SICOMAT : a system for SImulation and COntrol analysis of MAchine Tools

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SICOMAT : a system for SImulation and COntrol

analysis of MAchine Tools

Maxime Gautier, Minh Tu Pham, Wisama Khalil, Philippe Lemoine, Philippe

Poignet

To cite this version:

Maxime Gautier, Minh Tu Pham, Wisama Khalil, Philippe Lemoine, Philippe Poignet. SICOMAT : a

system for SImulation and COntrol analysis of MAchine Tools. IEEE/ASME International

Con-ference on Advanced Intelligent Mechatronics, AIM 2001, Jul 2001, Como, Italy. pp. 665-670,

�10.1109/AIM.2001.936546�. �hal-00362669�

COntrol analysis of MAchine Tools

M. Gautier*,M.T. Pham*, W. Khalil*,Ph. Lemoine *,Ph. Poignet ** InstitutdeRechercheenCommunicationetenCyberntiquedeNantes(I.R.C.Cy.N.)

1ruedelaNoe,BP92101,44321NantesCedex03,France.

Laboratoired'Informatique,deRobotiqueetdeMicrolectroniquedeMontpellier(L.I.R.M.M.) 161rueAda,34392MontpellierCedex05,France

Maxime.Gautier@irccyn.ec -nan tes .fr http://www.irccyn.ec-n ante s.f r

Abstract|This paperpresentsasoftwarepackage forthe simulation and the control analysis of machine tool axes. This package which is called SICOMAT (SImulation and COntrolanalysisofMAchineTools),providesalargevariety oftoolboxestoanalyzethebehavior andthecontrolofthe machine. The softwaretakes intoaccountseveralelements suchasthe exibilityofbodies,theinteractionbetween sev-eralaxes,theeectofnumericalcontrolandtheavailability toreducemodels.

I. Introduction

Theneedforthemanufacturertoreducethecostfor de-signingandevaluatingaprototypegoesthroughthe deni-tionofagoodsimulationtool. Thereforewedevelopa sim-ulationenvironmentabletoguidethedesignerinthechoice ofthecomponentsinterferinginthecompletemechatronic systemi.e. exiblemechanicalstructures, actuators, sen-sorsandcontrollers. Theeverincreasingjointspeedand ac-celerationofmachinetoolsleadstodevelopaccurate mod-elstakingintoaccountelasticityofstructureandjoints. A goodcompromisebetweenthecomplexityofadistributed elasticityapproachasniteelementmodelandthe simplic-ityofneglectingtheelasticitywitharigidbodymodelisto consider amulti-body modelwith lumped elasticitiesand rigidbodiesbasedonatechnologyanalysisofthesystem's components[1]. Ablockdiagramand alinearstatespace descriptionofoneaxisorseveraldecoupledaxesare imple-mented. Adescriptionofmulti-bodysystemsbasedonthe roboticformalismisalsoimplemented[2]. Theoriginality ofthisapproachistoprovideasystematicmethodto auto-maticallycalculate thegeometric,kinematicand dynamic models ofcoupled ordecoupled multi-axes machine tools, whateverthenumberofrigidandelasticdegreesoffreedom (dof)ofthesystem. Moreoverthesoftwarecontainsseveral toolstocompletelystudyagivenstructurefromthe model-ing(modalanalysis toolboxandmodelreductiontoolbox) to the control simulation. An other signicant point of thispackageisthe possibility totune thecontroller gains consideringthecomputernumericalcontroller(CNC) com-ponents(PIDwithfeedforwardcontrollerstructure,delays, quantization),themechanicalstructureandthedrivechain components included in the simulator. Two methods are availablein SICOMAT.Therstoneisatime approach

ondoneisbasedonafrequencyautomaticapproach,which guaranteesstabilitymarginsforagivenclosedloop band-widthusingoptimizationtechniques[3][4].

Thepaperisorganizedasfollows:section2describesthe globalenvironmentofthesimulatorandthestructure mod-eling,section3presentsthedierenttoolboxesavailablein thesimulator: modelreduction,modalanalysis,control de-signtechniques(timeand frequencyapproaches). Finally, section4givesanexampleofahigh-speedmachinewitha lineardirectdriveaxis.

II. Description of SICOMAT A. Mainmenuof thesimulator

Fig.1. Mainwindowofthesimulator

SICOMATis designedto easily set up thesimulation environment(mechanicalmodel,CNC,actuatorsand sen-sors model) aswell as the parameter values, such as the numberof massesand springsforthemechanics,the geo-metricalandinertialparameters,therepresentationofthe mechanicalstructurewithlinearstate-spacemodelorwith simulink blocks or with robotics formalism [2]. The user mayselectthedesiredcomponentsinadatabasethat con-tainscommonlyusedmotors,gearboxes,transmissionsand

zation due to CNC are also considered [3]. Thesoftware isentirelyboxes-drivenandenablestheusertodesignand modify avirtualprototype andto easily checkits perfor-mancesin a CAD approach without the need of the real prototype. Themainwindowofthesimulatorisshownon Figure1.

B. Trajectorygenerator

Several mechanical models are implemented in the li-braryof SICOMAT. They are chosen through 3 boxes, Figure1. Thebox'Number ofaxis'allowsto choose ma-chines withone ortwodecoupled linearaxis,orwith two coupled axes. The boxes 'Model on X axis' and 'Model on Y axis' dene the number of masses (M) and springs (S) of the lumped model for each axis respectively. The boxes'Description onX axis'and'Description onY axis' allowtochoosebetweenablockdiagramorasteady state-spaceoraroboticformalismdescriptionofthemechanical model. Inthat last case,someparametersof the descrip-tion are dened in 2 les whose names are given in the box'Associated functions to the model'. Clicking onthe 'OK'buttonrunstheautomaticcalculationoftheSimulink blockswhicharelinkedtogetherandassociatedwith Mat-labroutinestosimulatethesystemwhiletrackingdierent trajectories(straightline, circularinterpolation,),to per-form frequency and time analysis and to display results. AnexampleofasingleaxisisrepresentedonFigure 2.

position set point

Trajectory generator

position

time

position_reference

STOP

vel_ref

vel_mes1

vel_mes2

Ui_ref

Speed controller

Scope

position_reference

Scope

position

Save

Scheme

Quit

Ui_ref

load_position

position_measured

load_velocity

Power converter

Motor

Mechanical structure

position_ref

position_measured

vel_ref_motx

Position controller

Modify

Parameters

Modify

Scheme

u(1)>time_f*1.2

Error

Analysis

Fig.2. Exampleofasingleaxis

C. Modelingof the mechanics C.1 Descriptionofthesystem

Theexampleofamachinecomposedofamotor,a trans-missiongearingwithtwodrivingwheelsandabeltisgiven to illustrate the modeling methods, Figure 3. The mo-tiontransformationfromrotationtotranslationisachieved witharackandagearwheel. Inthisexample,themodelis simpliedto2MassesandoneStiness(2M1S),but more accuratemodelsareavailablein thesimulator.

Thefollowingnotationsareusedin Figure3: mot isthe driving torque. J m ,  m

are the inertia and the angular position of therotorof themotor respectively. J

pm , pm , x pm ,R pm

aretheinertia,theangularand linearpositions

Fig.3. Anexampleofamachineaxis

andtheradiusofthedrivingwheelsupportedbythemotor shaft respectively,with:

x pm =R pm  pm (1) J pc ,  pc , x pc ,R pc

arerespectivelytheinertia, theangular and linear positions and the radius of the driving wheel supportedbytherackandgearwheel,with:

x pc =R pc  pc (2) n b = Rpc R pm

is the ratio ofthe belttransmission, m c

is the massofthebelt. J

pig ,

pig ,R

pig

are respectivelythe iner-tia,theradius and theangular position ofthe gearwheel. k

11eq

istheglobaltorsionstinessbetween m andn b  pig . x cre ,m cre

arerespectivelythelinearpositionandthemass oftherack. x

M

standsfortheloadposition. M load

isthe loadmass.

Internal material damping, viscous and Coulomb fric-tionforcesarealsoconsidered: 

11eq

istheglobalmaterial damping coeÆcient between 

m and n b  pig ,  12eq is the global material dampingcoeÆcient between x

pc and x M , f 11eq

is the global viscous friction coeÆcientbetweenthe loadandthemotor.

C.2 Linearstatespacemodel

The state space model can be obtained from the La-grangianequationasrecalledhere:

M  X+

_

X+KX =F (3) X isthe(nx1)vectorof degreesoffreedomofthesystem, n is the numberof degrees of freedom F is the vector of drivingforces,isthedampingmatrix,M and Karethe massandstinessmatricesrespectively. Inthecaseofthe example,(3)iswritten with:

x=   m x M  ;F =  mot 0  (4) M=  J 11eq 0 0 J 12eq  (5) M 12eq =M cre +M load + J pig +J apig +J pc R 2 pig (6) J 11eq =J m +J am +J pm +m c R 2 (7)

am =  11eq + f11eq n 2 b R 2 pig f11eq nb R pig f11eq nb R pig  12eq +f 11eq ! (8) K= k 11eq n 2 b R 2 pig k 11eq n b R pig k 11eq n b R pig k 11eq ! (9)

Multiplying(3)bytheinverseofthemassmatrixleadsto:  X=M 1 F M 1  _ X M 1 KX (10) Andthestateequationfollows:

_ z=Az+BF (11) Wherez=  _ X X 

isthestatevectorand:

A=  0 n I n M 1 K M 1   ; B=  0 n M 1  (12) I n

isthe (nxn)identitymatrix. 0 n

isthe(nxn) matrixof zeros.

C.3 Simulinkblockdiagrams

This descriptionusesthe elementary blockdiagrams of thesoftware Simulink. The user drawsthe model just as with pencil and paper by using click-and-drag mouse op-erations. This method avoidsto express dierential equa-tionsinalanguageorprogram. Simulinkincludes a com-prehensivelibraryofsinks,sources,connectors,linearand nonlinear components. This approach provides a graph-ical insight which can facilitate the understanding of the model, but it is limited, for sake of simplicity, to models from therigidoneto the8Massesand 7Springs models. Theblock diagramsof the example(3), (4), (5), (6), (7), (8), (9),equivalentto thestateequation (11),is givenon Figure4.

4

load position

3

load velocity

2

motor velocity

1

motor position

s

1

s

1

k11eq

Stiffness

s

1

s

1

1/M12eq

Inertia2

1/J11eq

Inertia1

Coulomb &

Viscous Friction2

Coulomb &

Viscous Friction1

Rpig/nb

mu11eq

Rpig/nb

Rpig/nb

1

Motor

Torque

Fig.4. Example2m1simplementedasaSimulinkblockdiagram

C.4 Roboticsformalism

Another aspect of SICOMAT is to propose an origi-nalmethodofdescriptionbasedonroboticsformalism. [2] proposestoadaptmethods,whicharederivedfromrobotic in order to provide systematic and automatic model for

with elastic joints. The method can provide the kine-matic and dynamic models of such systems. To achieve this goal the method adapts some well-known tools and notations,whicharewidelyusedforrigidrobots. The tech-niqueconsistsonusingadescriptionbasedonthemodied Denavit-Hartenberg (MDH)[5] to denethe kinematicof the system. Given the robot geometric parameters and itsdynamicparameters,thegeometric,thekinematicand the dynamic models are calculated automatically by the SYMORO (SYmbolic MOdelling of RObots) software package [6]. This software provides the dierent models underCorMATLABcodeuseabledirectlyinthe MAT-LAB/Simulink environment. It should be noticed that foridenticationpurpose,thestandarddynamicmodelcan berewrittenintermsofaminimalsetofparameterscalled the base inertial parameters which are the only parame-ters that can be identied [7]. These parameters can be obtained from the classical inertial parameters by elimi-natingthose, which havenoeect on thedynamic model and by regrouping some others. This procedure reduces thecomplexityofthedynamicmodelandwillbeused sys-tematically hereafter in order to decrease the simulation time. Using the base parameters SYMORO calculates theminimaldynamicmodelusedforsimulationorcontrol. D. Electrical drivemodeling

Most of actual machine toolactuators are synchronous motors with PWM converters and include current loop with eld oriented control in the d-q frame. Thus it is assumed that the current loop can be modeled on q axis byarstordertransferfunction,betweenthecurrent set-pointandthedrivingtorque. Thesaturationofthecurrent referenceandthesuppliedvoltagearesimulatedtakinginto accounttheeect ofthe electromotiveforce (backemfE) [3].

E. ComputerNumerical Control (CNC)

ThecontrollersimplementedinindustrialCNCare usu-ally based on a cascade structure with a fast inner loop fortorque control and outer loops for speed and position control.Thisstructureimprovestherobustnessofthe con-troller with respect to the disturbances and modeling er-rors. The speed control loop is classically implemented with proportional and integral (PI) controllers (PI orIP structure) with anti-windup strategy. The position loop is designed with a P controller. In order to decrease the tracking errors,velocityand accelerationfeedforward sig-nalsmightbeaddedtothecontrolloops. Severalaspectsof thecontrolareconsideredinthesimulatorsuchas continu-ousordiscretetimecontrollaws,polesplacementmethod, timeorfrequencyapproaches.

III. Analysis and controltuning of amachine withSICOMAT

tor,adrivepulley oragearboxandatransmission,which canbeaball-screwgear,adrivepulleyorarackand gear-wheel, and aload. Manufacturer's data are given in les regroupedinadatabase. Thenamesofthelesneededfor amodel aregivenand canbemodiedwiththis function. ModifyScheme

Themainsimulator,Figure2,isautomaticallybuiltfrom four elementary Simulink schemes given in a library: the trajectory generator, the power converter, the controller andthemechanicalstructure. Theseblockscanbechanged tomodifythesimulator,takingnewonesfromthelibrary. SaveModelbox

Any new or modied simulator can be saved as anew simulator.

Analysisbox

Thisboxisdedicatedtoanalyzethe exiblemodesofthe mechanicalstructure, to reduce themodelorder,to com-putethetimeandfrequencyresponsesandtooptimizethe controllertuning. Clickingonthisboxopensthefollowing menu:

Fig.5. FunctionsoftheAnalysisbox

A. Modal analysis ofthe System

The "undamped system" function calculates the natu-ral frequenciesas the eigen values of (M

1

K) which de-nesthe undamped system(=0in (3)). The "damped system" function calculates the damping coeÆcients and thenaturalfrequenciesofthefullimplementedmechanical model calculated from the 'linmod' Matlab function [8]. Thecomponentsoftheeigenvectorsarealsocalculatedto beinterpretedasthecontributionofeachdegreeoffreedom onthe system. This isahelp to see thedominantmodes ofthe model and tochoosethe properbandwidth forthe controller.

B. Controllertuning

B.1 Initial tuningonasimplied rigidmodel

The user problem is then to tune the controller gains considering both the CNC components and the mechan-ical structure. A signicant point of SICOMAT is to

ed rigid model. Secondly these values initialize an op-timization procedure which uses the complete model im-plementedinthesimulatortoperformanaccuratetuning. Therearetwobasicapproachesofdesigningthedigital con-troller: the direct discrete-time design or the continuous controllerredesign[9]. Wechoosethesecond onebecause itallows continuous time techniquesto be used, specially thedesigninthefrequencydomainwhichensuresstability margins. Firstly,acontinuoustimecontrol lawisdened. Secondlyit is discretized and then it is approximatedby continuous transfer function, such that the gains can be calculated with a continuous controller which takes into account the eect of digital control in the bandwidth of theclosed loop. Detailscanbefound in [3], [4]. At rst, thegainsK

p ,T

i

ofthespeedloop,aretunedinordertoget aphasemargin' mv atafrequency! vit whichdependson thefrequencyf meca

oftherst exiblemodeoftheprocess (usually!

vit =2f

meca

=(4to 10)). Thenthe gainK v

of thepositioncontrolleriscalculatedinordertogetaphase margin'

mp

. The tuning must leadto a behaviorfor the speedloopsimilartotheFigure6. T

bov

(s)istheopenloop velocitytransferfunction.

Fig.6. Phasemarginofthespeedloopwiththerigidmodelandthe IPcontroller

B.2 Accuratetuning of thecontrollertaking into account thecompletemode

These values initialize next an optimization procedure using the full model to perform an accurate tuning. At this stage,the complete model implemented in the simu-latoris taken into account: lumped model of the exible mechanics, digital control and location of measurements. The'dlinmod' Matlabprocedure automatically calculates highorderdiscrete transferfunctions which makes impos-sibleto getanalyticalexpressions forthegains. Theyare calculatedwith optimization techniques, using the proce-dure'fmins',basedontheNelder-Meadsimplexmethod[8] in orderto satisfythephasemargins andbandwidths. In caseof thecompletemodel, thedelaysandtheoscillatory polesandzerointroducedbythenumericalcontrolandthe exiblemechanicsmakethegainstuningverydelicate. Too smallgainmarginmaybeobtainedinspiteofagoodphase margin(typically6dBgainmarginis needed). The tuning procedure consists then in computing again the gains by optimizationwithgainmargincriterion,startingfromthe

As analternativeto theautomatic and optimized gain tuning,atimeapproachproposedbyNCmanufacturersis implementedinSICOMAT.Themethodconsistson sim-ulating step responses tuning the parameters of the con-troller successively. At each iteration, the simulator per-formsasimulationwith thenewvaluesof theparameters ofthecontroller. Therststepis thetuningof thespeed loop. The integral gainis xed to a largevalue (0.5s) in order to move the integral eect to low frequencies, out-sideo thevelocitybandwidth. The proportional gainis adjustedrunningsimulationsofthevelocityclosedloopin ordertogetastepresponseovershootcloseto10%. Then the integral gainis adjusted to get a stepresponse over-shoot between20%and 40%.Thesecond stepis to adjust the proportional gain of the position controller in order toget adesired overshoot. Ateach iterationSICOMAT providesnumericalinformationonthetimerisingandthe overshoot.

C. Model reduction

The mathematical models obtained with SICOMAT are often highly order because theytake account the dy-namics of rigid bodies, the elasticity of bodies and me-chanical transmission, thedynamics of electricactuators, theeectofnumericalcontrolasdelays. OnediÆcultiesin designingcontroller for complexsystemslies in the prob-lem to represent a complexmodel by aequivalent model which has a smallernumber of degrees of freedom (dof). ThreemethodsareimplementedinSICOMAT:

1. The rst one is based on the calculation of the eigen-valuesand eigenvectorsof A matrix 12, which are sorted in order to cancel the m fastest modes of A with match-ing static gain. The state of the reduced model has lost itsphysicalmeaningwithrespecttothedofdenedbythe initialstatevector.

2. The second oneuses the partial Gramianoperators in ordertotakeintoaccountsomecontrollabilityand observ-ability aspectsofthesystem[10][11][12][13]. This method keepsthedrawbackof theinterpretation ofthedof ofthe reducedmodel.

3. Theaimofthethirdoneistokeepthemostsignicant dof of thereducedmodel amongthose of theinitial state vectorXof(3),asaresultofatechnologicalanalysisofthe mechanicalsystem. Thereducedmodel isthen calculated by regrouping serial or parallel masses and stinesses of thefullmodelwithverysimplerules. Thismethodisquite lessaccuratethanthersttwoonesfromasystemanalysis pointofview,but keepsaninterestingphysicalmeaning.

IV. Analysis and simulation of a 5M4Smodel A. Description ofthe system

SICOMAThas been devoted to alargenumberof in-dustrial cases. As an example, a model composed of 5 masses and 4 springs (noted 5M4S) will beconsidered in thispaper(Figure7). Thismodelrepresentsasingleaxis

pendicular axis. The two motor's primary are mounted like a gantry type, but very close side to side on a very rigidstructurein orderfor thegantrytobeconsidered as only one equivalent motor. The primary part is a short

Fig.7. 5M4SModelforahighspeedmachinetoolaxis

moving coil assembly and the secondary part is a long permanentmagnet assembly. The notationsused on Fig-ure 7are: is the driving force, R

o (O o ;x o ;y o ;z o ) is the referenceframe, M structure and k structure arerespectively themass ofthe structure and itsstiness w.r.t. the bed, m

secondary andk

secondary

arerespectivelythemassofthe secondarypartof the linear motor and its stiness w.r.t. the structure, m

prinary

is the mass of the primary part of the linear motor, m

sensor and k

sensor

are respectively the mass of the linear scale sensor head and its stiness w.r.t. the primary part, M

load and k

load

are respectively the mass of the load and its stiness w.r.t. the primary part. Shortly,thelumpedmodeliscomposedof: 5masses M structure , m secondary , m primary , M sensor , M load and 4 stinessesk structure , k secondary ,k sensor ,k load .

We will also consider internal material damping, vis-cous friction coeÆcients and Coulomb friction forces: 

structure

is thematerialdampingcoeÆcientofthe struc-ture, 

secondary

isthe material dampingcoeÆcientof the secondary partof thelineardrive, 

sensor

isthe material dampingcoeÆcientoftheload,

load

isthematerial damp-ing coeÆcient of the sensor head support. F

vmotor is the viscous frictioncoeÆcientbetweenprimaryandsecondary partofthelineardrive,F

Coulombmotor

istheCoulomb fric-tionforcebetweenprimaryandsecondarypartofthelinear drive.

These simulations are carried out with the follow-ing parameters for the 5M4S model: M

structure = 3667kg, m secondary = 232kg, m primary = 92:305kg, M sensor = 270:2kg, M load = 0:008kg, k structure = 1e9N=m, k secondary = 1e12N=m, k sensor = 3:8e8N=m, k load =1e7N=m, structure =19:15N=(m=s), secondary = 107:70N=(m=s),  sensor = 4:6548N=(m=s),  load = 0:0089N=(m=s),F vmotor =88:1N=(m=s),F Coulombmotor = 142N F vmotor andF Coulombmotor

areissuedfromidentication results.  structure ,  secondary ,  sensor and load are given

B. Mechanical exiblemode analysis

Thefrequencyanalysistoolboxgivesthemechanical fre-quencies,thepulsationandthedampingcoeÆcientsofthe system. Weobserveinthisexample(Figure8)arstmode near from f

meca

= 80Hz. The bandwidths of velocity and position loop can be then respectably choose equal to ! vit = 125:6rad=s (2f meca =4) and ! pos = 31:4rad=s (2f meca =16).

Fig.8. Frequencyanalysisofthesystem

C. Controllertuning

The velocity phase margin ' mv

of each axis is chosen equalto 45

o

withaPIstructure. Thefrequencyandtime responsesofthevelocitylooparegiveninFigure9.

−600

−500

−400

−300

−200

−100

0

100

−80

−60

−40

−20

0

20

40

Open Loop Phase (deg)

−6 dB

−3 dB

0 dB

2.3 dB

6 dB

Open Loop Gain (dB)

Speed Nichols Charts

0

0.05

0.1

0.15

0.2

0.25

0.3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Step response of speed loop

Time (s)

Speed (m/s)

Fig.9. Frequencyandtimeresponsesofthespeedloop ThedierentloopsonNicholsdiagramsoftheFigure 9 aredueto thepoorlydampingmodesoftheprocess. The phasemargin'

mp

ofthepositionloopisequalto80 o

. The frequencyandtimeresponsesofthepositionlooparegiven inFigure10. −400 −350 −300 −250 −200 −150 −100 −50 0 −50 −40 −30 −20 −10 0 10 20 30 40

Open Loop Phase (deg)

−6 dB

−3 dB

0 dB

2.3 dB

6 dB

Position Nichols Charts

Open Loop Gain (dB)

0

0.1

0.2

0.3

0.4

0.5

0.6

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Step response of position loop

Time (s)

Position (m)

Fig.10. Frequencyandtimeresponsesofthepositionloop Thecontrollertuningisperformedinordertoachievethe desiredphasemargins.Byselectinginthedesigncontroller toolbox,thefrequencyoptimizationproceduredescribedin the Section 3.2.2, the following parametersare computed in Table I. The performances obtained with this set of

the speedloopof ' mv

=45 with abandwidth of ! vit

= 126rad=s. Fortheposition loop,weobtained'

mp =80 o with abandwidthof! pos =33:5rad=s. Parameters K p (s 1 ) T i (s) K v (s 1 ) Initial tuning 94.26 0.009 24.8 Optimizedtuning 97.1 0.009 30.26 TABLEI

Designofthecontroller

V. Conclusion

This paper presentsthe software package SICOMAT, which is devoted for the simulation and the prediction of the closed loop performances of high-speed machine tool axis. The simulations are carried out in the Mat-lab/Simulink environment. Several toolboxes give the user theopportunityto completelymodeland analyzeits process. The mostimportantcontributionfor the model-ingisthemechanicalmodeling,whichisbasedona multi-bodystructuremodelwithlumpedmassesandelasticities. The analysis is performed through the calculation of the mechanical exible modes, the controller tuning and the computation of the dynamic behavior. Classicalmachine tool axesare implemented in a databaseorcanbe easily createdbytheuser. Futureworks willconcernthe exten-sionofthis workforanynaxes.

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