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9. Introduction to Neural Networks and Its Application to Control of SMAs Part 3

111Instructor: Dr. Song

Dept. of Mechanical Engineering

Part 3

A New Approach to Precision Tracking Control of Shape

Memory Alloy Actuators using Neural Networks and

Sliding-Mode based Robust Controller

Shape Memory Alloy Wire Actuator

LVDT Position

Sensor

Current Amplifier

Bia SpringLinear

Bearing

0 50 100 150 2003

4

5

6

7

8

9

10

11

12

13

Time (sec)

Position(mm)

Active Control of SMA Wire - Case 1

....Actual Controlled Output

____Desired Output

Control of Smart Structures

Topic 9Introduction to Neural Networks and Its Application to Control of SMAs

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1. EXPERIMENTAL SETUP

Shape Memory Alloy Wire Actuator

LVDT Position

Sensor

Current Amplifier

Bia SpringLinear

Bearing

The Single Wire Test Stand

Nickel-Titanium SMA wire (30.48 cm in length and 0.381 mm in diameter).

dSPACE Data Acquisition and Real Time Control system

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2. MODELING SMA WIRE HYSTERESIS USING

NEURAL NETWORKS Generating Training Data from SMA Wire Actuator

Frequency = 1/60 Hz

Applied Voltage = 0.1 to 4.0 volts (sinusoidal)

0 50 100 150 200 250 300

0

0.5

1

1.5

2

2.5

3

3.5

4Appl ied Voltage and Current - Training Signal

.....Voltage _____Current

Time (sec)

Voltage(volt)andCurrent(amp)

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666Instructor: Dr. SongDept. of Mechanical Engineering

0 0.5 1 1.5 2 2.5 3 3.5 40

2

4

6

8

10

12

14

Displacement v/s Voltage

Voltage (volt)

Displaceme

nt(mm)

Training Data - Displacement

0 50 100 150 200 250 3000

2

4

6

8

10

12

14Displacement - Training Signal

Time (sec)

Displacemen

t(mm)

Cooling

Heating

The SMA Wire hysteresis

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Neural Network Model of SMA Wire

Plant Model Network Structure

Training Technique - Back Propagation Learning

Training the Plant Model

Plant(SMA Wire)Plant(SMA Wire)

Plant Model

(Neural

Network)

Plant Model

(Neural

Network)Voltage

Displacement

ActualDisplacement

ErrorTag

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Inverse Modeling of SMA Wire using Neural Network

Inverse Model Network Structure

Training Technique - Back Propagation Learning

Plant

(SMA

wire)

Inverse

Model

(NN)error

DisplacementVoltage

Voltage

Tag

Training the Inverse Model

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Training RMS error = 0.0332 volts

The Inverse Model

0 2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

4Inverse Model Results

Displacement (mm)

Voltage(vo

lt)

....Neural Network Output

____Experimental Data

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Testing the Inverse Controller using SIMULINK

Des i red D isp laceme nt

Model ing Resul t (Displacement)

volt

In1 O ut1

ta g

posit ion

pos i

error

pouts im

vouts im

p{1}y{1}

Plan t Mode l

p{1} y{1}

I nverse M ode l

6 .5

Numerical Simulation of Active Control of SMA Wire

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Training RMS error = 0.0322 mm

Numerical Simulation of Active Control of SMA Wire (contd)

Using a sinusoidal command signal

0 10 20 30 40 50 600

2

4

6

8

10

12

14

Time (sec )

Displacement(mm)

Comparing Simulation Result with Desired Signal (Sinusoidal)

.. . .Sim ulation Output__ __ Des ire d Out pu t

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3. CONTROL SYSTEM DESIGN

Define:

Robust Controller

: a linear feedback action functioning as a

Proportional plus Derivative (PD) control.

: a feed-forward term

kD r

Tanh a ra f : a robust compensator and to compensatefor the hysteresis to increase control

accuracy and stability

if

e y y= d r e e= +

( )NN f Dk Tanh ai i i r r = + NNi : the neural network feed forward controller to cancel the hysteresis

i y yf fd dk T= +( )

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The Feed-forward Term

This feed forward current is designed to provide the

approximate amount of current required for the SMA

actuator to follow the desired path. The actuator systemwith a bias spring is approximately a first order system

with a time constant T, if the current is considered as the

input and the displacement is considered as the output.

i y yf fd dk T= +( )

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The Control Block Diagram

KD

Robust

Comp. R Gain

Command

Saturation

Feedback Signal

Command Signal

Programmable

Power Supply

Real-Time Control System

NNC

t

LVDT Sensor

Amplified Command Signal

Low Pass

Filter

SMA Wire Experiment

Feed Forward

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Experimental Validation

Using the Neural Network Controller without feedback

0 50 100 150 2000

2

4

6

8

10

12

14Track ing Control of SM A W ire using only NN C ontroller

Time (sec)

Position(mm)

. . . .Ac tual Controlled Output

____Des ired Output

RMS error = 0.7492 mm

4. EXPERIMENTAL RESULTS

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Experimental Validation (contd)


0 50 100 150 200 250 3009.5

10

10.5

11

11.5

12

12.5

Time (sec)

Position(mm

)



____Desired Output

Case Study - Case 2

Frequency = 1/60 Hz

Stroke = 2 mm

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0 50 100 150 200 250 300 3503

4

5

6

7

8

9

10

11

12

13

Time (sec)

Position(mm

)


....Actual Controlled Output____Des ired Output

Case Study - Case 3

Frequency = 1/90 Hz

Stroke = 8 mm

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0 100 200 300 400 500 6003

4

5

6

7

8

9

10

11

12

13

Time (sec)

Position(mm

)

Ac tive Control of SMA Wire - Case 4

....Actual Controlled Output____Desired Output

Case Study - Case 4

Frequency = 1/120 Hz

Stroke = 8 mm

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RMS error = 0.1387 mm0 50 100 150

7.5

8

8.5

9

9.5

10

10.5

11

11.5

12

12.5

Time (sec)

Position(mm)



____Desired Output

Case Study - Case 5

Frequency = 1/15 Hz

Stroke = 4 mm

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RMS error = 0.1387 mm0 50 100 150

7.5

8

8.5

9

9.5

10

10.5

11

11.5

12

12.5

Time (sec)

Position(mm)



____Desired Output

Case Study - Case 5

Frequency = 1/15 Hz

Stroke = 4 mm

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The Experimental Results Table


CASE FREQUENCY

(Hz)

STROKE

(mm)

RMS ERROR

(mm)

1 1/30 8 0.064

2 1/60 2 0.1018

3 1/90 8 0.2747

4 1/120 8 0.0927

5 1/15 4 0.1387

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25I D S

5. CONCLUSIONS

An approach using neural networks and based on sliding-

mode robust controller is developed for tracking control of

a SMA wire actuator. Experiments were conducted and successfully

demonstrated that shape memory alloy actuators with the

proposed control design can follow the referencecommand.

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