Controlled Mechanical
Systems with Friction
CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN
Hensen, Ronnie H.A.
Controlled mechanical systems with friction / by Ronnie H.A. Hensen. - Eindhoven :
Technische Universiteit Eindhoven, 2002.
Proefschrift. - ISBN 90-386-2693-2
NUGI 841
Trefwoorden: geregelde mechanische systemen / wrijving / niet-lineaire dynamica / stick-
slip trillingen / systeemidentificatie / regelsysteemontwerp
Subject headings: controlled mechanical systems / friction / nonlinear dynamics / stick-slip
oscillations / system identification / controller design
Printed by University Press Facilities, Eindhoven, The Netherlands
Cover design by Jan-Willem Luiten
Copyright c by R.H.A. Hensen
All rights reserved. No parts of this publication may be reproduced or utilized in any form or
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mation storage and retrieval system, without permission of the copyright holder.
This work forms a part of the research program of the Dutch Institute of Systems and Control
(DISC).
Controlled Mechanical
Systems with Friction
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven,
op gezag van de Rector Magnificus, prof.dr. R.A. van Santen,
voor een commissie aangewezen door het College voor Promoties
in het openbaar te verdedigen op
donderdag 21 februari 2002 om 16.00 uur
door
Ronnie Herman Anna Hensen
geboren te Elsloo
Dit proefschrift is goedgekeurd door de promotoren:
prof.dr.ir. M. Steinbuch
en
prof.dr. H. Nijmeijer
Copromotor:
dr.ir. M.J.G. van de Molengraft
Summary
In high-performance motion systems, such as pick-and-place machines, friction can severely
deteriorate performance and can introduce negative side effects such as tracking errors, large
settling times or limit cycles. It is expected that many of today’s high-performance motion
systems will gain both speed and accuracy if friction is taken into account in the controller
design. To this end it seems useful that the friction present in these systems is modeled with
an appropriate friction model and that the corresponding model parameters are identified.
The resulting model can be used for either controller synthesis or closed-loop analysis of the
occurring friction-related phenomena such as limit cycles.
The scope of this thesis is three-fold and will focus on (i) the development of identification
procedures for mechanical systems with friction, (ii) control synthesis for mechanical
systems with friction and (iii) the analysis of friction induced hunting limit cycles. The latter
is a friction induced phenomenon for a single mass system with friction and a PID controlled
regulator task.
To model friction in mechanical systems two grey-box models, which combine physical
”white” knowledge of the system at hand with ”black” model structures, are presented. The
two black-box model structures, i.c., a Neural Network model and a Polytopic Linear Model
(PLM), are both capable of identifying friction characteristics that are left unexplained by
first principles modeling. In an experimental case-study, both grey-box models are applied
to identify a rotating arm subject to friction. An extended Kalman filter is used iteratively
and off-line for the estimation of unknown parameters in these models.
In contrast to the above static grey-box models, dynamic friction models, such as the
LuGre model, are capable of modeling more practically observed friction phenomena. For
example the so-called ‘presliding’ displacement regime, i.e., spring-like behavior for near
zero velocity, is covered by the LuGre model whereas the presented grey-box models both
lack this property. For the identification of this ‘presliding’ displacement regime an efficient
frequency domain identification procedure is presented. The identification procedure
for the dynamic model parameters of the LuGre model, i.e., (i) the stiffness and (ii) the
damping of the presliding phenomenon, is reduced to a single experiment. Time domain
validation experiments on a servo mechanism show accurate estimates of the dynamic model
parameters for the linearized presliding behaviour.
With respect to the first objective of this work, it can be concluded that both time and
frequency domain identification are essential to model and understand all dynamical
properties present in a mechanical system with friction. This mixture is most powerful when
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