB range
Phase is independent ofstress and strain
Cut−off frequency varies withwire diameter
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What Happened to the Hysteresis?
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A Problem
When FlexinolTM wires are used in an antagonistic−pairactuator, they quickly develop a two−way shape memoryeffect, in which the wires actively lengthen as they cool,even if the tension on the wire is zero.
The wires can become slack as they cool.
Remedy: An anti−slack mechanism that maintains aminimum tension on both wires at all times.
Symptom:
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Anti−Slack Mechanism
left SMA
right SMA
powerlimit
powerlimit
anti−slack
anti−overload
map
Fcmd
Pmax,LPmax,R
Pcom
PLFL
FR
RL
RR
Fdiff
Fdiff
differentialforce
controller
++
+−
−+
−+
PR
Pdiff
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Anti−Slack Mechanism
left SMA
right SMA
powerlimit
powerlimit
anti−slack
anti−overload
map
Fcmd
Pmax,LPmax,R
Pcom
PLFL
FR
RL
RR
Fdiff
Fdiff
differentialforce
controller
++
+−
−+
−+
PR
Pdiff
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Anti−Slack Mechanism
Pcom FL
FR
+−
Fminanti−slack
minKas
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Anti−Slack Mechanism
Pcom FL
FR
+−
Fminout
in
minKas
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0 2 4 6 8 10 12 14 16 18 20−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5D
iffer
entia
l For
ce (N
)
Time (s)
ReferenceActual
0 2 4 6 8 10 12 14 16 18 20−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Diff
eren
tial F
orce
Err
or (N
)
Time (s)
0 2 4 6 8 10 12 14 16 18 20−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
Diff
eren
tial F
orce
(N)
Time (s)
ReferenceActual
0 2 4 6 8 10 12 14 16 18 20−5
−4
−3
−2
−1
0
1
2
3
4
5x 10−3
Diff
eren
tial F
orce
Err
or (N
)
Time (s)
without anti−slack with anti−slack
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Another Problem
We want the actuator to be as fast as possible. Thespeed can be increased by means of
a faster heating rate, and/or
a faster cooling rate.
A faster heating rate is more beneficial and easier toimplement.
problem: how to achieve faster heating without risk ofoverheating?
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Why Focus on Heating?
Excerpt from FlexinolTM data sheet:
Diameter(mm)
Current(mA)
ContractionTime (sec)
Off Time70C
Off Time90C
0.050
0.075
0.100
50
100
180
1
1
1
0.3
0.5
0.8
0.1
0.2
0.4
If we use the recommended safe heating currentsthen, for a thin wire, heating takes longer thancooling.
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Rapid Electrical Heating
To obtain a rapid response from an SMA wire, we needa heating strategy that
allows large heating powers when there is no risk ofoverheating, but
allows only a safe heating power when there is a riskof overheating.
This can be accomplished by
measuring the electrical resistance of the wire, and
calculating a heating power limit as a function of themeasured resistance
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Electrical Resistance vs. TemperatureThe electrical resistance (of nitinol) varies with themartensite ratio, and therefore also with temperature,because the resistivity of the martensite phase is about20% higher than the resistivity of the austenite phase.
Res
ista
nce
Temperature
heating
cooling
~20%
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Calculating the Power Limit
operating temperature too hot
Rth
1. Choose a threshold resistance, Rth, which is equal tothe hot resistance of the wire plus a safety margin.
safetymargin
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safe
unsafepowerlevels
Calculating the Power Limit
2. Calculate the power limit, Pmax, as a function of themeasured resistance, Rmeas.
RthPmax
Rmeas
Psafe
Phigh
Rramp
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Rapid Heating Mechanism
left SMA
right SMA
powerlimit
powerlimit
anti−slack
anti−overload
map
Fcmd
Pmax,LPmax,R
Pcom
PLFL
FR
RL
RR
Fdiff
Fdiff
differentialforce
controller
++
+−
−+
−+
PR
Pdiff
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0 1 2 3 4 5
−3
−2
−1
0
1
2
3D
iffer
entia
l For
ce (N
)
Time (s)
ReferenceActual
0 1 2 3 4 50
1
2
3
4
5
6
Forc
e (N
)
Time (s)
Left SMARight SMA
0 1 2 3 4 5
−3
−2
−1
0
1
2
3
Diff
eren
tial F
orce
(N)
Time (s)
ReferenceActual
0 1 2 3 4 50
1
2
3
4
5
6
Forc
e (N
)
Time (s)
Left SMARight SMA
without rapid heating with rapid heating
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Yet Another Problem
Rapid heating can produce excessively high tensions onthe wires, which can cause damage.
remedy: an anti−overload mechanism that cuts theheating power if the tension goes too high.
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Anti−Overload Mechanism
left SMA
right SMA
powerlimit
powerlimit
anti−slack
anti−overload
map
Fcmd
Pmax,LPmax,R
Pcom
PLFL
FR
RL
RR
Fdiff
Fdiff
differentialforce
controller
++
+−
−+
−+
PR
Pdiff
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Anti−Overload Mechanism
left SMA
right SMA
powerlimit
powerlimit
anti−slack
anti−overload
map
Fcmd
Pmax,LPmax,R
Pcom
PLFL
FR
RL
RR
Fdiff
Fdiff
differentialforce
controller
++
+−
−+
−+
PR
Pdiff
−+
−+
Yee Harn’sversion
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Anti−Overload Mechanism
FL
FR
anti−overloadFmax
+− maxKao
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0 1 2 3 4 5 6 7 8 9 10
−3
−2
−1
0
1
2
3D
iffer
entia
l For
ce (N
)
Time (s)
ReferenceActual
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
Forc
e (N
)
Time (s)
Left SMARight SMA
0 1 2 3 4 5 6 7 8 9 10
−3
−2
−1
0
1
2
3
Diff
eren
tial F
orce
(N)
Time (s)
ReferenceActual
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
Forc
e (N
)
Time (s)
Left SMARight SMA
without anti−overload with anti−overload
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Conclusion
A new architecture for high−performance force control ofantagonistic−pair SMA actuators has been presented,comprising
a PID controller for accurate control of the actuator’soutput force (i.e., the differential force);
an anti−slack mechanism to enforce a minimumtension on both wires;
a rapid−heating mechanism that allows faster heatingrates, but protects the wires from overheating; and
an anti−overload mechanism that protects the wiresfrom mechanical overload.
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EpilogueThis control system has been found to work in thepresence of large motion disturbances, and it has beenused as the inner loop in a position control system thatachieves high setpoint accuracy.
Acknowledgement: The experimental results graphs appearing inthis talk are taken from Yee Harn’s Ph.D. thesis.
For more details, seeYee Harn’s Ph.D. thesisY. H. Teh & R. Featherstone, "An Architecture for Fast andAccurate Control of Shape Memory Alloy Actuators", Int. J.Robotics Research, 27(5):595−611, 2008.
http://users.rsise.anu.edu.au/~roy/SMA/