Model based friction compensation for an electro-mechanical actuator of a Stewart platform

Maarten Willem van der Kooij Friday, November 4th 2011

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Intro – Moog

• Former Fokker company• Located in Nieuw Vennep• Employees:

• Netherlands 160• Worldwide 10.000

2

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Intro – Stewart Platform

3

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Intro – Stewart Platform

4

• 6 degrees of freedom• Electromechanical vs. hydraulic actuators

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

8 9 10 11 12 13 14-1.5

-1

-0.5

0

0.5

1

1.5x 10

-3

Vel

oci

ty [

m/s

]

Time [s]

CommandedMeasured

8 9 10 11 12 13 14-1.5

-1

-0.5

0

0.5

1

1.5x 10

-3

Acc

ele

rati

on [

m/s

2]

Time [s]

Intro – Friction

5

• Friction opposes the direction of relative velocity

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Intro – Current method

6

• Simplified model• ‘Moog’ compensation

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Overview

7

Friction Phenomena

Friction Models

Friction Model ID

Measurement Set-up

System Identification

FFWD Compensation

Adjustments

Theory

Identification

Implementation

Conclusions

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Theory – Friction Phenomena

8

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Lund-Grenoble model

• Force equation

• State equation

where

Theory – Friction Models

9

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Theory – Friction Models

DNLRX model

• Presliding model

• Sliding model

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Overview

11

Friction Phenomena

Friction Models

Friction Model ID

Measurement Set-up

System Identification

Theory

Identification

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Identification – Measurement Set-up

12

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Equation of Motion

1. System Identification including simple friction model

2. Identify friction in nonlinear region

Identification – System Identification

13

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Identification – Friction Model Identification

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Identification – Check

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69.2 69.3 69.4 69.5 69.6 69.7 69.8 69.9 70 70.1 70.2-2

0

2

4

6

8

Time [s]

Cur

rent

[A

]

Measured

LuGre modeled

DNLRX modeled

69.2 69.3 69.4 69.5 69.6 69.7 69.8 69.9 70 70.1 70.2-0.2

-0.1

0

0.1

0.2

0.3

Time [s]

Vel

ocity

[m

/s]

69.2 69.3 69.4 69.5 69.6 69.7 69.8 69.9 70 70.1 70.20

0.1

0.2

0.3

0.4

Time [s]

Abs

olut

e cu

rren

t er

ror

[A]

LuGre modeled

DNLRX modeled

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Overview

16

Friction Phenomena

Friction Models

Friction Model ID

Measurement Set-up

System Identification

FFWD Compensation

Adjustments

Theory

Identification

Implementation

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Implementation

17

• Comparison of three situations

• Standard test cycle signal• Sinusoidal signal 0.2 Hz – 20mm amplitude (‘low acceleration’)

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Implementation – Initial Compensation Results

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4 4.02 4.04 4.06 4.08 4.1 4.12 4.14 4.16 4.18 4.2-2

0

2

4

6x 10

-3

Time [s]

Vel

oci

ty [

m/s

]

Low acceleration test signal

CommandedNo compensationLuGre stdDNLRX std

4 4.02 4.04 4.06 4.08 4.1 4.12 4.14 4.16 4.18 4.2-0.02

0

0.02

0.04

0.06

0.08

Time [s]

Acc

ele

rati

on [

m/s

2]

4 4.02 4.04 4.06 4.08 4.1 4.12 4.14 4.16 4.18 4.2-5

0

5

Time [s]

FF

to

rqu

e [

Nm

-sca

led

]

29.72 29.74 29.76 29.78 29.8 29.82 29.84 29.86 29.88 29.9 29.92-0.05

0

0.05

0.1

0.15

Time [s]

Vel

oci

ty [

m/s

]

Standard reversal bump test signal

29.72 29.74 29.76 29.78 29.8 29.82 29.84 29.86 29.88 29.9 29.920.5

0.55

0.6

0.65

0.7

0.75

Time [s]

Acc

ele

rati

on [

m/s

2]

29.72 29.74 29.76 29.78 29.8 29.82 29.84 29.86 29.88 29.9 29.92-5

0

5

Time [s]

FF

to

rqu

e [

Nm

-sca

led

]

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Implementation – Model Adjustment

LuGre • Reduce compensation when leaving presliding

DNLRX • Reduce number of parameters

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Implementation – Results

20

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Implementation – Results: tracking error

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Overview

22

Friction Phenomena

Friction Models

Friction Model ID

Measurement Set-up

System Identification

FFWD Compensation

Adjustments

Theory

Identification

Implementation

Conclusions

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Conclusions

• Velocity tracking error reductionby 80% on average for

• Adjusted DNLRX model• Adjusted LuGre model• Initial DNLRX model

by 69% on average for• Initial LuGre model

• The current is predictable with an absolute average error of 0.1 A

• Further work is needed on• Influence of load• Influence of actuator orientation

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Questions?

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?

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Appendix Slides

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

LuGre Adjusted

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Control of the Actuator / Platform

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Position Control

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Derivation of the equation of motion

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Commanded Velocity Tracking Improvement

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

31/…

System Model

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

System Identification Static Model

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

DNLRX

Dynamic Non Linear Regression with direct application of eXcitation

Cost function used in optimization

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Implementation – ‘Moog’ Algorithm

34

Two tuning methods• Manual• Automatic

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Prediction error

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

System Identification

36

Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Validation Data Set

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Motor Cogging

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Motor Cogging

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

Acceleration, vel, Tff

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Model based friction compensation for an electromechanical actuator of a Stewart platform

Theory

Identification

Implementation

Conclusions

• Copper losses• i^2 * R

• Iron losses (magnetic losses)• Hysteresis losses (magnetization of ferromagnetic materials)• Eddy current losses

• Mechanical losses

41

Losses in the motor