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/[email protected] Manufacturing Science and Technology
PO Box 883, Kenmore, Qld 4069, Australiae-mail: [email protected]
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
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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-
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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
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IdentifiedEstimated
5 6Time[s]
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\", \.... \
".\
".'".1
~1
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~~~
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\ :/ ".' :"o "J ,:, .•••' ;:
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~ -2 I~~:.~:~.. ~.,..:~..:..~ 0: '. _~ ;"#'/ ,,' I·'~\.: •. ; .• .; ;0 ~.'::.:-' ,.2 I -. - ~ :":il~~'rV" ,~, I , I
-4 I I , I
I I "\ / \ I
~ ',,, ,,."I I ~'
, 'I ~
\ .< I·
-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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