Friction Problems in Servomechanisms�

Modeling and Compensation Techniques

Jan Tommy Gravdahl�

Department of Engineering Cybernetics

Norwegian University of Science and Technology

Trondheim

Outline of this presentation❏ Introduction

❏ Friction models

�� Static models

�� Models with time delay

�� Dynamic models

❏ Friction compensation

�� Non�model based compensation

�� Compensation based on static friction models

�� Compensation based on dynamic friction models

�� Comparision of compensation schemes

❏ Concluding remarks

Friction

❏ Friction is the tangential reaction force between two surfaces

in contact

❏ Friction depends on contact geometry and topology� proper�

ties of the surface materials� displacement� relative velocity

and lubrication

❏ Very complex phenomenon� composed of several physical

phonomena in combination� Modeling most often empirical�

❏ Friction in servomechanisms can cause limit oscillations�

known as stick�slip� and regulationtracking errors�

❏ Friction causes wear in the system and reduces lifetime�

❏ Friction is dissipative� that is� it can only extract energy from

the system

Magnied section of a photo of a highly polished steel surface�

Halliday and Resnick ��� ��

Schematic drawing of two surfaces in contact� G�afvert �������

Surfaces built up by asperities�

True contact occurs between asperities� asperity junction

Asperity widht� typically ���m� slope� �� ��� �steel��

Friction � de�nition of terms

❏ Static friction �stiction�� The force �torque� needed to initi�

ate motion from rest

❏ Dynamic �Coulumb� friction� A friction component indepen�

dent of velocity

❏ Viscous friction� Velocity dependent friction between solid

and lubricant

❏ Break�away� The transition from rest �stiction� to motion

�dynamic friction�

❏ Break�Away force� The amount of force needed to overcome

static friction

❏ Dahl�e�ect� Elastic deformation of asperity junctions behaves

like a linear spring for small displacements

❏ Stribeck e�ect� Decreasing friction with increasing velocity

at low velocities� Caused by �uid lubricants�

Friction models for constant velocity� Static models

Classic results for constant velocity�

❏ Coulomb friction

Friction force proportional to normal load�

F � Fcsgn�v�� Fc � �FN � Known by L� da Vinci �������

rediscovered by Amontons ������ and developed by Coulomb

��� ��� Not neccesarily symmetric�❏ Static friction�stiction

Intruduced by Morin �� ���� Might be greater than Coulumb

friction

❏ Viscous friction

Velocity dependent friction� Ex� Friction force proportional

to velocity�

F � Fvv� Reynolds �� ��� Caused by viscosity of lubricants�

❏ Negative viscous friction

Introduced by Stribeck ������� The Stribeck e�ect�

Other static models

❏ Karnopp ��� ��� Stribeck friction with a dead zone around

zero velocity to make simuations less time consuming�

❏ Hess and Soom ������� F �v� ��

�Fc� �FS�Fc�

���v�vs���Fvv

�A sgn�v�

❏ Armstrong�H�elvoury�������

F �v� ��

�FC � �Fs � FC�e��v�vs��

� Fvv�

A sgn�v�

❏ The �v�vs���term model the Stribeck e�ect

❏ Canudas de Wit et�al �������

F �v� � �Fc � ��jvj��� � ��v�sgn�v�

Modeling for adaption� linear in parameters�

❏ All these models are discontinious for v � �� An approxima�

tion with a nite slope through the origin would not re�ect

the physical phenomena� Karnopp ��� ���

Various static modelsF

v

f)

F

v

e)F

F F F

v

v v v

a) b) c)

d)

a� Coulumb d� Stribeck e�ect

b� Coulumb�viscous e� Karnopp

c� Coulumb�viscous�stiction f� Hess and Soom

Armstrong� etc

The generalized Stribeck curve

F

v

II III IV

I

I No sliding� elastic deformation

II Boundary lubrication

III Partial �uid lubriacation

IV Full �uid lubrication

Models with time delay

These models include the phenomenon known as frictional mem�

ory �or lag� by using Ff�v� t� � Fvel�v�t� �l��

velocity

FrictionFriction

velocity

lag

time

Hess and Soom ������� F �v� t� ��Fc �

�FS�Fc�

���v�t��l��vs��� Fvv

�sgn�v�

The Armstrong ������ seven parameter model�

F �x� v� t� �����

����x� if v � � �pre sliding displacement��

FC � Fs��� td�

�

���v�t��l��vs���sgn�v� � Fvv� ifv �� �

Includes stiction� Stribeck e�ect� Dahl e�ect and lag� but re�

quires switching and many parameters

Dynamic friction models

Static models do not capture observed friction phenomena like

� the hysteresis observed experimentally by Hess and Soom

������� Low velocity � time delay not accurate enough

� position dependence like the Dahl e�ect� Asperity junctions

behave like linear springs before break�away�

� variations in the break�way force�Break-away force

Force rate

Friction

Dispalcement

� Friction models involving dynamics are neccessary to describe

the friction phenomena accurately

The Dahl model

Inspired by the stress�strain characteristic from solid mechanics�

Dahl ���� � proposed the model�

dFdx

� ��

BB���F

FCsgn�v�

�CCA

��

where x is displacement� Friction depends only on position� In

the time domain �� � ���F � �z

�z � v ��jvj

FCz

A generalization of Coulomb friction�

dFdx

� � � F � Fcsgn�v��

The Dahl model models pre�sliding displacement and frictional

lag� but not stiction or the Stribeck e�ect�

The bristle model �Norw�� bust�

Proposed by Hessig and Friedland ������� Models the micro�

scopic contact points of the asperity junctions�

(x_i-b_i)

Sliding body

Stationary surface

N bonded bristles

Uses an algorithm to calculate

F �

NXi��

���xi � bi�

WhereN is the number of bristles� �� is the sti�ness and �xi�bi�

is the de�ection�

As jxi � bij � �s� the bound snaps� and a new is formed�

Ine�cient due to complexity

The reset integrator model

❏ Proposed by Hessig and Friedland ������ to make the bristle

model computationally feasible

❏ Instead of snapping a bristle� the bond is kept constant at

the point of rupture

❏ Strain in bond�

dzdt

�����

��� if �v � � and z � z�� or �v � and z � �z��

v otherwise

❏ Friction force� F � �� � a�z�����v�z � ��dzdt

❏ Stiction achieved by a�z� �����

��a if jzj z�

� otherwise

❏ Much easier to simulate than the bristle model� but care must

be taken in handling the discontinuities

The models of Bliman and Sorine

❏ Bliman and Sorine ����������� stress rate independence

❏ F depends on sgn�v� and s��

Rt� jv�� �jd�

❏ F a function of path and not velocity

❏ Model given by

F � CTxs

dxsds

� Axs �Bvs

❏ �� order model can be reduced to Dahl model and further to

Coulomb

❏ �� order� A � IR���� B� C� xs � IR��

Correctly models stiction� Emulates Stribeck e�ect by using

two Dahl models in parallel� Olson et�al ���� �� not true

Stribeck e�ect

The LuGre �Lund�Grenoble� dynamic friction model

❏ Introduced by Canudas de Wit et�al� ������❏ An extension of the Dahl model

❏ Based on bristle de�ection in an average sense

❏ Models both Stribeck e�ect� stiction� frictional lag and vary�

ing break�away force

F � ��z � ��dz

dt� ��v

dzdt

� v �

jvj

g�v�z

g�v� � FC � �FS � FC�e�� vv���

❏ Only one rst order di�� equation

Other friction modeling techniques

❏ Neural networks

Dominguez et�al ������ model the dynamic friction of a ser�

vomotor using neural networks� The resulting model includes

Stribeck e�ect and frictional lag� but failed to model other

known friction phenomena� Du and Nair ��������� � more

promising�

❏ Spectral analysis

Popovi�c and Goldenberg ���� � use spectral analysis to

model the position� and velocity dependent friction of a servo

motor� Friction force is represented by a Fourier series�

Ff�q� �q� � A�� �q� �

NXj��

Aj� �q� sin�

BBB�

Cj�Bj� �q�

�CCCA

Veried experimentally� Accuracy can be improved by in�

creasing N � the number of DFT components

Comparative studies of friction models

Haessig and Friedland ������ compare the bristle model� the re�

set integrator model� the Dahl model� the static Karnopp model

and the classical Stribeck model� Results�

� Dahl� No stiction

� Karnopp fast� bristle and classical slow �in simulations�

� The classical model wrongly predicts limit cycles

� Implementation� Karnopp hard� Dahl and reset integrator

easy

G�afvert ������ compares the Bliman and Sorine models to the

LuGre model� Conclusion� LuGre includes more friction phenom�

ena than Bliman and Sorine�

Conclusion� The LuGre model is probably the most accurate

dynamic friction model avaliable

Friction compensation

Tasks in servomechanisms that require friction compensation�

Precision positioning� Velocity reversal and Velocity tracking

Approaches to solve the friction problem�

❏ Friction avoidance� design for control

� Lubricant selection� �uid �oil� grease� or dry �te�on� dia�

mond�

� �Ball� bearings� active control� magnetic� piezoelectric

� Redesign of physical system� inertia reduction

❏ Non�model based friction compensation

� PDPID

� Dither�

❏ Model based friction compensation

� Estimating the friction force F by F using a friction model

and compensating for friction by adding F to the control

� The estimate F can be xed �identied o�ine� or adaptive

Non model based compensation techniques❏ Dither

� Introduction of a high freq� oscillation keeps the system in

motion� avoiding sticktion� �in use on e�g� gun mounts�

� Analysis with describing functions �Balchen ����� or av�

eraging �Mossaheb �� ��

� Normal dither �external vibrator� modies friction� tangen�

tial dither �control input� modies the in�uence of friction

❏ Impulsive control

� Achieve high precision positioning by applying a series of

small impacts� when in stick� Yang and Tomizuka ��� ��

Adaptive pulse width control�

❏ PDPID�

� The regulator problem is stable under PD control�

� Tracking may lead to stick�slip limit cycles�

� Integral action reduces steady�state errors � hunting

Model based compensation techniques

OverviewServoMotors

ServoMotors

Method

Problem

Application

FrictionModel

Dynamic

Other N DOFManipulator

PID adaptive

Regulation Tracking

Static

Reg Track Reg Track Reg Track

N DOFManipulator

estimation RobustPassivity Nonlinear

System models

The study of compensation techniques will be restricted to the

following two applications

�� Servomotors driving a load with friction�

J �� � u� Ff

where J is the moment of inertia� � is the angular velocity�

u is the input torque and F f is the friction torque�

�� Robotic manipulators in N DOF with friction in the joints�

D�q��q � C�q� �q� �q � g�q� � u� Ff �

where q � IRn� joint angles� D�q�� inertia matrix� C�q� �q� �q�

vector of Coriolis and centrifugal terms� g�q� � gravity� u �

IRn� control torques and Ff � IRn� friction torques� Only

friction in joints included� Can also have friction when in

contact with environment �force control��

Position regulation for �DOF mass system

Southward et�al �������

❏ System has similar eq� of motion as a servomotor

❏ Uses static Stribeck and Karnopp friction models

❏ Control law� PD � nonlinear �discontinuous� friction com�

pensation�

K_p x+F_c(x)

x

Fs

Fs

F

❏ Global asymptotic stability proved by LaSalle�s theorem using

Dini deriviatives

❏ Position regulation conrmed by experimental results

Adaptive position tracking for servo

Friedland and Park ������������

❏ Position tracking of servo with static Coulomb friction

❏ Adaption of unknown Coulomb friction�

Fc � z � kjvj�

�z � k�jvj����u� F �v� Fc�

�sgn�v�

� Fc � Fc asymptotically�

❏ Control law� u � PD � F �v� Fc�

❏ Position tracking conrmed in simulations� also when includ�

ing viscous friction�

❏ Experimentally conrmed by Mentzelopoulou and Friedland

������ for Coulomb friction� and by Amin et�al ������ for

viscous friction❏ Extended to two DOF manipulator by Yazdizadeh and

Khoasani ������

Friction compensation with static friction models

Adaptive velocity tracking for a tracking telescope

Gilbart and Winston �������

❏ The rst result on adaptive friction compensation

❏ System� a motor driving an optical telescope

❏ Friction modeled as classical Coulomb friction

❏ MRAC� u � K��t� ��p �K��t����m � � ��m� �K��t�sgn� ��p� �z �

Friction est�

❏ GAS proven by Lyapunov

❏ Controller was implemented on a ��in optical telescope used

for tracking satellites

❏ The application requires velocity of motor to pass through

zero

❏ Adaption eliminated dead zone encountered in zero crossings

❏ RMS tracking error reduced by a factor of six due to friction

compensation�

High precision position control

❏ Kim et�al� �����a� study a servo motor driving a xy table

❏ The friction model used is the Armstrong ��parameter model

❏ A �tracking controller� brings the system within a

small distance � from the reference� Then fuzzy�PD

ym yPlant

Fuzzy PD

Trackin contr.

❏ Tracking controller� Adaptive sliding mode � friction comp�

Paramters in friction model found using Evolution Strategies�

❏ Fuzzy rules tuned by Experimental Evolutionary Progr�

❏ Experiments conrm position error less than ��m�

❏ Position error in an area dominated by the Dahl e�ect� em�

phasizing the need for accurate friction models

❏ Extended by Kim et�al� �����b� to tracking

Adaptive friction compensation in manipulators

Canudas de Wit et�al �������

❏ Low velocity tracking of the last link in �DOF manipulator

❏ Uses the static friction model

F �v� � �Fc � ��jvj��� � ��v�sgn�v�

Linear in unknown parameters❏ Controller structure

u � � m� I�v � mgr cos�q� � Ff

v � feed forward � PID

Ff � �T��t�� � estimated

estimation algorithm� Exponentially weighted least squares�

❏ � used to avoid friction overcompensation� which is

shown to cause oscillations

Position regulation of N DOF robot manipulator

Cai and Song �������

❏ Position regulation of manipulator with Coloumb friction and

stiction

❏ Uses the Karnopp friction model� with zero dead band in

stability analysis

❏ Control law� PD�adaptive gravity compensation and robust

friction compensation�

u � �Kv �q �Kpq �G�q�� non

non�i � �msi tanh�iqi

❏ Similar in spirit as Southward et�al ������� but continuous�

❏ Convergence to a set by LaSalle�s theorem� Size of the set

depends on �i�

❏ Conrmed by simulations

Song et�al ���� Tracking of N DOF manipulator

Friction compensation with dynamic friction models

Position tracking of airborn servo

Walrath ��� ���

❏ Studied stabilization of airborn pointing and tracking tele�

scope

❏ A servomotor produces a corrective torque to compensate for

gimbal bearing friction

❏ Observed that friction responds continuously to velocity re�

versal� Static model not su�cient � Dahl�s model

❏ Probably the rst reference to employ a dynamic friction

model in control design❏ Controller � u � Proportional � F

❏ The estimate F was calculated using the Dahl model� Adap�

tion on model parameter�

❏ Experimentally veried� Reported of a factor ve improve�

ment in RMS pointing error

Position control of servomotor

Khorrami et�al �������

❏ Considers a servomotor driving a load with friction

❏ Dynamic friction modeled with LuGre model

❏ Uses a robust adaptive variable structure controller�

u � ��BTPx� �BTPx� T tanh��a� bt�BTPx��

with update law

�� � kBTPxk�� � �

❏ The unmeasurable friction states are treated as bounded dis�

turbances

❏ Globally asymptotically stable

❏ Also give similar results using backstepping when considering

compliant transmission with friction at both motor and load

side�

❏ Result extended in Sankaranarayanan and Khorrami ������

to the low velocity tracking problem

Position tracking for servomotor

Canudas de Wit and Lischinsky �������

❏ Study position tracking for a servomotor

❏ Use dynamic LuGre model

❏ The parameters of the LuGre model estimated numerically

from experiments

❏ Fixed friction compensation� u � Js�xr�JH�s�e� F where

H�s� depends on controller choise �PD� ltered PID�

❏ Adapting normal force variations�

u � Js�xr � JH�s�e� ��z � ��dz

dt� ��v

dzdt

� v � ���jvj

g�v�z � ke �

d�dt

� ����jvj

g�v�z�zm � z�

❏ Adaption also for temperature changes

❏ Convergence e� � by Lyapunov� Conrmed experimentally�

Position tracking for manipulators

Vedagarbha et�al �������

❏ Consider the problem of position tracking in a manipulator

with dynamic friction in the joints

❏ Use the dynamic LuGre model in each joint

❏ Employ nonlinear observers to estimate the unmeasurable

friction states� and presents convergence results both for

adaptive and non�adaptive controllers�

❏ Control law� u � w � �� �q�z � kcr� where w is represents

dynamics to be cancelled out� �� �q�z is the estimated friction

torque and r is the ltered tracking error

❏ Adaption is studied for unknown �linear� parameters in LuGre

model and for variations in the normal force�

Position tracking of manipulator

Panteley et�al ��������� ��

❏ Study position tracking in manipulators using LuGre

❏ Main point� Treat the friction compensation problem as a

disturbance rejection problem

❏ The part of the friction force dependent on z is regarded a

disturbance� and the linear �viscous� component is compen�

sated by the adaptive controller❏ Designs an adaptive controller using passivity arguments�

❏ An adaptive Slotine and Li controller strictly passies the

system and an outer loop �tanh� rejects the disturbance�

u � �Kds���� � � �Y��q� �q� qr� �qr�� Y�� �q�� Y�� �q� s��

�� � �Ts� � T � �

❏ Results conrmed experimentally

Comparative studies of compensation schemes

Leonard and Krisnaprasad ������� position tracking of servo

❏ Compares � di�erent controllers�

�� PID

�� Dither

�� MRAC based on Gilbart and Winston ������� asymmetric

Coulumb�Stribeck� AS

�� Computed torque � int��friction comp�� four di�erent

static models of friction

�� Based on Walrath ��� ��� Computed torque � int�� dy�

namic Dahl friction comp�

❏ Compared experimentally

❏ Problem� track a sinusoidal reference trajectory

❏ Conclusions�

�� Model based controllers better than PID and dither

�� The Dahl based controller outperformed the other

Comparasions� contn�

❏ Du and Nair ������

Compare their NN controller with the adaptive schemes of

Canudas de vit et�al� ������ and Friedland and Park �������

NN perform better� but computationally intensive

❏ Canudas de Wit and Lischinsky ������

compare their adaptive LuGre based controller with a PID�

No contest�

❏ Panteley et�al ���� �

Passivity approach compared to Amin et�al� ������� based on

adaptive scheme of Friedland and Park ������� Performance

similar for sinusoidal trajectories� passivity based better for

complicated trajectories� Amin requires knowledge of J

Concluding remarks

❏ Friction is a complicated phenomenon� Many approaches to

model friction� Classic� Ff � Ff�v��

❏ The trend is toward using dynamic friction models� where the

state of the art is the LuGre model�❏ Dynamics are required to explain observed friction phenom�

ena�

❏ Two main approaches to friction compensation� I� Non model

based and II� Model based

❏ Model based � u � unom � Ff � where Ff can be calculated

e�g� by the use of adaption and estimation� Recent publica�

tions also employ disturbance rejection schemes�

References on modelling and control of friction

Updated May ��� ����

The literature was collected during the PhD�study of�

Jan Tommy Gravdahl

Dept� of Engineering Cybernetics

Norwegian University of Science and Technology

N����� Trondheim� Norway

Telephone ��� ��������Fax� ��� ��������Email� TommyGravdahl�itkntnuno

References

�Alvarez�� J AlvarezRam�irez� R GarridoMoctezuma� and O Rojas Compensation of friction vie uncertainty estimation in an electrohydraulic drive In Proceedings of the ��th IEEE Conf� onDecision and Control� pages ���������� San Diego� CA� ����

�Amin�� J Amin� B Friedland� and A Harnoy Implementation of a friction estimation and copmenstaion technique IEEE Control Systems Magazine� pages ������ August ����

�Armstrong�� B Armstrong Friction� Experimantal determination� modeling and compensation In Pro�ceedings of the ���� International conference on robotics and automation� pages ��������������

�Armstrong�� B ArmstrongH�elouvry Stickslip arising from stribeck friction In Proceedings of the ���International conference on robotics and automation� pages ���������� Cincinatti� OH� ����

�Armstrong�� B ArmstrongH�elouvry Control of machines with friction Kluwer� Boston� MA� ����

�Armstrong�� B ArmstrongH�elouvry Stick slip and control in low speed moption IEEE Transactions onAutomatic Control� ����������������� ����

�Armstrong�� B ArmstrongH�elouvry� P Dupont� and C Canudas de Wit A survey of models� analysis tools and compensation methods for the control of machines with friction Automatica����������������� ����

�Armstrong�� B Armstrong and B Amin Pid control in the presence of static friction� A comparisopn ofalgebraic and describing function analysis Automatica� �������������� ����

�Bai�� EW Bai Parametrization and adaptive compensation of friction forces Int� Journal ofadaptive control and signal processing� ������������ February ����

�Barabanov�� N Barabonov and R Ortega Necessaray and su�cient conditions for passivity of the lugrefriction model Preprint� ����

�Baril�� CG Baril and PO Gutman Performance enhancing adaptive friction compensation foruncertain systems IEEE Transactions on Control Systems Technology� ������������� ����

�Bliman�� PAJ Bliman Mathematical study of the dahl�s friction model Eur� J� Mech� ASolids��������������� ����

�Bliman�� PA Bliman and M Sorine Easytouse realistic dry friction models for automatic controlIn Proceedings of the �rd European control conference� pages ���������� Rome� Italy� ����

�

�Cai�� L Cai and G Song A smooth robust nonlinear controller for robot manipulators with jointstickslip friction In Proceedings of the ���� IEEE conference on robotics and automation�pages �������� ����

�Canudas�� C Canudas de Wit and V Seront Robust adaptive friction compensation In ��� pages���������� ����

�Canudas�� C Canudas de Wit� P No�el� A Aubin� and B Brogliato Adaptive friction compensationin robot manipulators� low velocities The International journal of robotics research� pages�������� ����

�Canudas�� C Canudas de Wit Robust control for servomechanisms under inexact friction compenasationAutomatica� �������������� ����

�Canudas�� C Canudas de Wit� H Olsson� KJ �Astr�om� and P Lischinsky A new model for control ofsystems with friction IEEE Transactions on automatic control� �������������� March ����

�Canudas�� C Canudas de Wit and P Lischinsky Adaptive friction compensation with partially knowndynamic friction model Int� Journal of adaptive control and signal processing� ������������February ����

�Dominguez M Dominguez� JM Martinez� and JM Michelin Dynamic friction identi�cation using neuralnetworks

�Drakunov�� S Drakunov� GD Hanchin� WC Su� and �U �Ozg�uner Nonlinear control of a rodless pneumatic servoactuator� or sliding modes versus coulomb friction Automatica� ��������������������

�Du�� H Du and SS Nair Identi�cation of friction for control at low velocities In Proceedings ofthe ���� American Control Conference� Albuquerque� NM� ����

�Du�� H Du and SS Nair Low velocity friction compensation IEEE Control Systems Magazine������������� April ����

�Dupont�� PE Dupont Avoiding stickslip through pd control IEEE Transactions on automatic control����������������� ����

�Dupont�� PE Dupont and Dunlap EP Friction modeling and pd compensation at very low velocitiesASME J� of dynamic systems measurment and control� ������������ ����

�Elhami�� MR Elhami and DJ Brook�eld Sequetial identi�cation of coulomb and viscous friction inrobot drives Automatica� �������������� ����

�Friedland�� B Friedland and YJ Park On adaptive friction compensation In Proceedings of the �thIEEE Conf� on Decision and Control� pages ���������� Brighton� England� ����

�Friedland�� B Friedland and YJ Park On adaptive friction compensation IEEE Transactions onAutomatic Control� ����������������� ����

�Friedland�� B Friedland and S Mentzelopoulou On estimation of dynamic friction In roceedings of the��nd IEEE Conf� on Decision and Control� San Antonio� TX� ���� ��������

�Gafert�� M G�afvert Comparision of two friction models Master�s thesis� Lund Institute of Technology�����

�Gafert�� M G�afvert Comparision of two friction models In Proceedings of the ���� IEEE Internationalconference on control applications� pages �������� Hartford� CT� October ����

�Gilbart�� JW Gilbart and GC Winston Adaptive compensation for an optical tracking telescopeAutomatica� ����������� ����

�

�Haessig�� DA Haessig� Jr and B Friedland On the modeling and simulation of friction ASME J� ofdynamic systems measurment and control� ������������ ����

�Hess�� DP Hess and A Soom Friction at a lubricated line contact operating at oscillating slidingvelocities ASME Journal of Tribology� ��������������� ����

�Jain�� S Jain� F Khorami� N Ahmad� and S Sankaranarayanan Friction compensation for drivewswith and without transmission compliance In Proceedings of the ���� American ControlConference� Albuquerque� NM� ����

�Karnopp�� D Karnopp Computer simulation of stickslip friction in mechanical synamic systems ASMEJ� of dynamic systems measurment and control� ������������ ����

�Kim��a JH Kim� JY Jeon� SW Lee� and K Koh Highprecision control of positioning systemswith nonsmooth nonliearities In Proceedings of the ��th IEEE Conf� on Decision and Control�Kobe� Japan� ����

�Kim��b JH Kim� HK Chae� JY Jeon� and SW Lee Identi�cation and control of systems withfriction using accelerated evolutionary programming IEEE Control systems magazine� pages������ ����

�Leonard�� NE Leonard Adaptive friction compensation for bidirectional lowvelocity position trackingIn Proceedings of the ��st IEEE Conf� on Decision and Control� pages �������� Tuscon� AZ�����

�Lin�� CF Lin� TJ Yu� and X Feng Fuzzy control of a nonlinear position testbed with backlashand friction In Proceedings of the ��th IEEE Conf� on Decision and Control� Kobe� Japan�����

�Maron�� JC Maron Nonlinear identi�cation and observer based compensation of friction in mechanicalsystems In Proceedings of the ���� NOLCOS� pages �������� Capri� Italy� ����

�Olsson�� H Olsson and KJ �Astr�om Observerbased friction compensation In Proceedings of the ��thIEEE Conf� on Decision and Control� pages ���������� Kobe� Japan� ����

�Olsson�� H Olsson� KJ�Astr�om� C Canudas de Wit� M G�afvert� and P Lishinsky Friction models andfriction compensation European Journal of Control� ���� To appear

�Panteley�� E Panteley� R Ortega� and M G�afvert An adaptive friction compensator for global trackingin robot manipulators In Proceedings of the SYROCO���� ����

�Panteley�� E Panteley� R Ortega� and M G�afvert An adaptive friction compensator for global trackingin robot manipulators System � Control Letters� ���� To appear

�Popovic�� MR Popovi�c and AA Goldenberg Modeling of friction using spectral analysis IEEE Trans�actions on roboticsa and automation� �������������� ����

�Radcli�e CJ Radcli�e and SC Southward A property of stickslip friction models which promotes imitcyclw generation In ��� pages ���������� ��

�Rantzer�� A Rantzer Friction analysis based on integral quadratic constraints In Proceedings of the��th IEEE Conf� on Decision and Control� pages ���������� Kobe� Japan� ����

�Sankaranarayanan�� S Sankaranarayanan and F Khorami Adaptive variable structure control and applications to friction compensation In Proceedings of the ��th IEEE Conf� on Decision andControl� pages ���������� San Diego� CA� ����

�Serrarens�� AFA Serrarens� MJG van de Molengraft� JJ Kok� and L van den Steen h� controlfor supressing stickslip in oil well drillstrings IEEE Control Systems Magazine� ������������April ����

�

�Song�� G Song� RW Longman� and L Cai Integrated adaptiverobust control of robot manipulatorswith joint stickslip friction In Proceedings of the ���� IEEE International Conference onControl Applications� pages �������� Hartford� CT� ����

�Sothward�� SC Southward� CJ Radcli�e� and CR MacCluer Robust nonlinear stickslip friction compensation ASME J� of dynamic systems measurment and control� ������������ ����

�Tung�� ED Tung� G Anwar� and M Tomizuka Low velocity friction compensation and feedforwardsolution based on repetetive control ASME J� of dynamic systems measurment and control������������� ����

�Vedagarbha�� P Vedagarbha� DM Dawson� and M Feemster Tracking control of mechanical systems inthe presence of nonlinear dynamic friction e�ects In Proceedings of the ���� American ControlConference� Albuquerque� NM� ����

�Walrath�� CD Walrath Adaptive bearing friction compensation based on recent knowledge of dynamicfriction Automatica� pages �������� ����

�Yang�� S Yang and M Tomizuka Adaptive pulse eidth control for precise positioning under thein�uence of stiction and coulomb friction ASME J� of dynamic systems measurment andcontrol� ������������ ����

�Yao�� B Yao� M AlMajed� and M Tomizuka High performance robust motion control of machinetools� An adaptive robust control approach and comparative experiments In Proceedings ofthe ���� American Control Conference� Albuquerque� NM� ����

�Yazdizadeh�� A Yazdizadeh and K Khorami Adaptive friction compensation using a lyapunovbaseddesign scheme In Proceedings of the ��th IEEE Conf� on Decision and Control� pages ���������� Kobe� Japan� ����

�