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

184 Pages·2011·6.65 MB·English

Department of Precision and Microsystems Engineering
Model based friction compensation for an electromechanical
Stewart platform actuator
Name: M. W. van der Kooij
Report no: EM 11.034
Coach: ir. E.J.H. de Vries
Professor: Prof. dr. D.J. Rixen
Specialization: Automotive
Type of report: Master Thesis
Date: Delft, November 1, 2011

Model based friction compensation
for an electromechanical actuator
of a Stewart platform
Maarten Willem van der Kooij
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Model based friction compensation for
an electromechanical actuator of a
Stewart platform
Master of Science Thesis
For the degree of Master of Science in Mechanical Engineering at Delft
University of Technology
Maarten Willem van der Kooij
November 1, 2011
Faculty of Mechanical, Maritime and Materials Engineering (3mE) Delft University of
·
Technology
The work in this thesis was supported by Moog B.V. located in Nieuw Vennep. Their coop-
eration is hereby gratefully acknowledged.
Copyright ©
All rights reserved.
Abstract
MoogintheNetherlandsproduces, amongotherproducts, motionplatformsthatcanbeused
for flight and drive simulation. Generally, the motion platforms are driven by electromechan-
ical actuators. The performance of these actuators is limited by friction, which is a force
that opposes the direction of relative velocity. Naturally, this is most noticeable when the
direction of relative velocity changes, as it implies a sudden change in the friction force. This
sudden change in friction force makes it difficult to control a zero velocity crossing smoothly.
When the motion platform is used for flight or drive simulation this nonsmooth zero velocity
crossing can be felt by the user, making the simulation less realistic. Of course, one can pre-
dict a zero velocity crossing and apply some extra force on the system during a zero velocity
crossing. Currently a simple algorithm is used to do exactly this, but unfortunately things
are not that easy. This algorithm turned out to be insufficient in predicting the extra force
for all zero velocity crossing situations the actuator is subject to. Therefore the purpose of
this thesis is to identify a more elaborate friction model and use this model for feedforward
friction compensation to ensure a smoother zero velocity crossing.
The first part of this thesis gives an overview of the friction modeling literature of the past
decades. Two models are of special interest: the LuGre model as proposed by Canudas de
Wit et al. in 1995 and the DNLRX model proposed by Rizos and Fassios in 2005.
In the second part of this thesis the two models of interest are identified on a 1 degree
of freedom test set-up, consisting of one motion platform actuator connected to a test-rig.
Since it is not possible to directly measure the friction with sufficient accuracy a system
identification is performed. All terms in the equation of motion of the system are identified,
except for the friction. The friction signal is then measured as being the residuals of the
equation of motion and the two models of interest are identified on this data. It is shown
that the DNLRX model is able to properly predict the friction during a zero velocity crossing
whereas the LuGre model gives better predictions outside of the zero velocity regime. The
system model including either one of the models is able to predict the motor current based
on the actuator position, velocity and acceleration with an average error of less than 0.09
ampere.
The third part of this work focusses on the implementation of the friction models. Both the
models are used for feedforward friction compensation out of the range they were identified
Master of Science Thesis
ii
on: at varying actuator positions with a variety of accelerations during the zero velocity
crossing. Afterinitialmeasurementsthetwomodelsareslightlyadjusted. TheLuGremodelis
adjustedtoreducetheovercompensationitgives,theDNLRXmodelisadjustedtoreducethe
number of parameters. When using the LuGre model for feedforward friction compensation
the commanded velocity tracking error is reduced by 69 %. When using the DNLRX model,
the adjusted DNLRX model or the adjusted LuGre model the commanded velocity tracking
error reduction is around 80 %.
Master of Science Thesis
Table of Contents
Preface xi
1 Introduction 1
1-1 Moog. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1-2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1-3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1-4 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
I Theory 7
2 Friction Phenomena, Models and Compensation Methods 9
2-1 Experimentally Observed Phenomena . . . . . . . . . . . . . . . . . . . . . . . . 9
2-2 Friction Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2-3 Friction Compensation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Friction Model Identification Methods 35
3-1 LuGre Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3-2 DNLRX Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 40
II Experimental Identification 43
4 Experimental Set-up 45
4-1 Hardware and Working Principle of the Set-up . . . . . . . . . . . . . . . . . . . 45
4-2 Acquiring a Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4-3 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4-4 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Master of Science Thesis
iv Table of Contents
5 Identification of System Parameters 63
5-1 Decoupled Identification of System Parameters . . . . . . . . . . . . . . . . . . 64
5-2 Coupled Identification of System Parameters and Sliding Friction . . . . . . . . . 67
5-3 Absolute Values for the System Parameters . . . . . . . . . . . . . . . . . . . . 76
5-4 Validation of Identified Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5-5 Conclusions on the System Identification and Method . . . . . . . . . . . . . . . 83
6 Identification of Friction Models 87
6-1 Motor Cogging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6-2 LuGre Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6-3 DNLRX Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6-4 Comparison of the LuGre, DNLRX and the Static Models . . . . . . . . . . . . . 99
III Model implementation and experimental validation 101
7 Friction Compensation 103
7-1 Implementation of the Models and Adjustments to the Set-up . . . . . . . . . . 103
7-2 Initial Comparison of the Compensation Methods . . . . . . . . . . . . . . . . . 106
7-3 Adjusting the Friction Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7-4 An Extensive Comparison of the Compensation Methods . . . . . . . . . . . . . 117
8 Conclusions and Recommendations 123
8-1 Relating back to the Objectives of the Thesis . . . . . . . . . . . . . . . . . . . 123
8-2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Appendices 126
A Data of the experimental set-up 129
A-1 Testrig and actuator data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A-2 Datasheet of the Phase motor . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A-3 Measurements done on the torque constant . . . . . . . . . . . . . . . . . . . . 138
B Calculations 139
B-1 Bristle stiffness calculation according to Lischinsky . . . . . . . . . . . . . . . . 139
B-2 System identification for pre selected fixed inertias . . . . . . . . . . . . . . . . . 141
B-3 Gradient, Hessian and covariance matrix at the system identification optimum . . 142
B-4 Calculating the covariance matrix from the Hessian . . . . . . . . . . . . . . . . 143
B-5 Equations of motion of the 1-DOF testrig . . . . . . . . . . . . . . . . . . . . . 146
C Measurements 149
C-1 System Identification Validation Measurements . . . . . . . . . . . . . . . . . . 149
C-2 Dynamic Parameter Identification Measurement . . . . . . . . . . . . . . . . . . 152
Master of Science Thesis