Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten...
-
Upload
gyles-nash -
Category
Documents
-
view
227 -
download
0
Transcript of Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten...
![Page 1: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/1.jpg)
Model based friction compensation for an electro-mechanical actuator of a Stewart platform
Maarten Willem van der Kooij Friday, November 4th 2011
![Page 2: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/2.jpg)
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
![Page 3: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/3.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Intro – Stewart Platform
3
![Page 4: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/4.jpg)
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
![Page 5: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/5.jpg)
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
![Page 6: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/6.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Intro – Current method
6
• Simplified model• ‘Moog’ compensation
![Page 7: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/7.jpg)
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
![Page 8: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/8.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Theory – Friction Phenomena
8
![Page 9: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/9.jpg)
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
![Page 10: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/10.jpg)
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
10
![Page 11: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/11.jpg)
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
![Page 12: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/12.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Identification – Measurement Set-up
12
![Page 13: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/13.jpg)
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
![Page 14: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/14.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Identification – Friction Model Identification
14
![Page 15: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/15.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
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
![Page 16: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/16.jpg)
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
![Page 17: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/17.jpg)
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’)
![Page 18: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/18.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
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
]
![Page 19: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/19.jpg)
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
19
![Page 20: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/20.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Implementation – Results
20
![Page 21: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/21.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Implementation – Results: tracking error
21
![Page 22: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/22.jpg)
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
![Page 23: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/23.jpg)
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
23
![Page 24: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/24.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Questions?
24
?
![Page 25: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/25.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Appendix Slides
25
![Page 26: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/26.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
LuGre Adjusted
26
![Page 27: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/27.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Control of the Actuator / Platform
27
![Page 28: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/28.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Position Control
28
![Page 29: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/29.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Derivation of the equation of motion
29
![Page 30: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/30.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Commanded Velocity Tracking Improvement
30
![Page 31: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/31.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
31/…
System Model
![Page 32: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/32.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
System Identification Static Model
32
![Page 33: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/33.jpg)
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
33
![Page 34: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/34.jpg)
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
![Page 35: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/35.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Prediction error
35
![Page 36: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/36.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
System Identification
36
![Page 37: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/37.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Validation Data Set
37
![Page 38: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/38.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Motor Cogging
38
![Page 39: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/39.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Motor Cogging
39
![Page 40: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/40.jpg)
Model based friction compensation for an electromechanical actuator of a Stewart platform
Theory
Identification
Implementation
Conclusions
Acceleration, vel, Tff
40
![Page 41: Model based friction compensation for an electro- mechanical actuator of a Stewart platform Maarten Willem van der Kooij Friday, November 4 th 2011 TexPoint.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649d9e5503460f94a88212/html5/thumbnails/41.jpg)
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