Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint

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


Theory

Identification

Implementation

Conclusions

Intro – Stewart Platform

3


Theory

Identification

Implementation

Conclusions

Intro – Stewart Platform

4

• 6 degrees of freedom• Electromechanical vs. hydraulic actuators


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


Theory

Identification

Implementation

Conclusions

Intro – Current method

6

• Simplified model• ‘Moog’ compensation


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


Theory

Identification

Implementation

Conclusions

Theory – Friction Phenomena

8


Theory

Identification

Implementation

Conclusions

Lund-Grenoble model

• Force equation

• State equation

where

Theory – Friction Models

9


Theory

Identification

Implementation

Conclusions

Theory – Friction Models

DNLRX model

• Presliding model

• Sliding model

10


Theory

Identification

Implementation

Conclusions

Overview

11

Friction Phenomena

Friction Models

Friction Model ID

Measurement Set-up


Theory

Identification


Theory

Identification

Implementation

Conclusions

Identification – Measurement Set-up

12


Theory

Identification

Implementation

Conclusions

Equation of Motion

1. System Identification including simple friction model

2. Identify friction in nonlinear region

Identification – System Identification

13


Theory

Identification

Implementation

Conclusions

Identification – Friction Model Identification

14


Theory

Identification

Implementation

Conclusions

Identification – Check

15

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


Theory

Identification

Implementation

Conclusions

Overview

16

Friction Phenomena

Friction Models

Friction Model ID

Measurement Set-up


FFWD Compensation

Adjustments

Theory

Identification

Implementation


Theory

Identification

Implementation

Conclusions

Implementation

17

• Comparison of three situations

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


Theory

Identification

Implementation

Conclusions

Implementation – Initial Compensation Results

18

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

]


Theory

Identification

Implementation

Conclusions

Implementation – Model Adjustment

LuGre • Reduce compensation when leaving presliding

DNLRX • Reduce number of parameters

19


Theory

Identification

Implementation

Conclusions

Implementation – Results

20


Theory

Identification

Implementation

Conclusions

Implementation – Results: tracking error

21


Theory

Identification

Implementation

Conclusions

Overview

22

Friction Phenomena

Friction Models

Friction Model ID

Measurement Set-up


FFWD Compensation

Adjustments

Theory

Identification

Implementation

Conclusions


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

23


Theory

Identification

Implementation

Conclusions

Questions?

24

?


Theory

Identification

Implementation

Conclusions

Appendix Slides

25


Theory

Identification

Implementation

Conclusions

LuGre Adjusted

26


Theory

Identification

Implementation

Conclusions

Control of the Actuator / Platform

27


Theory

Identification

Implementation

Conclusions

Position Control

28


Theory

Identification

Implementation

Conclusions

Derivation of the equation of motion

29


Theory

Identification

Implementation

Conclusions

Commanded Velocity Tracking Improvement

30


Theory

Identification

Implementation

Conclusions

31/…

System Model


Theory

Identification

Implementation

Conclusions

System Identification Static Model

32


Theory

Identification

Implementation

Conclusions

DNLRX

Dynamic Non Linear Regression with direct application of eXcitation

Cost function used in optimization

33


Theory

Identification

Implementation

Conclusions

Implementation – ‘Moog’ Algorithm

34

Two tuning methods• Manual• Automatic


Theory

Identification

Implementation

Conclusions

Prediction error

35


Theory

Identification

Implementation

Conclusions


36


Theory

Identification

Implementation

Conclusions

Validation Data Set

37


Theory

Identification

Implementation

Conclusions

Motor Cogging

38


Theory

Identification

Implementation

Conclusions

Motor Cogging

39


Theory

Identification

Implementation

Conclusions

Acceleration, vel, Tff

40


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

Documents

Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint