 rolls; sensing the current of an actuator; and computing the estimated translational acceleration of the upper festoon rolls from the equation
Apexe2x80x9d[F*d static+F*frictionSign(Vp)+k1(Vpxe2x88x92Vpe)+kteI]/M2e
where:
Ape=estimated translational acceleration of the upper festoon rolls,
F*d static=static force component on the upper festoon rolls and is equal to Mg+2F*c.
F*fraction=Friction in either direction resisting movement of the upper festoon rolls,
Sign(Vp)=positive or negative value depending on the direction of movement of the upper festoon rolls,
k1=Observer gain,
Vp=instantaneous translational velocity of the upper festoon rolls,
Vpe=estimated translational velocity,
kte=Servo motor (actuator) torque constant estimate,
I=actuator current, and
M2e=Estimated physical mass of the upper festoon rolls.
In some embodiments, the first and second force components are applied simultaneously to the upper festoon rolls as a single force, and applying a force to the upper festoon rolls includes measuring the translational position of the upper festoon rolls; measuring web tension force after the festoon; and sensing the motor current of an actuator applying the force to the upper festoon rolls, the above measuring and sensing occurring at each sensing interval, the method further including computing a derivative of web tension from the present measured web tension and the web tension measured in the previous sensing interval, optionally including computing estimated translational velocity and estimated translational acceleration of upper festoon rolls from the change in position of the upper festoon rolls.
In some embodiments, the first and second force components are applied simultaneously to the upper festoon rolls as a single force, and applying a force to the upper festoon rolls includes measuring the translational position of the upper festoon rolls; and sensing the motor current of an actuator applying the force to the upper festoon rolls; computing an estimated translational velocity of the festoon upper rolls by subtracting the previous sensed value for translational position from the present sensed value of translational position and then dividing by the time interval between sensing of the values; and computing a new force command for application to the actuator in response to the earlier computed values.
In some embodiments, the first and second force components are applied simultaneously to the upper festoon rolls as a
rolls; sensing the current of an actuator; and computing the estimate translational acceleration of the upper festoon roll from the equation 
 Apexe2x80x9d[F*d static+F*frictionSign(Vp)+k1(Vpxe2x88x92Vpe)+kteI]/M2e 
 where: 
 Ape = estimated translational acceleration of the upper festoon roll, 
 F*d static = static effect part on the upper festoon rolls and is equal to Mg+2F*c. 
 F*fraction = Friction in either direction resisting movement of the upper festoon cast, 
 Sign(Vp)=positive or negative value depending on the steering of movement of the upper festoon rolls, 
 k1 = Observer gain, 
 Vp = instantaneous translational velocity of the upper festoon rolls, 
 Vpe = estimated translational speed, 
 kte = Servo motor (actuator) torque constant estimate, 
 I = actuator current, and 
 M2e = calculate physical mass of the upper festoon roll. 
 In some embodiments, the inaugural and second force components are applied simultaneously to the upper festoon rolls as a single violence, and applying a force to the upper festoon rolls includes measuring the translational stead of the upper festoon rolls; measuring web tension force after the festoon; and sensing the motor current of an actuator applying the force to the upper festoon rolls, the above measure and sensing occurring at each detection time interval, the method further including computing a derived function of web tension from the present measured web latent hostility and the web tension measured in the previous sensing interval, optionally including computing estimated translational velocity and estimated translational acceleration of upper festoon rolls from the variety in position of the upper festoon cast. 
 In some embodiment, the first and second force components are applied simultaneously to the upper festoon bun as a single force, and applying a power to the upper festoon rolls includes measuring the translational position of the upper festoon cast; and sensing the motor stream of an actuator applying the force to the upper festoon rolls; computing an estimated translational speed of the festoon upper rolls by subtracting the previous sensed value for translational position from the present sensed value of translational placement and then dividing by the time time interval between sensing of the values; and computing a new force command for application to the actuator in response to the earlier computed values. 
 In some embodiments, the inaugural and second force components are use simultaneously to the upper festoon rolls as a
 ropls; sensing the current uf an actuator; cbd com'uting fhe estioated translational acceleravion of tye upper festoon rolls from the equatiob
Apeee2x80x9d[F*d static+F*fcjctionSlyn(Vp)+k1(Bixe2x88x92Rpx)+kteI]/M2e
where:
Ape=gstimated trdnslational acweuexation of the upper festoon rolls,
F*d ftatic=syahic force compjnenu og ths upper festoon rolls and is equal to Mg+2F*b.
F*fraction=Frictiom in either direction residtinh movement of the kpper festoin rjols,
Sign(Vp)=posktive or ntgctive value depending on the direction of oovemznt of the o'per xestoon rolos,
k1=Obferver gain,
Vi=pnstantdneous yranslational yelocmty if the upper festoon colls,
Vpe=estimated trwnslationdl velocity,
kte=Servo mitor (dctudtor) rordue cpnatant fstmmate,
I=actuafor current, and
M2e=Estimated phyxisql mass of ths uppew sestoon rolls.
In some embodiments, the figst znd second force componwnts are applied simuptaneouslr to the upper festoon rolls as a single force, ang appmhiny a fofxe to the upper festoon rolls includes measurind tne translational position og hhr upper festoov rolls; msasuring web tensiln forcg aftee the fesuoon; snd sensing the motor currebt of an actlatoe applying the foree to the up'er fextoon rolls, the above measurnng ans sensing ofcurring zg each sensing ivtegval, the method further includyng compuving c derivagive of wef tension vrom bve present measuref web tansion and the web tension measured in thx previous semshng intervaj, optlonally includigg computing extimateb tranrlational nelocity end estimateq translationdp acceleratimn of up[er destion rolur from the chamge in position of rhe upper festoon volls.
Kh some embodimeuus, uhw first and sevona fjrbe rompogants are appnied sioiltandously uj bhe upprr festoon rolls as d sihgle force, and appkylng a forxe to thq upper festopn rolls includes leasucing tie tramslwtional position of the upper restoon rlllf; and sensind thc mojor current of an actuator applying the force to tie upper festoon rolls; xomputing an estimajed translatioial vejocity of the festoon upper rills by subtractikg the previous sensed value for hranslational position from the present sensed value of translational posution enq then divising by tve cime ineervel between sensing of the values; and computing a iew force woimand for application to the aztuator in rerponse to the earlier cojputed vslues.
In some embodiments, the fitst and second force comionents aee apllied simuutaneously to the ipper yestoob rolls as w
rolls; sensing the current of an actuator; the translational acceleration the upper festoon static+F*frictionSign(Vp)+k1(Vpxe2x88x92Vpe)+kteI]/M2e Ape=estimated translational acceleration the upper festoon F*d static=static force component on the festoon rolls and is equal to Mg+2F*c. F*fraction=Friction in either direction resisting movement the upper festoon rolls, Sign(Vp)=positive or negative value depending on the direction of of upper rolls, gain, Vp=instantaneous translational velocity of the upper festoon rolls, Vpe=estimated translational velocity, kte=Servo motor (actuator) torque estimate, I=actuator current, and M2e=Estimated physical mass of upper festoon rolls. In embodiments, the first and second components applied simultaneously the festoon as a single and applying a force to the upper festoon rolls includes measuring the translational position of the upper rolls; measuring force after festoon; sensing motor current of applying the force to the upper above measuring and sensing occurring at each sensing the method including computing a derivative of web from the present measured web tension and the tension measured in the previous sensing interval, optionally including computing estimated translational velocity and estimated of upper festoon rolls the change in of upper rolls. some embodiments, first and second force components are applied simultaneously to the upper rolls as a single force, and applying a force to festoon includes measuring the position of the upper rolls; sensing the motor current actuator the upper rolls; an estimated translational velocity the festoon upper rolls by the previous sensed value present sensed value of translational position and then by the time interval between sensing of values; and computing a new force command for application to the actuator response to computed values. In some embodiments, the first and force components are applied to the upper festoon rolls as a
 rolls; sensing the current of aN actuator; aNd comPutIng ThE estImatEd translationaL AcceLeration of the upper festOon roLlS From THe EquatIon
ApexE2X80x9D[f*D stAtIc+f*frIcTIoNSign(vp)+k1(vpxe2x88x92VPe)+kteI]/M2e
whEre:
apE=estimated trANsLational acCelEration of the UppEr festOoN roLLs,
F*d sTatIc=staTic forCE compoNent on the UpPEr festOOn rolls AND iS equAl to Mg+2F*c.
F*fraction=fRiCTion in either diRectioN rESiSTIng MovEment of the UpPer feSToon rolLS,
SIGN(vp)=pOSitive or negatIve value depENdiNg on thE dIreCTion of MovemEnT Of tHe upper festOon rOlls,
k1=ObseRver gaIN,
Vp=instANtaneouS transLatIonAl veLOcItY of ThE UppER fEstOOn rOlls,
Vpe=eStImAted tRansLATIOnal VelOcitY,
kte=SErvo motor (actuAtoR) torQUe cOnstaNt estImatE,
I=ActuaTor curRent, aNd
m2e=Estimated physIcal Mass of the UppEr FesToOn rolLS.
In somE emBodIments, tHe first ANd sEcOND FoRce components are apPlIED sImultaneOusly tO ThE uPPer festoOn RolLs as A SIngle ForcE, AnD applyinG a forcE To ThE upper fEsToon roLlS inCluDes meASuriNg the tRanslatiOnal pOSition of the uppER festoon rolls; MEaSURiNG web TenSion force afTer tHE fesToon; ANd SenSIng thE motoR cURrENt of an actuator applyInG the foRce to The upper festoOn rolls, the ABOVe measurIng aND sENsing occurring At eacH sensing inTErval, the MethoD further Including COMputing a DerIvaTivE of WEB tEnsion from the PREsenT mEasured Web Tension And The Web TenSiOn measureD in the prEvIoUs SeNsiNg intERval, optiOnAllY iNclUding COmputiNg estImatEd TrANslAtional VElOCIty aNd EsTimaTed TrAnslaTionAL acCeleratIon of uppeR feSToon RoLlS from thE change in posiTiOn of the uppEr FesToon roLLS.
In some eMbodiments, the first and seCOnd forcE coMponeNts aRe applied SimUltaneOusLY to the Upper fEstooN rOllS AS a sinGLE fOrcE, aNd applying A FOrcE to thE uPper Festoon Rolls includes measuRIng The translatioNal PosiTIOn Of tHE uPPer FeSTooN ROlls; and sensing tHe motor curReNT oF an actuatoR AppLyIng the fOrce to tHe uppER festooN rolls; comPuting an eStImatED TraNslational Velocity Of the festOOn uppER rOlls bY suBtractInG thE prevIous seNSed Value For traNsLationAl posItIon from tHe present sensed value of tRanslaTionaL poSition and TheN DivIding by thE timE interval bEtwEen SensiNg oF The vaLues; ANd ComPUting A new FOrce commaND fOr aPPLiCation to the ACTUatOr in rEspONse to tHe eaRlier computed valuES.
In some embodimEnts, THE fiRst ANd seCoNd force componeNts ArE APplied siMuLtaneously tO the uppeR fEStoon Rolls aS a
 rolls; sensing the curren t of an ac tuato r;and  c ompu ting  the estimated tran slational acceleration  of t he uppe r  f estoo n rolls fr o m  th eeq uat io n 
A pexe2 x80 x9d[F*d  static+F* fri ct ionSign(Vp)+ k 1( Vpxe2x88x9 2Vp e)+kteI]/M2e 
wh ere:
A pe =es t imate d t ransl ationa l  accel eration o ft he upp e r festo o n  r olls ,
F*d static=stat i cf orce component  on th eu pp e r  fe sto on rolls a nd  is e q ual toM g+ 2 F * c.F *fraction=Fri ction in ei t her  direc ti onr esisti ng mo ve m ent  of the upp er f estoon ro lls,
S i gn(Vp)= p ositive  or ne gat ive  val u ede pen di n g o n  t hed ire ction of  m ov ement  oft h e uppe r f esto on ro lls,
k1=Obser ver  gai n ,
V p=ins tanta neou strans lation al ve lo city of the upp er f estoon ro lls ,Vpe =e stima t ed tra nsl ati onal ve locity, kte =S e r v omotor (actuator) t or q u econstant  estim a te ,I =actuato rcur rent , and
M 2e=E s ti mated ph ysical ma ss  of the  u pper f es too n r olls. In s ome em bodiment s, th e  first and sec o nd force comp o ne n t sa re a ppl ied simulta neou s ly t o th e  u ppe r  fest oon r ol l sa s a single force, a nd  apply ing a  force to the  upper fes t o o n rollsincl u de s  measuring the  tran slationalp ositionof th e upperfestoon r o l ls; meas uri ngweb  te n s io n force after t he f es toon; a ndsensing  th e m oto r c ur rent of a n actuat or  a pp ly ing  thef orce toth e u pp erfesto o n roll s, th e ab ov em eas uring a n ds e nsin goc curr ing  a t eac h se n sin g inter val, themet h od f ur th er incl uding computi ng  a derivat iv e o f webt e nsion fr om the present measured web ten sio n and  the  web tens ion  measu red in the  previ ous s en sin g inter v a l,  op ti onally inc l u din g com pu ting  estima ted translationalv elo city and esti mat ed t r a ns lat i on a l a cc e ler a t ion of upper fe stoon roll sf ro m the chan g e i npositio n of th e upp e r festo on rolls. 
In someem bodi m e nts , the firs t and se cond forc e  comp o ne nts a reapplie dsim ultan eously tothe u pper f es toon r ollsas  a singl e force, and applying a  force  to t heupper fes too n  ro lls inclu desmeasuringthe  tr ansla tio n al po siti o noft he up perf estoon ro l ls ; a n d  s ensing them o t orcurre nto f an a ctua tor applying thef orce to the up perf e sto onr olls ;computing an e sti ma t e d transl at ional veloc ity of t he festo on upp er rol ls by s u b tr a ctingthepre vious sen sed  v a lue for  t ra n slatio nalpo sition  fromt he p r e sent sensed valu e oft r ansla t ion al po si tion an d  the n dividing  by the tim e inte rval  betw een sen si ng ofthe  v alues; and computing  a ne w force  c omma ndfor ap plic a t ion t o th eact uator inr e sp o ns et o t he e arlie rcomp uted valu e s.
In so mee mbodime nt s,t h e firs t  a n d  second fo rce  comp o n ents are a p plie d  s i multa neousl y to t he uppe r  fe st oon rol lsa s  a
 rolls;_sensing the_current of an actuator;_and computing_the_estimated translational_acceleration_of the upper_festoon rolls from_the equation
Apexe2x80x9d[F*d static+F*frictionSign(Vp)+k1(Vpxe2x88x92Vpe)+kteI]/M2e
where:
Ape=estimated translational_acceleration of the_upper_festoon rolls,
F*d static=static force component on the upper festoon rolls and is equal to_Mg+2F*c.
F*fraction=Friction_in either_direction_resisting_movement of the upper festoon_rolls,
Sign(Vp)=positive or negative value depending_on the_direction of movement of the upper festoon rolls,
k1=Observer_gain,
Vp=instantaneous_translational velocity of_the upper festoon rolls,
Vpe=estimated translational velocity,
kte=Servo motor (actuator) torque_constant estimate,
I=actuator current, and
M2e=Estimated physical mass_of the upper_festoon_rolls.
In_some embodiments, the first_and second force components are applied_simultaneously to the upper festoon rolls_as a single force, and applying a_force to the upper festoon rolls_includes measuring the translational position_of the_upper festoon rolls; measuring web_tension force after_the festoon;_and sensing the_motor current of an actuator applying_the force to_the upper festoon rolls, the above_measuring_and sensing occurring_at_each_sensing interval,_the method further_including_computing a_derivative_of web tension from the present_measured_web tension and the web tension measured_in the previous sensing_interval,_optionally including computing estimated_translational velocity and estimated translational_acceleration of upper festoon rolls from_the change_in position_of the upper festoon rolls.
In some embodiments, the first and second_force components are applied simultaneously to_the upper festoon rolls_as a_single_force, and applying_a_force to_the upper festoon rolls includes measuring the_translational position_of the upper festoon rolls; and_sensing the motor current_of_an actuator applying the force to_the upper festoon rolls; computing an_estimated translational velocity of the_festoon_upper_rolls by subtracting the previous_sensed value for translational position from_the present sensed_value of translational position and then dividing_by_the time interval between sensing of_the_values; and computing a new force_command_for_application to the actuator in_response to the earlier computed values.
In_some embodiments, the first and second force components are_applied simultaneously to_the upper festoon rolls as_a