1

Achieving High Performance fromShape Memory Alloy (SMA) Actuators

School of Engineering,The Australian National University

© 2006 R. Feathersto ne, Y. H. Teh

this talk was presented at theIEEE ICRA workshop on Biologically−Inspired Actuation,

Shanghai, Friday May 13, 2011

Roy Featherstone(reporting the work of Yee Harn Teh)

© 2011 Roy Featherstone

2

The Testbed

antagonistic pairof SMA wires

load cells

precision linear stage

lockable pulley withoptional pendulum load

3

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

4

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 )

5

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

6

Differential Controller

Fcmd

Pmax,L Pmax,R

Fdiff

Pdiff−

+ Kp

−1

Td s minmax

+−

+++

+−

min

max

1Ti s

differential force controller

7

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

8

What Happened to the Hysteresis?

9

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:

10

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

11

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

12

Anti−Slack Mechanism

Pcom FL

FR

+−

Fminanti−slack

minKas

13

Anti−Slack Mechanism

Pcom FL

FR

+−

Fminout

in

minKas

14

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

15

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?

16

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.

17

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. Temperature

The 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

20

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

22

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

For

ce (

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

For

ce (

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

25

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

26

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

For

ce (

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

For

ce (

N)

Time (s)

Left SMARight SMA

without anti−overload with anti−overload

28

Extension to Position and Stiffness Control

Position

method: close an outerposition loop around theforce controller

result:

Stiffness

method: redefine the errorsignal to be the force error intracking the commandedstiffness

result:

very high accuracylow speed

very high accuracyhigh speed

Recommendation: Use Stiffness Control

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Summary

A new architecture for high−performance control of SMAactuators 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.

30

Lessons

High performance can be achieved by studying thebehaviour of the plant, discovering how to push theplant safely towards its performance envelope, anddesigning a control architecture accordingly

1.

2. In general, such an architecture has 3 components:

a command−following component,

a performance−optimization component, and

a performance−limiting component with explicitknowledge of the plant’s performance envelope

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The experimental results graphs appearing in this talk aretaken from Yee Harn’s Ph.D. thesis.

For more details, see

Yee Harn’s Ph.D. thesis

Y. 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.cecs.anu.edu.au/~roy/SMA/

Acknowledgements:

Most of the work reported here was done by Yee Harn Teh

The stiffness controller (which has not been published) wasimplemented by Sylvain Toru