Model-Based Friction COIllpensation in Hy-draulic Servo Sy-steIlls

A. Bonchis1,3, Q. P. Ha1,3, P. I. Corke2,3, and D. C. Rye1,3

1Department of Mechanical and Mechatronic EngineeringThe University of Sydney, NSW 2006, Australia

e-mail:adrian/quang.ha/rye@mech.eng.usyd.edu.au2CSIRO Manufacturing Science and Technology

PO Box 883, Kenmore, Qld 4069, Australiae-mail: pic@cat.csiro.au

3eRe for Mining Technology and EquipmentPO Box 883, Kenmore, Qld 4069, Australia

Abstract

In the general framework of tracking control ofhydraulic servo systems, this paper presents acomparison between two main possibilities toinclude friction information in the picture: ex­perimental identification and estimation. Ex­periments were first conducted in order to finda suitable representation for friction in the sys­tem. We then looked at two observers re­ported in the literature (known as Friedland­Mentzelopoulou and Tafazoli) for simultane­ous on-line estimation of friction and veloc­ity. Additionally, we developed a new variable­structure observer for the same purpose. In or­der to compare results, a model-based frictioncompensator using acceleration feedback con­trol has been used. The best tracking perfor­mance has been achieved using the identifiedfriction model, at the expense of considerabletime spent with the experimental identification.Friction estimation using nonlinear observersare a viable alternative as far as model-basedfriction compensation is concerned, but a lossof accuracy occurs.

1 IntroductionAdequately coping with friction is a must nowadays forposition and force controllers, that are given tight perfor­mance specifications. Friction considerably diminishesthe force or torque available at the actuators, and theloss can be anywhere from 10-15% [16] and up to 30%[3]. Compensating for friction can be done using model­based and non-model-based methods. Here we will focusour attention on the former one, which basically requirethat the controller must be provided with quantitative

184

information on friction. As direct measurement of fric­tion is not possible, two options are experimental frictionidentification and the use of nonlinear friction observers.Note that in the end, both methods entail the use of amodel, and finding some constants (model and estimatorparameters) .

In hydraulic servo-systems, friction is generally mod­elled as a constant plus a velocity dependent term[11, 10]. Many practical instances have seen the 'veloc­ity term dropped from the model and friction assumedconstant. For the system at hand, experimental fric­tion identification has been conducted. The result wasa practical model for friction, incorporating a Coulombcomponent and head and rod-side pressure dependentterms [2]. The identified pressure dependent model iscapable of describing friction at low velocities, whichis one of the main issues in motion control. A classicstatic-kinetic template has also been applied to the ex­perimental data. A velocity threshold value has beenidentified, where the friction slope changes by an orderof magnitude.

Nonlinear reduced-order observers have been used forfriction estimation. In essence, these observers are as­suming friction to be of Coulomb type. They requireposition measurements and velocity estimates [4], [13],or velocity measurements [5], as well as the amount ofthe external force exerted on the moving part. In or­der to increase robustness of estimates against parameter .variation, a new observer was developed using a variablestructure systems approach [7].

To compare the two different approaches, as well asthe observers among themselves, a friction compensationcontrol has been applied. In electrical servo systems, thisis a straightforward technique, due to the proportional­ity between the control current and the output torque.This is hardly the situation in hydraulic servo systems.

F.. ... x,v

. ...•...••.•..........•.•.,. -4

500

1500

1000~""""""'" .

~ 0 ~ [ ; ; : : : .

.2 .

~ -500 ........•..j ~ ; :.: ; : ; .

Figure 2: Experimental friction.

200150100_2500'---~----'------I.__..J--_-J.-_-l..__L...----J

-200 -150 -100 -50 0 50PWton VeIoctty (mmla)

P T

Figure 1:· Experimental setup. and has been emphasised before [1]. To achieve it, awarm-up procedure was devised and used.

Acceleration feedback has been used in order to achieve·friction compensation in this case [14], on the groundthat the estimated. acceleration bears friction informa­tion.

In the. following section, we -Will concentrate on. theconfiguration of .. the system .used for the study of fric­tion in the hydraulic cylinder. Section 3 details the twofriction models, as they emerged from the experimentsconducted. It also looks at the observer-based frictionestimation, including the new variable structure (VS)observer. The results ofapplying them for friction com­pensation are show.n in Section 4. Conclusions drawnfollow in Section 5.

2 System>Configaration

The experimental setup .•• is part ofa4-DOF.generic min­ing manipulator developed by CMTEjCSIRO as a testbed for research in automation.·.of heavy-duty hydraulicequipment [8]. The axis on which experiments were con­ducted consistsofadoubleiacting,.single-side rod hy­draulic cylinder, driven via a proportional directionalcontrol valve,as shown.in Figure 1. Typical transducersprovide measurementsofpiston positiouandpressures atboth ports.. Experiments for friction. id~ntification wereconducted. in open loop, with the control signal to theamplifier .varying between ± 9V.

Because of open .l()op control and. the presence of hy­draulic hoses of considerable length it was necessary toensure that a constant control input would result in con­stant flow rates, which justifies the presence of the twoflow meters installed at the cylinder ports. One of themain concerns was that' of achieving repeatability in fric'"tion identification experiments.. This is a critical issue

3 Getting Quantitative Information onFriction

3.1 Friction Models and ParameterIdentification

The simplest way to study friction in mechanisms is toconsider a motion with constant velocity between theparts' in relative motion. A quick look at the equation ofmotion for the piston reve'als that in this case, frictionequals the hydraulic force. Indeed:

(1)

wherepl,P2 are the pressures at the cylinder ports,AI, A2 the piston. areas, Fj •• the. friction force, M thepiston mass .and x its. displacement. A constant.· volt­age has been applied to the valve's servo-amplifier,andsteady~statehasbeen reached after a certain time inter­vaL .• Raw data obtained has.··been visualised inFi~ure 2where friction is plotted as a function of velocity.•. It canbe ·seen· that friction· displays>two distinct. zones ·both inextension and retraction. . A sharp increase in friction .oc­curs in areas close to the origin, corresponding to smallvelocities, whereas for values of .velocity.. above a .certainthreshold, the rate ofincrease is one.order of ma~nitudesmaller. Friction. magnitude wasifound. to .begreater inretraction than in extension.

The explanation relies on the particular configurationof seals. As the cylinder isofadouble action type, sealson the piston must have to be>symmetrical to work inboth directions...>Atthe •. pistonrod .'. gland however, thewipers only .work during retraction, when they .have. toremove any dil'tfrom.theexposedpart of the rod. Natu­rally then, friction is greater durin~.the retraction move-

185

ModelCoefficients

RMS RMSNo Ext Ret1 XI,2,3,5 :j:. 0, X4 = 0 189N 304N2 XI,2,3,4,5 f=. 0 9.12N 11.0N3 XI,3,4,5 :j:. 0, X2 = 0 9.62N 11.8N4 XI,5 :j:. 0, X2,3,4 = 0 102.6N 151N

Table 1: Friction models and corresponding RMS errorsfor extension and retraction

moving under the influence of some external forces, in­cluding friction.

The Friedland-Park ol>server [5] represents friction asa constant times the sign of velocity, which is actuallythe symmetric Coulomb friction model. It estimates theconstant usi:mg measurements' of velocity, and externalforces other than friction acting on the body subjectedto friction. The equations of the nonlinear reduced-orderobserver are postulated in the form

F=iJ;.sgn(v)

it = z - klvl lJ

Z=k· p·lvI JJ -1

• (w - iz) •sgn(v)

(3)

(4)

(5)

(9)

(6)

(7)

(8)

(10)

(11)

(12)

FJ = -L2·(j

~ =v -(jim

v= Zv + kv • x

Zv = -kv •v+ u

u =w - it · sgn(v)

3.3 The Variable Structure FrictionObserver

Developments in the theory of discontinuous observerswith a variable structure [15] encouraged the develop­ment of a new friction and velocity observer [7]. Themain advantage·sought is to enhance the'robustness ofthe observer against plant parameter variations. Thediscontinuous observer cali be described by

with u representing the nett acceleration, Zv the velocityestimator state, and kv being the design parameter. Aslightly changed version h~ been introduced by Tafazoliet al.[13], by replacing (7) with

where F is the estimated friction, iJ; the parameter to beestimated, v the measured velocity, w the accelerationdue to forces other than friction and z is the observerstate. Selection of the two design parameters, the gaink > 0 and the exponent p > 0, is based on the condi­tion that the estimation error converges asymptoticallyto zero, and v is bounded away from zero.

In many instances however, position instead of ve­locity measurements are available, and as such a ve­locity observer was added to replace velocity measure­ments in the above equations. The new observer, knownas the Friedland-Mentzelopoulou friction observer, esti­mated velocity as

200

Figure 3: Pressure based friction model.

-25~~ -150 -100 -50 0 50 100

Pilton VIIIoc:itV .""".]

~-600

c.s!lia: -1000L. · ..:.· .. ·· ·:· .. · · ;.·· , J.':.· ···· , :- -i

-1500~'"''''''.,,: ~ ; ,J •• .: ;; :•••• , , .;

mente A general model was considered first:

where XI, ... ,5 are the coefficients to be determined, Pl,2

pressures at the cylinder ports, and v the piston speed.The coefficients were determined for several particular

cases. A Maximum Likelihood approach was used to de­termine the best fit. Table 1 lists the models tried andthe corresponding Root Mean Square of the error vec­tor in each of the cases. As indicated, the identificationof parameters was performed separately for the pistonextending/retracting case. Although model number 2gives the closest fit, model number 3 can be chosen todescribe friction as it has a simpler expression and prac­tically gives the same error as model 2. For the valuesidentified for Xs (64 in extension and 0.1405 in retrac­tion) the loss of accuracy is less than 1% when the veloc­ity dependent term is neglected. The friction computedusing this model is shown in Figure 3.

3.2 Adaptive Friction Observers

The concept of an observer for a dynamic system wasintroduced by Luenberger [9]. An observer-based ap­plication for friction estimation and .compensation wasreported in [5]. In this section, the system for which ob­servers are considered, is a single degree of freedom mass,

186

10

ReferenceActual

ReferenceActual

5Time[.}

(a) Path following performance.

0.259

0.2615

0...

0.2585

! 0.261

io...~!

i 0.26c:2l0.2595

0.26 .

0.16"-'--~---'---'-"";'----'------'-----l-_--l-_--4.._--l

0.17

0.18

~0.23iii10

.22

i 0.21

S..§ 0.2

l0.19

0.24

0.25

cr =M · sgn(x- x) (13)

with M > 0, L 1 , and L 2 being the observer parame­ters, x, v, and FJ representing position, velocity andfriction respectively, with the usual 'hatted' notation forestimates. Using results from the singular perturbationtheory, the convergence of the observer has been provedfor L 1 < 0 and L 2 > O. The switching action in theobserver dynamics (13) results in chattering in the con­trol signal, with the potential danger of excitingiihighfrequency dynamics. To avoid this, a fuzzy reasoningtechnique [6] replaces the signum function (13) with

u = M · tanh(Y - Y) (14)ley

4 Simulation StudyTo test the options for proviciiIlg friction information dis­cussed so far,anacceleration feedback. control. has beenused. This algorithm has been successfully applied byothers [14] in an attempt to implement a friction com­pensation scheme for.hydraulic servo-positioningsys­tems. In. DC .electric(motors,the .•proportionality be­tween thec0I.Il.mandcurrent .and motor t()rque ·iconsid­erablysiInplifies.(the task.. This (prop()rti()nalityis notpresent .•.• iJ1hydraulic .• actuators..••••..• By .using accelerationfeedback however, the controller receives indirectly a hinton the. friction level in the system.

The control law for friction compensation is given by

1.21.151.05 1.1Time[.}

0.258'-----...r..----I--..........II..---....L.-_--I-__4--,;_~_--J

0.9 0.95

Figure 4: Simulated position tracking using friction com­pensa.tionoased on the identified friction·· model.

(b) Delay and error.

Ithas to be mentioned that while the identified frictionmodel accounts for a difference in the/level of friction inextension aIldretraction, all the observers are using asimpleCouloIIlbmodelforfriction.However, they canperform reasonably well in instances where friction isnot constant and symmetrical (whienistne case in mostpractical )situations) .. asisho'WJ1 in Figure 7.

Con'trollerperformance ..hen using. either.,ofthe ·,ob­servers/to<compensate<forfriction,canoeimproved·byusingi/differentgains(a, (3}>ineitensionand retraction.Toexemplify,Figure8show8ithe control signal using theVS ••··observer.with a.controller.having.the .•sameand· thendifferent) set.)•. of gains, .. depending.on/the•motion .. direc­tion. Ani important<aspect))is r()bustllessoftheobser~ers

to system.· parameters/.varia.tion.<Totest .. it,ithesupplypressure. has beenchangedfrom80barto20barandthe

with the"controller gains a and (3 chosen in first instancebased on a heuristic method described in<lt2], and thentuned ··to further· improve the performance of the posi­tioning system.

Using the identified friction model or one of the fric­tion observers described in Section 3, the accelerationestimate.a.. needed in .•·(15) can be·coIIlputed. Allfrictionobservers also<provide ..a velocity estimate v.using<directposition IIleasurement,whileinthec~eofcoIIlpensationusing the friction IIlodel,vis the output of .a .. low-passfiltered ...•. differentiator,/whose•.equations.are.similar to .. (6)and (9). The friction observers considered in this workwere Friedland-Mentzelopoulou, Tafazoli, and tbe newVS observer. However, results are presented involvingthe use of the· latter two,··as .the Tafazdliobserver is animprovem.enti··ove~.F'riedlan~-:MentzelopOlllou.

Figure 4 shows the siIIlulated tracking .~erformance us­ing the identified friction model to. c~mIlensate for fric­tion... BycoIIlparison, •••••• ~it'\lre5/shows .the .performanceobtained with.theTafa~oliandVS .. observers..Trackingerror of a compensator based on the identified /frictionmodel.was.also.coxnparedagai.nst the error obtained witha PD .control,witbout.compensating for. friction. Simu­lation results are shown in Figure 6.

187

X 10-3S"...----r---....,....-------,---------r------,--Y'"""---.,----r---_.

IdentifiedEstimated

5 6Time[s]

"\ ,\

\", \.... \

".\

".'".1

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I \ I

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~ -2 I~~:.~:~.. ~.,..:~..:..~ 0: '. _~ ;"#'/ ,,' I·'~\.: •. ; .• .; ;0 ~.'::.:-' ,.2 I -. - ~ :":il~~'rV" ,~, I , I

-4 I I , I

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-8 ~ ",' \ II~~. ~?,! :..:'~'~ ~tion

105 6Time[s]

-3

:[1ot:

~ 0

!CL -1

]:1gw 0g~Q. -1

-2

-3

(a) Tafazoli observer.

5 6Tme[s]

(b) VS observer.

Figure 6: Tracking error with and without friction com­pensation (compensation based on identified model).

identified model was used. However, less time and effortwas needed to tune the observers than to carryon theexperimental identification. Due to manufacturing tol­erances, material properties, etc, identification has to bedone for each actuator separately, which amplifies thetime requirements. The level of accuracy when' com­pensating using the Tafazoli and the VS observer wassimilar, but the VS observer proved to be more robustto system parameter changes. The friction 'lag' estimateof the VS observer does not affect the positioning error.Compared with a PD control, all the friction compensa­tion methods investigated here resulted in a reduction ofthe tracking error with at least a factor of 1.6 in exten­sion and 2.2 in retraction.

Figure 5: Tracking error when compensating using iden­tified friction model and the Tafazoli and VS observers.

inertial load from 6kg to 96kg. Position error due tothis change for the controllers using estimates from theTafazoli and VS observer are shown in Figure 9.

Acknowledgements

This-work was funded by the Cooperative.>Research·Cen­tre for Mining Technology and Equipment Brisbane,Australia. The authors also would like to thank theircolleagues Graeme Winstanley and Stuart Wolfe fromthe Automation group,CSIRO Australia for their help.

5 ConclusionsModel-based friction compensation can be done in hy­draulic servo systems using experimentally identifiedfriction models or using nonlinear friction observers. Interms of tracking performance the best result was dis­played by a controller using friction computed in accor­dance with an experimentally identified model. The fric­~ion observers considered in this work were Friedland­Mentzelopoulou, Tafazoli, and a new VS observer. Whenfriction was compensated using their estimates the track­ing error was (50 ... 80)% bigger than the case when the

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188

1000r---..,.--~- --r--....,--~----r--.,..-----..,

10

Ta I ObserverVI er

5TimI(.]

.":··I';';;:--""";:·:·~~... I

:- ,,: ./ " ".'~\:: I, l . \\ I

,~,~

5 6Time (a]

-2000L-_~_--I-_---.L.__o&.-_-'--_--L.._-"__J...-.-'

1

Identified FrictiOnTafazoll ObserveVSObserver

Figure 7: Friction computed using identified frictionmodel and estimated by the Tafazoli and VS observers.

Figure 9: Positioning error as a result of changes in thesystem parameters.

Figure 8: Control using same and different sets of gains(0:, (3) in extension/retraction and a VS observer.

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