02-AutomatedWelding

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Multiplexed and Distributed Controlof Automated WeldingCharalabos C. Doumanidis

lthough modem sensor technology and control algorithmsA ave enabled in-process regulation of arc w elding, classicalsingle-torch actuation methods provide only a few welding con-ditions that can be modulated in real time to control multiple weldgeometry characteristics. Todecouple the procesr dynam ics andsimultaneously control thermal characteristics of the w eld, mul-The author is with Tufts University, Depurrnietit of Mechur i icdEngineering , Medfor-d, MA 0215.5.

tiple virtual heat inputs are implemented by rapid periodic recip-rocation (timesharing) of the single torch on the weld surface.Dynamic analytical, numerical and linearized experimental proc-ess models are developed for the design of adaptive MIMOcontrol systems of both geometrical and thermal characteristics,and their performance is tested in rejecting disturbances andfollowing setpoint changes. To maximize the ran ge of achievableweld features, a continuous heat distribution and temperaturemonitoring on the entire weld surface is finally adopted. Thenecessary vector-scanning trajectories of the torch are regulated

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W l e IRepresentative Control Systems inWelding Research LiteratureResearchers Ref Year Method Model Control Inputs Outputs Sensor RemarksSmith, Bennett 1974 GTAW pulse-s ep current backbeadradiation photoelectric On-off controlGladkov e t al. 3 1977 PAW analog voltage penetrationestimate Various materialsackbeadion. voltage

line scancameraVroman-Brandt 4 1978 P-PI,analogcomputervelocity pool width@ fixeddistance

Problems with delaysand nonmin. phaseGTAW

Boughton-Rider-Smith 5 1978 PulsedGTAW 2ndorder On-off, P current,velocity backbeadwidth,topsidewidth

photocell Full penetration,partial penetration

Chi-Yin-Gao 6 1980 PAW PWM voltage backbeadradiation photoelectric Keyhole PAW

1980~

1980

~

1982

GMAW several several Estimated penetration39

10

openlclosedloopon-off

weld fillet,penetrationbackbeadwidth

Hunter-Bryce-Doherty, CookNomura et al.

staticempirical~

Full penetration,disturbance rejectionSAW arc lightin tensity4 Rphotosensorsinfrared

current

~

Domfeld-Tomi-zuka-Langari Measurability,causality,identificationvelocity backbeadtemperatureGMAW 2nd orderw l2 zeros MRAC

Hardt-Garlow-Bates. Weinert 11.12 1985 GTAW nonlinearthermal linear PI current,velocity pool crosssection opticalbackbeadtemperatureFull penetration, n-(Tidentification

suzuki 13 1987 GTAW 2nd orderempirical adaptivedeadbeat current,velocity backbeadwidth optical Full penetrationDoumanidis 14 1988 GMAW analytical,

expermultivariabladaptive doubletorchpower

heat-affectedzone andcooling rate

IR pyrometrycamera Timeshared multi-torch configuration

Miyachi-Masuhuchi 15 1989 GTAW numerical open-loop lateraltorchpowerdistortion,root gap stylusprofilometerLaserinterferomtr.

Large process delays

Hale 16 1989 GMAW 2nd orderempirical nonlinearsliding-modevelocity,wirefeed bead widthand height active optical(Laser) Partial penetration

Song 1991_ _ _1992

GMAW analytical optical and IRpyrometer On-line penetrationestimator17

18

multivariabladaptivemultivariabladaptive

velocity,wirefeedweaving,current

width &backbeadtemperaturepool andHAZ widthwidth,penetration,coolingrate, fill

infraredpyrometer Weaving amplitudemodulationMasmoudi GTAW numericalCook,Banerjee,Einerson, Cho,Richardson

19-23 1992 GTAWGMAW empirical,neural nets 1 near,fuzzy logic several infraredpyrometrycoaxial vision

Under development

GTAW G as Tungsten A rc Welding SAW Submerged Arc Welding

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in real time by a distributed-parameter control strategy, inte-grated to the weld design software for flexibility in production.Actuation Limitations in Welding Process

Mechanized and robotic welding is now commonplace inindustrial practice, for its well-known eco notech nical advantagesover manual methods. Th ese include increased productivity andquality of the welds, as well as health and safety benefits for thewelder. However, the replacement of the human operator by awelding robot is not without problems, since the elimination ofthe human sen ses and judgement deprives mechanized w eldingof the superior flexibility and adaptability of manual control,especially in handling process variations a nd disturbances. It isthe purpose of in-process welding control system s to compen satefor these essential functions, or even surpass them by incorpo-rating feedback of welding characteristics, which are unobserv-able to humans, such as infrared temperature measurements.Furthermore, modem control systems modulate the weldingconditions in real time according to rigorous, sophisticated algo-rithms, thus insuring superior control authority and process per-formance.The developments in the field of in-process welding controlhave been dramatic in the last two decades. With the exceptionof seam tracking guidance systems, which are not examined

because they relate only m arginally to the nature of the processitself, most representative research efforts in this area are listedin Table I [1]-[23]. As it appears clearly, the availability ofcomplex nondestructive sensor technology permits real-timemeasurement of an increasing number of w eld characteristics, toinsure a com plete description of the weld quality and productiv-ity. Also, the progress in dynamic modeling of the weldingprocess, through various analytical, numerical, and empiricalmodels, provides the basis for designing high-performance, m ul-tivariable control systems for the regulation of these weldingoutputs. Of course this must be d one by in-p rocess modulationof the welding conditions (i.e., inputs), ensuri ng decoupled con-trol of the process outpu ts through real-time measurement andfeedback of the latter [24]. Unfortunately, as indicated on thetable, modem automated welding actuation techniques did notevolve much from the traditional manual methods of torch ma-nipulation, and they currently provide only a limited number ofmanipulatable welding conditions fo r process control. This is thecase for all industrial techniques, including shielded metal arcwelding (SMAW ), which employ s a consumable length of m etalelectrode coated with protective fluxes to a void oxidation of themelt, as well as gas metal arc welding (GM AW ), using continu -ou s feed of cons uma ble electrode wire from a reel and a separateinert gas (e.g., argon) supply for protection, or gas tunsten arcwelding (GTAW), employing a permanent (nonconsumable)tungsten electrode for autoge nous fusion of the weld materialunder inert gas shielding.

The purpose of this article is to illustrate these fundamentalactuation limitations, which stem from the nature of the weldingprocess and cannot be relaxed by sensing or control improve-ments. Th ese will be attributed to the spatially localized, nonuni-form character of the welding inputs (such as torch velocity,wirefeed rate, etc.) as well as outputs (such as bead width, coolingrate), which leads to a lumped-parameter formulation of theirmodeling and control strategies. This analysis will eventuallypropose the redesign of mode m welding techniques in the frame-

f I Q

Fig. 1. GMA welding geometrical arrangem ent.work of their suitability for in-process control, by introducingmodifications such as the multiple virtual torch configuration.These actuation schemes will take specific advantage of auto-mated welding, and are not necessarily implementable by thehuman operator. Finally, the spatially continuous, uniform natureof the respective inputs (heat distribution) a nd measured outputs(surface temperatures) will reformulate their regulation in thedistributed-parameter control domain.

,~~~, WELD BEAD WIDTH AF TrR POSITIVE VE,LOClTY STEP.

.00507 ~-20. -15. -12. -8. -4 . 0 0 4. 8. 12. 15. 20. 24TIME ( S ),0041,0037,0033E ,0029,0025.0021

-WELD BEAD DEPTH AFTER P OSITIVE VELOCITY STEP.

.0017-15Z -9. -6 . -3. 0 0 3 . 6 . 9 12. 15. 18.WELD POOL HEIGHT AFTER P OSITIVE VELOCITY STEP.

TIME (S).,0040,0038

A ,0030

0020,0015,0010-20. -15 -12 -8. -4 . 0.0 4 . 8. 12. 15. 20. 24.TIME (S).

Fig. 2 . Step responses o the weld geometry ajter a torch velocitychange jkom 1,=6 to J O mmls. -: E,xperimental data. - - -:Analytical model.- -. -:Linearized model.

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Geometry Modeling of the WeldIn Table I it can be noticed that the regulated weldin g charac-weld bead geometry characteristicsmicrostructureand material propertiesresidual stresses and distortion.Undoubtedly most of the in-process welding control systemsregulate geom etrical characteristics of the weld bead, because of

their dominant influence on the mechanical properties of thejoint, as well as the availability of real-time optical measuremen tmethods (e.g., for bead width) and estimation models (e.g., forbead penetration). For partial penetration butt GM AW of mildsteel plates, this bead geometry is illustrated in Fig. 1, and canbe described by three lumped welding outputs: the pool width w,penetration depth d, nd reinforcement height h. These must becontrolled in-process by modulating three welding inputs: thetorch power Q , velocity v and w irefeed rate f . The controllerdesign will be based on a hybrid analytical as well as on adynamic experimental process model.

teristics can be classified in three distinct categories:

Analytical ModelIn the solid region, the conduction temperature field T result-ing from the heat influx from the fingeredpoo1, can be obtainedby sup erposition of two partial fields, generated by two fictitious

Gaussian heat distributions on the surface and centerplane of theweld. Under the quasi-stationary (Rosenthal) assumptions ofconstant process conditions, the composite field T is:

where the torch efficiency n and distribution are identifiedin-process through temperature measurements at points T y an dTz. A detailed description of this integrated real-time model isgiven in [25].

Experimental M odelBesides the hybrid analytical model above, the design of ageometry control system is based on a linearized dynamic ex-perimental model, derived by off-line process identification inthe neighborhood of the nominal w elding conditions. Starting atthis operating point, positive and negative step changes areimposed separately to each one of the welding inputs, i.e., thetorch power Q,velocity v and wirefeedf, as summarized in Table11. The respective experimental transients of the welding outputs,Le., the bead width w and height h , are m easured optically, and thepenetration d is measu red by off-line longitudinal sectioning [16].Fig. 2 shows these step responses of w, d, and h during test #3,obtained by un filtered and filtered measurement, by the analyticalmodel, and by a linearized first order model fitted o the experimentaldata, and expressed in the form of transfer functions:

k=inf 0 L

where To is the preheat temperature, D the plate thickness, p,c,athe density, heat capacity and therma l diffusivity of the material,and (nl,ol),(n2 ,02)the artial efficiencies and distribution radii ofthe two com ponents of the heat input pair. In automated welding,where the process conditions are constantly adjusted by thecontroller, this expression applies in its differential (Greensfunction) form. The calculated temperatures at points T y an d T zadjoining the pool width w and depth d can be used for theirestimation , by interpola tion of the so lidus isotherm Tm .

In the weld pool cross section, the two flow streams can bedescribed by scalar state variables, i.e., their total masses mi,average velocities vi and equivalent temperaturesTi. The evolu-tion of these stream states is govemed by the respective scalarmass, mom entum and energy balances, which take into accountthe stream interactions as well as the boundary effects at the solidand the surface interface. Changes of the pool width w and depthd due to melting or solidification depend on the local states ofstreams 1 an d 2 , respectively, while the bead height h can bedetermined by a m ass balance of the molten reinforcement.Last, the GMAW torch effects are modeled by a G aussiansurface distribution of heat, momentum, and mass from theconsumable electrode, and partitioned to the two streams 1 an d2 according to the position r of their interface as follows:

where the time constants t and gains K are tabu lated in T able 11.In the absence of oversh oot effects in the experime ntal responses ,this first-order modeling simp lifies the controller design relativeto higher-order models in [25]. These individual transfer func-tions can be assembled into a 3x3 transfer matrix. The analyticalmodel can also be m ade to match the responses of the linearizedone at the steady state by a sligh t recalibration of its parameters(n,o),ndicating an apparen t alteration of the torch characteristicsafter the step.

Multiple Torch ConfigurationAs indicated by the gains K in Table 11, such a 3 input x 3output weld geometry system is completely coupled, since eachof the m odulated welding conditions ( Q , v f i affects substantiallyeach of the geometrical characteristics (w,d,h),lthough throughwidely different transient dynamics, Le., time constants t. Th eperformance of such a welding system under closed-loop controlis effectively improved by adopting welding inputs of uniformnature, configured so as to exert a selective (i.e., decoupled)

influence on certain welding outputs [141.Since the torch powerQ in Table I1 exhibits the smallest parameter alterations forpositive and negative deviations from the nom inal conditions,and thus approaches linearity in its effects, multiple torch systemsat various arrangements and with independently modulated

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Table I1Identification Tests for the Analytical Model and Dynamics of the Linearized Model

Test#

12345

Variable From 1 To Widthw Depth d Height hv o r f ti v KU td Kd th KI ,Power 2.5 kW 3.0 kW 0.75 2.12 0.52 1.67 0.82 -0.22Power 2.5 kW 2.0 kW 0.78 1.83 1 0.57 1.74 0.69 -0.17Velocity 6 /s 10 /s 0.6 -0.75 0.4 -0.30 0.8 -0.15Velocity 6 mm/s 4/s 1.4 -1.7 ~ 1.2 -0.32 0.7 -0.24 -Wirefeed 600id min 800irdmin 0.95 0.026 ~ 0.65 ,0094 0.4 ,0042

power can be used for lumped welding control. Alternatively,multitorch configurations can be regarded as an in-process im-plemen tation of preheating or postheating process sta ges, whichare usually practiced off-line to obtain the necessary weld beadpenetration without excessive metallurgical effects in a limitedheat affected zone.

Such a 3x3 welding system for bead geometry control inlongitudinal welding of op en cylindrical shells (Fig. 3) employ snonconsumable lateral torches Q2 and a backbead torch Q3 inaddition to the primary GMAW torch Ql. The secondary torchesQ2 and Q3 have a preferential effect on streams 1 and 2 in theweld pool respectively (Fig. l ) , hus providing decoupled controlof the width w nd penetration d. These are estimated by theanalytical model through temperature measurements T y and T z ,respectively, by a line scan ning IR camera, which also measuresthe bead height h directly.

Since such multitorch configurations involve the complexityand cost of multiple independent power sources as well aspotential interference between the torches, a single heat sourcecan be timeshared (Le., multiplexed in time) by rapid repetitivereciprocation on the weld surface, so as to imitate the effect ofmultiple torches [141. In the ex ample of long itudinal GTAW ofthe cylindrical shells in Fig. 4, both the torch power Q(Q and itsmotion v(Y) relative to the work piece are modulated to supply acontinuous circumferential heat distribution q(y ) providing thelumped heat inputs Ql and Q2 (virtual torches):

Line ScanIR Cameram ~Fig. 3.Multitorch welding and thermal line scan sensing ofan opencylindrical shell.where L is the distance and T he transition time between Ql andQ2. Notice also that the modulated rotation of the workpiece toimplement the double-torch arrangement enables the periodicmeasurement of temperatures T,. nd Tz by a single spot pyrome-ter.

For GTA welding of stainless steel pipes in Fig. 4, the widthw and depth d of the bead can be regulated through the directlymeasurable temperatures ry nd T- respectively. For a maximumbead width wd , he temperature Tyd at this distance must byspecified as less or equal to the solidus temperature of thematerial Tnl,while for full penetration of the shell the temperatureTzd must be specified higher that Tm.For this 2-input (Q1,Qz) x2-output (T J Z ) system, the parameters of the linearized dynamicmodel

are identified a s before and co llected in Table 111. Notice tha t thesmall values of Kz for Q2 indicate an almos t decoupled effect ofthe secondary heat input on temperature T,. n the width direction,as expected. This model forms the basis for the design of a 2x 2adaptive thermal controller in the following sections.

Thermal Modeling in WeldingBesides weld bea d geom etry, thermal characteristics such asthe final microstruc ture and prop erties of the material as well asthe residual stresses and distortion of the joint are imp ortant weldquality descriptors. In particular, nucleation of certain undesir-able equilibrium material phases requires regulation of the heataffected zone isotherm Th, while the formation of nonequilibriumstructures is characterized by the centerline cooling rate at acritical temperature Tcr.In the previous section it was realized that the few lumpedwelding inputs of the GMA W and GTAW processes (Q,v , j ) werebarely sufficient for regulation of the basic geometric weldingoutputs (w,d,h) . f thermal characteristics of the weld are to becontrolled simultan eously to the geome trical ones, the introduc-tion of additional inputs (virtual torches), implem ented by timemultiplexing of a nonconsumable torch, and positioned so as tocause decoupled effects becomes the only feasible approach. Inthe GMAW arrangement of Fig. 5, a seco ndary trailing torch Q2

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Pyro

v /Y\

Test To Temperature T,Ky fv~ Input From

I Q i 2.5 kW 3.0 kW 421 3.582 Qi 2.5 kW 2.0 kW 445 3.813 Q2 5 0 0 W 600W 173 2.104 0 2 500W 4 0 0 W 722 2.61

Q2 I

TemperatureT,KZ t z

316 3.86402 4.2323 5.1521 6.20

Fig. 4. Multiplexed virtual torch welding and temperature measurement of an opencylindrical shell. (a )Geometrical arrangemen t and pipe rotation. (b)Modulation of torchpower; velocity and heat distribution.

follows the primary Ql along the centerline, located so as not toaffect the heat affected zone (HAZ) width HZ , and thus providedecoupled control of the cooling rate CR [14]. This secondarytorch can be considered as an in-process implementation of apostheating (annealing) or multipass cycle. Open-loop laser pre-heating as well as lateral [151 and weav ing [181 orches have alsobeen adopted in the literature to control material properties,distortions and weld geometry in an off-line fashion.Furthermore, instead of regulating the HAZ width HZ to aspecified value HZd, the peak temperature T p observed along asideline at distance HZd from the centerline can be controlled tothe HA Z isotherm temperature Th. Again, the cooling rate CRcan be substituted by he temperature drop Td that it causes duringone sam pling period of the controller, to the centerline point atthe critical temperature Tcr.The two temperature outputs Tpan dT d are measured directly in-process by line scans af an IRpyrometry camera alon g the sideline and centerline respectively,and regulated through the heat inputs Ql an d Q2, implementedthrough torch reciprocation as in Fig. 4.The design of a thermalcontrol system will be based on a dynam ic numerical simulationof the temperature field, as well as on a linearized experimentalmodel as before.

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Numerical SimulationThe com putational simulation of the ther-mal field in arc welding [14] integrates thetransient conduction equation (Fourier) indiscrete time steps t and space elements s,using an explicit Eulerian f ini te differenceformulation:

Ti(x+_As,y fAs ,z fAs; t) 6T(x ,y ,z , t )AS 2

To encompass the solidus Tm and the heataffected zone (HAZ) T h sotherms, the modeluses a fine and a coarse grid, respectively,which follow the motion of the heat source(Fig. 6). It can also handle multiple torcheswith arbitrary heat distributions, and the basicbutt welding arrangement can be easily ex-tended to more general configurations. Thesimulation provides for initial preheat andconvective-radiative heat transfer from theboundaries, as well as temperature-depend-ent material properties and latent transforma-tion effects. Also, the thermal convection inthe pool is accounted for by equivalent an-isotropic conduction through directional con-duction coefficients. The torch efficiency anddistribution parameters (n,o)are calibratedexperimentally. The simulation also gener-ates temperature and phase field sectionmaps, as well as temperature hill and iso-therm section contours and 3D surfaces.

Experimental ModelStarting at the nominal conditions, a linearized model of thethermal dynamics is again derived by experim ental positive andnegative step perturbations of the heat inputs Ql an d Q2, an dformulated through d elayed first order transfer functions of thewelding outputs T pan d Td:

I 01 02

I Y IFig. 5. Input-output definition of the thermal system.

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Q1 0 2

Controller WeldingProcessID - Actuator-ilter r+

I Largegrid grid I

a

Fig. 6.Arrangement of the numerical simulation.

Secondary- loop

The experimental transients for butt GMAW of mild steelplates during test #1, together with the calibrated numericalsimulations and the linearized model responses are show n on Fig.7. The param eters of the transfer functions are again determinedthrough fitting of the linearized transients to the experimentaldata, and collected in Table IV. Notice the decoup led effect of thesecondary heat input Q2 on the temperature drop Td , as well as

'Parameters 8ParameterC-

TemperatureMeasurement

the improved linearity and similarity of dy-namic parameters, attributed to the adoption ofthermal outputs (Tp,Td )and heat inputs (Qi, Q2)of uniform nature.Lumped Adaptive Control SystemFor both the geometrical and thermal weld-ing m odels of Tab les I11 and IV, respectively, hedifferences n the values of the dynam ic parame-ters for positive and negative step of the sameinput variable, as well as the variations of the

torch parameters ( n , o ) , ndicate the nonlinearityof the welding process. Becau se of thermal driftof the material properties, the process is alsononstat ionary ( t ime-varying). Addit ionally,many disturbances in the welding geometry,ambient conditions and process characteristicsare reflected as intemal parameter alterations.All these effects call for in-process identificationand adaptation of the control system to the pa-rameter uncertainty, as well as robustness tounmodelled welding dynam ics. Other require-ments include closed-loop stability in weldingranges ofpractical interest, satisfactory ime per-formance and suitability of the MIMO controlstrategy to the input-output structure of thelinearized model.The experimental process models can bewritten in a discrete-time, autoregressive mov-ing average (ARM A form as:

-( t+d)=O . x ( t )

where Y=[T,TzlTor[T pTdITis he vector of welding outputs andd are their respective delays. _V is an augmented state vectorincluding current and n previous values of the outputs Yas wellas current and m previous values of the inputs Y=[Qi Q21T, wherem an d n are the degrees of the numerator and denominatorpolynom ials of the respective transfer functions. The parametermatrix 0 , nitially estimated from the values in Tables I11 and IV,is updated by a recursive adaptation law, based on the orthogon alprojection of the state vector Y on its measured error:

where y is the adaptation gain and 6 the samp ling period. If thedelays d and orders m an d n of the system dynamics are known,and the sampling period 6 is long enough to cover the measure-ment, computation and process delays or nonminimum phaseeffects, then the ARM A equation is invertible and forms the basisof a stable deadbeat control law. Given a set of desired outputs&, his equation can be solved for the necessa ry welding inputsy in the vector 45, on the basis of the estimated parameters 0 ( t ) :

Solve for g ( t ) : Y d( t+ d )=O(t) ._V(t) .It can be shown that this multivariable adaptive strategyensures the boundedness of inputs II and outputs Y , he conver-

gence of parameters 0 and asymptotic tracking of the specifiedoutput values&.The original algorithm [26], [27] was m odified

1 PRIMARY HEAT INPUT POSITIVE STEP RESPONSES.9 -70. I 0 1- p -80.g. 880.4 860. Ka p -90.Y -85.

-95.40.820. -100.0. 5. 10. 15. 20. 25. 30. 0. 5. 10. 15. 20. 25. 30.

I TIME (S). TIME (S).Fig. 7. Step response o the thermal system after a heat input changefrom Qi=2.5 to3 kW 000 Experimental data. -: Numerical simulation- - -:Linearized mo del.

IFig. 8. Adaptive thermal welding control system.

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15801560 17000 5 10 15 20 0 5 10 15 20Time (s) Time (s)

ToI I

1 Q1 2.5 kW 3.0 kW

Time (s) Time (s)

Temperature Tp TemperatureTdKP tP dP Kd td dd0.239 2.57 0.50 0.0340 4.55 0.96

I I ~ I

Fig. 9. Closed-loop responses of output temperatures Ty , Tz and heat inputs QI , Q2after a velocity disturban ce v=6 to 5 m d s .

234

OUTPUT RE SPONSES TO A STEP COMMAND.890. -70.-75.80.. 870. - -80.860. a?L g -85.5 850.

840.830. -95.820. -100.

-p -90.

TIME (S). TIME (S).E S T O A S2850. 650.2800. 600.2750. 550.5 450.700.6 E 8 400.

350.2550. 300.2500. 250.

500.

0. IO. 20. 30. 40. 50. 60. 0. IO. 20. 30. 40. 50. 60.TIME (S). TIME (S).

Qi 2.5 kW 2.0 kW 0.250 2.72 0.55 0.0439 4.05 1.06Q2 5 0 0 w I .0 kW 0.0008 0 0 0.0405 3.75 0.1442 500 W 0.0 w 0.0028 0 0 0.0421 2.52 0.34

Fig. 10.Closed-loop responses o fou tpu t temperaturesTp, Td, and heat inputs Qi,Q2after a change of the reference setpoint. 000: Experimental data. -: Numericalsimulation. - - -: inearized model.

to include saturation of the w elding inputs withantireset windup to avoid bum-through, lack offusion and exce ssive porosity of the weld. Also,the adaptation gain y is modulated in-process toavoid singularities and optimize the numericalconditioning of the d eadbe at contro l law. Finally,a second external feedback loop with feedfor-ward filters is employed to smooth the deadbeateffects and improve the closed-loop perform-ance (Fig. 8).

Closed-LoopWelding PerformanceAs already explained, the bead cros s sectiongeometry in GTA welding of cylindrical stain-less steel shells (Fig. 4) can be described by thetemperatures TJ an d Tz adjoining to the maxi-mum w idth and penetration locations. These areregulated in process through the virtual heatinputs Ql and Q2of the timeshared torch, accord-ing to the multivariable adaptive strategy abov e.The closed-loop behavior of this geometry con-trol system in rejecting process disturbances istested when the welding velocity is suddenlyreduced from the nominal 6 I s to 5 m d s ,thus initiating a n increase of the weld pool size,and the respective transients are shown in Fig. 9.The numerical simulation, adapted and em-ployed as a butt GTAW process model underfeedba ck control, matches well the experimentalmodel responses of the temperature outputs.However, the modeling im perfections are mani-fested as differences between the steady-statevalues of the required heat inputs after the dis-turbance transients. Despite these deviations, theeffects of the torch deceleration are com pletelyrejected by the adaptive controller.In the same way, the thermal characteristicsof the HAZ and cooling rate in robotic GMAWof mild steel plates can be controlled via theequivalent peak and drop temperatures (Tp, d)through the multiplexed torch powers (Q I Q2)ofFig. 5 , by a similar 2x 2 adaptive deadbeat con-troller. The responses of the resulting closed-loop system are assessed during a step referencecommand to the specified Tpd, T dd (Fig. 8), cor-

Table IVIdentification Tests for the Dynamic Parameters of the Linearized ModelI I I I I

I I I

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responding to a wider, steeper temperature hill on the weldsurface, and plotted in Fig. 10.Again, thenumerically simulatedtransients of the outputs and the responses of the linearized modelmatch the experimental behavior of the feedback system, al-

-50.

-100.

-150.Ina2k -200.

600. 700. 800. 900. 1000TPEAK (K).

Fig. 11.Simultaneous control range of temperatures T p an d T d bythe heat inputs QI an d Q2.

A ControlRobot Ah.

I( 11 /\\\TorchAHeat Trajectories 1 Measurements

Fig. 12. Implementation and trajectories of distributed weldingsystem with IR eedback.

though static differences between the model predictions appearas deviations of the respective heat inputs at the steady state.Despite this, the desired reference temperatures are eventuallyobtained exactly in all cases.The range of achievable welding output setpoints (Tpd ,Tdd)ofthis thermal system can be determined by nu merical simulation,and it is depicted in F iq 11,as a mapping of the unsaturated heatinput pairs U=[Ql Q2] to the resulting steady state temperatureoutputsr(m)=T p T d l T . The feasible reference setpoints are insidethe envelop line. Although the slopes of the two constant-inputcurve families generally denote a coupled input-output depend-ence, the angles between the curves indicate the preferentialeffect of Ql on T p nd Q2on T d , as expected. The high total powerend of the reachable area corresponds to a single flattenedtemperature hill on the w eld surface, thus resulting in a coupled,limited control authority, while the low powe r end correspondsto two widely separated peaks of the temperature hill, resultingin deco upled, more e fficient regulation.

Distributed-Parameter Welding ControlSince Fig. 11indicates that specification of a desired setpoint(Tpd ,Tdd) outside the enveloped region in not achievable by thiswelding process, it is evident that lumped heat inputs fromdistinct virtual torches Qi, Q2 allow independen t variation of thewelding ou tputs in a limited controllable range. Moreover, local-ized thermal measurements on the weld surface enable the esti-mation of limited observable intemal w eld characteristics, suchas the bead p enetration, HAZ width, etc. Both limitations stemfrom the lumped , concentrated actuation and sensing techniquesinherent in the welding process, and they are clearly not aconsequence of the open or closed-loop control method.

As already realized, carefully arranged configurations of mul-tiplexed virtual torches and spot temperature measurements en-able decoup led control of mu ltiple distinct weld features throughreshaping of the thermal field in the w elded parts. However, abroad-range regulation of the total thermal distribution in theworkpiece is needed forcombined control of structure, propertiesand stress conditions of the material. Thus, a generalization ofthe ideas above suggests a continuous heat distribution on theentire accessible weld surface, with its intensity independentlymodulated at each b oundary location. Similarly, the estimationof the intemal thermal field necessitates full surface m easure-ments during the process. Such a distributed-parameter formula-tion of w elding modeling and control insures maxima l flexibilityin identification and regulation of all weld quality and produc-tivity m easures simultaneously.

As before, the distributed heat actuation in w elding can beimplemented by repetitively scanning the weld surface with asingle torch and by modulating its thermal power as a functionof its position, so as to mimic a c ontinuous spatial distribution.This scanning m otion can be performed in a raster fashion, i .e.,by periodical sweeping of a static orthogonal pattem on the weldsurface and by adjusting the heat input for each raster element.Rather, a vector scanning technique will be emp loyed, in whichthe torch follows dynamically controlled trajectories on thesurface to implem ent the specified heat distribution. This tech-nique is more en ergy efficient and less demanding in terms ofbandwidth of the welding equipmen t. The method is illustratedin Fig. 12, where a GTAW torch is cycled in a fast repetitivemotion pattem along longitudinal sideline paths at v arious dis-

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tances from the centerline of the butt weld. The torch power Q ( t )is adjusted and its trajectory X ( t ) , Y ( t ) s modulated by coordi-nated motion of the w orkpiece by the servodriven table and thetorch by the high-speed robot, so that the desired heat distributionq(X ,E t) is implemented. The temperature field on the weldsurface T(x ,y; t) is monitored by an IR pyrometry camera with aservoed mirror scanner.Fig. 13 compares these temperature fields measured on thetop surface for conventional and scanned GTAW of thin (3 m m )stainless steel plates, under identical process conditions (arclength 3 mm, voltage 15 V, current 100 A, inert gas Ar-2%02flow of 0.4 Ids).The travel speed in the traditional technique was3 /s, while the a verage velocity of the torch reciprocation inthe scanning method was 120 m d s . Clear ly s canned weldingresults in a more un iform longitudinal temperature distribution,with sm ooth transverse thermal gradients. This temperature hillgenerates an elongated weld p uddle with controlled melt solidi-fication, and a heat ffected zone with regulated coo ling rates.

TRAD. WELD MEASURED FIELD

SCAN WELD MEASURED FIELD

Fig. 13. Top surface temperature hills f o r traditional and scannedGTAW measured by infrared pyrometry.

These thermal effects result in a favorable metallurgical structurein the weld, and consequently superior mechanical properties ofthe w eld joint.Distributed -Param eter Modeling

In the literature, the mathematical (functional operator) analy-sis of distributed -param eter system s [28]-[32] has failed so far toprovide useful c ontrol design tools for practical manufacturingprocesses. Useful modeling insight to the thermal distribution isprovided by an ana lytical conduction solution for the temperaturef i e ld , der ived us ing Green s funct ion analys i s 1341. If

T(x ,y ,z; t:X,Y,~)s the temperature of the (x ,y ,z ) point at time tbecause of a unit heat input from the torch at point (X,Y,O) at time7, nd h is the surface convection coefficient, then:

m 1T(x , y , z ; f: , Y ,Z )=k=-- 8pc[xa( t- r )13

- x - X ) ~ (y-Q2 +( ~ - 2 k - D ) ~ h ( t - ~ )4a( t -z) - P C DIn longitudinally uniform welding, in which the process condi-tions (including part geometry, fixturing, material preheat, andambient conditions) do not vary along the centerline, this three-dimensional Greens function is reduced to a two-dimensionalfield T(y,z;t:Y,T).he resulting longitudinally invariant tempera-ture field applies to certain industrially important cases such asstraight plates, pipe girth, and flange welding. A lso for thin, fullypenetrated welded plates, the G reens field will be one-dimen-sional T c y ; t : Y , ~)Fig. 14). Beca use of the linea rity of this therma lproblem, the hea t distribution q ( X ,Y;T) on the weld surface willproduce a temperature field T(x,y,z;t)y supe rposition:

T(x ,y ,z; t)=T(x ,y ,z:O)

+f $(x,y, T(x ,y ,z; t:X , Y , T ) . ~ ( X , Y , T )XdY.dz0

which simplifies to a single time integral convolution for atimeshared heat input q ( X ( T ) , Y ( T ) ; T ) from a single torch. Noticethat the numerical simulation already developed can also be usedas a distributed temperature field mode l for add itional flexibilityin handling realistic thermal conditions and for improved accu-racy with non linear heat transfer phenomena.

Distributed-Parameter Estimation and ControlFor real-time estimation of the temperature field, a co mputa-tionally efficient quasilinear, adaptively-weighted superpositiontechnique is used, as it comb ines the advantages of the analytical,

THERMAL DISTRIBUTION ACROSS THINS.S. PLATE2500 I2000 k 0 . 5 ~ Timet=0.5.1.1.5..5s 1

I I-1 2 3 4 5y Distance from Centerline (m) xlO-3

Fig. 14 . Temperature ield T(y;t)generated in (I thin stainless steelplate by a single torch reciprocation along the centerline Y =O at t=O.

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numerical, and experimental off-line models. This in-processthermal observer is necessary in direct real-time parameter iden-tification, and it is based o n a two-dimensional convolution ofthe Greens temperature field similar to the previous equation.However, rather than determining the Greens function analyti-cally, this is compu ted off-line under realistic process conditionsby the num erical simulation, calibrated so as to match the experi-mental measurements on the part surface. Also, instead of calcu-lating the Greens function values in real time, these are storedin a 3-D look-up table for various surface distances of the torch,depths in the p late and elapsed times. In-process convolution ofthese data needs o nly to consider numerically signifi- ant com-ponents (Le., from neighboring and recent heat inputs) to thedesired level of accuracy. Although this quasilinear superpositionapplies strictly to limited ranges of welding conditions, thet he r m a l p r oces s non l i nea r i t i e s a r e s m oo t h and l oca l l yr - I

Fig. 5. Trajectory Y ( X ) andpowe r Q(X)control based on the errore(x ,y)of the temperature field T(x ,y) rom the specified Td(x,y) o r aflange weld.

linearizable in wide ranges through appropriate adjustment(weigh ting) of the heat distribution q in the equation above. Thesimplici ty and spat ial - temporal decoupledness makes thismethod well suited for efficient parallel computation of only thenecessary thermal field values.

Instead of the deadbeat co ntrol law used previously, a moreefficient strategy for vector modulation of the torch motion isdeveloped on the basis of direct specification of a desired thermaldistribution. Planning of the torch trajectories is based on aspecified temperature field Td(x,y,z;t), etermined by computa-tional simulation hrough optimization of some welding perform-ance criterion. Altematively, if a satisfactory pilot weld can beproduced experimentally in the laboratory by some weldingtechnique, its surface temperature field is measured by ther-mographic pyrometry, recorded as a function of time and speci-fied as Td n order to be reproduced by the distributed weldingcontrol system. In both cases, if e is the deviation (erro r) of thein-process measured temperature field T from the desired Td,he nthe torch is driven along the locus Y ( X )of the transverse maxim aof this error surface e (Fig. 15). The heat input per unit lengthq ( X , Y ( x ) ; t ) equired to determine the torch power Q (t) is a linear(e.g., PID), but can also be any nonlinear functionfof this localerror:

Thermal error: e(x ,y ,z ; t)=Td(x,y,z;t) - T(x,y,z;t)Trajectory Y(X ) : e /dy (X ,Y(X) ,O;t )=0

Heat input q(X) :q(X ,Y(X) ; t )=f[e(X,Y(X),O;t)] an d Q =Torch power & speed:Q(t) =Q/dt and X ( t ) =Q(t)l/Qq X , f X ) t)dXwhere 1 and dt are the length and duration of a single reciprocationof the torch. A nalogous trajectory control can b e obtained if,instead of specifying Td to regulate HA Z-related characteristics,

the cooling rate aT&t is set for nonequilibrium structure control,or the thermal gradient VTd to describe residual stresses orthermal distortion.

Advantages of Distributed WeldingAs already explained, distributed parameter control of thethermal field in welding provides comprehensive in-processregulation of the final weld bead geometry, microstructure, andproperties of the material, as well as residual stresses or jointdistortion. Thus, it can be used for optimization of lumpedwelding quality or productivity measures, such as the static anddynamic strength of the weld, fracture toughness, geometrictolerances corrosion and oxidation resistance, or any weightedcombination of these indices. The scanning torch actuation onthe weld surface can implem ent any arbitrary heat distribution,including conventional single-torch or multiple virtual torcharrangements, and temperature sensing on the entire weld surfaceprovides all necessary measurements for estimation of intemalcharacteristics, such as the bead cross section. As a result, dis-tributed w elding yields superior control and observation author-ity in the broadest possible operating ranges, and d ecouples thetimelspace dependence of the lumped actuation and sensing inclassical welding. E xperimental investigation of these beneficialeffects is currently in progress (Fig. 12).These advantages of multiple virtual torch and distributedwelding techniques have been obtained primarily through theredesign of co nventional welding methods, i .e., modification oftheir process co nfiguration so as to take advantage of modemcontrol and estimation strategies. Indeed, distributed weldingdiffers from traditional techniqu es currently practiced in industryboth in spatial distribution and in process evolution over time.Classical welding is a localized, serial process [35], i.e., thethermal field and the w eld bead are developed sequentially intime, in longitudinal increments. In con trast, distributed w eldingis a parallel process, since the weld is heated and the bead isdeposited simultaneously in the longitudinal direction, in pro-gressive cross-sectional increments. Thus it can provide a longi-tudinally invariant thermal field, with several advantages inprocess speed an d efficiency, improved linearity of the weldingdynamics, elimination of preheating and postheating require-ments, as well as weld bead defects associated with starting andextinguishing the torch.Last, the mu ltiplexed virtual torch and distributed weldingcontrol and estimation methodology ana lyzed in this article isdirectly interfaceable to the product and process design software,by sharing the same geo metric modeling descriptions of objectsand motions. The part geometry, the material and process condi-tions are typically developed on a compu ter-aided design (CAD )system, and transferred to the controller design software. Thiswill retum to the geo metric modeling environment, the optimalprocess schedule and the scan trajectory descriptions for theactuator and the sensor. It will also provide estimates of theperformance indices and suggest modifications of the part ge-ometry and process conditions, such as the fixturing areas on the

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surface. This interactive redesign of the thermal process will beaimed at the optimizationof its control and observation authority,by com bining the product and control system design proceduresin an integrated fashion, with the c oncomitant benefits for theproduction and quality of industrial welding.References

[l ] C.J. Smith, Self-adaptive control of penetration in tungsten inert gasweld, Advances W eld. Proc., pp. 272-282, 1974.[Z] A.P. Bennett, The interaction of material variability upon process re-quirements in automatic welding, Advances Weld. Proc. , 1974.[3] E.A. Gladkov, A.I. Akulov, A.V. Petrov, 0.1.Sokolov, and.4.N . Aleksan-drov, An automatic stabilizer of penetration in plasma welding with apenetrating arc, Weld. Prod. U.S.S.R. vol. 24, pp. 26-27, Nov. 1977.[4] A.R. Vorman and H. Brandt, Feedback control of GTA welding usingpuddle width measurement, Welding J. , pp. 742-746, Sept. 1978.[ 5 ]P. Boughton, G . Rider, and E.J. Smith , Feedback of weld penetration in1978,Adisances Weld. Proc. pp. 203-209, 1978.[6] Y. Chi, D. Yin, and Y. Gao , Closed-loop control of weld penetration inpulsed plasma arc welding,Weld. Prod., vol. 1, pp. 11-17, Feb. 1980.[7] J.J. Hunter, G.W. Bryce, and J. Doherty, On-line control of the arcwelding process, Dev. Mech. Auto. Robot. Weld. , pp. 37-49, 1980.[8]. G.E. Cook, Feed back and adaptive control to process variables in arcwelding, De\: Mec h. Auto. Robo t. Weld., pp, 321-329, 1980.[9] H. Nomura, Y. Satoh, K. Tohno, Y. Satoh, and M. Kuratori, Arc lightintensity controls current in SA welding system , I. Welding Metal Fa b., pp .457-463, Sept. 1980.[ lo ] D.A. Domfeld, M . Tomizuka, and G. Lan gari, Modelling and adaptivecontrol of arc welding processes,M eus. Control Batch Manufact., pp. 53-64,Nov. 1982.[ l l] D.E. Hardt, D.A. Garlow, and J.B . Weinert, Amo del of full penetrationarc welding for control system design. Trans. ASME J . D y n . Sysf., Meas.Control, vol. 107, pp. 40-46, Mar. 1985.[I21 B.E. Bates and D .E. Hardt, A real-time calibrated thermal model forclosed-loop w eld bead geometry c ontrol, Trans. ASME J . Dyn. Syst. , Meas.Control, p. 25-33, Mar. 1985.[131. A. Suzuki. D.E. Hardt, and L. Valavani, Application of adaptive controltheory to on-line GTA weld geometry regulation, Trans. ASME .I. Dyn.Syst., Meas. Conrrol, pp. 93-103, Mar. 1991.[14] C.C. Doumanidis and D .E. Hardt, Simultaneous in-process control ofheat affected zone and cooling rate during arc welding, Welding J . , vol. 69/5,pp. 186 s-l96s, May 1990,[15]. H. Miy achi, In-process control of root-gap changes during butt weld-ing, Ph.D. thesis, Dept. of Mechanical Engineering , M.I.T., 1989.[16] M. Hale, Multivariable geometry control of welding , presented atASME Winter Ann. Meet., Symp. Manufact. Proc. Modeling Control, Dec.1990.[17] J.B. Song and D.E. Hardt, Multivariable adaptive control of beadgeometry in GMA welding,p resented at ASME WAM S ymp. Welding, Dec.1991.[18] R. Masmudi and D.E. Hardt, Multivariable control of geometric andthermal properties in GTAW, presented at 3rd ASM Conf. Trends W eldingRes., Gatlinburg, TN , June 1992.

[191 H.S. Ch o, Application of AI to welding process autom ation, in Proc.ASME JapaniUSA Symp. Flex . Auto. , July 1992, pp. 303-308.[20] G.E. Cook, K. Andersen, and R.J. Barrett, Computer-based controlsystem fo r GTAW, in Proc. ASME JapunlUSA Symp. Flex. Auto. , July 1992,pp. 297-301.[21] P. Banerjee and B.A. Chin, Front side sens or based dynamic w eldpenetration control in robotic GTAW, in Proc. ASME JapanlUSA Symp.Flex. Auto. , July 1992.[22] C.J. Einerson, H.B. Smartt, J.A. Johnson, D. Light, and K.L. Moore,Development of an intelligent system for cooling rate and fill control inGMAW, in Proc. ASME JupanlUSA Symp. Flex . Auto. , July 1992.[23] R.W. Richardsn and C. Conrardy, Coaxial vison-based control ofGMAW , in Pm c. ASME JapaniUSA Symp. Flex . Auto. , July 1992.[24]. J.L. Schiano, J.H. Ross, and R.A. Weber, Modeling and control ofpuddle geometry in gas-metal arc welding, in Proc. 1991 Amer. ControlCons., Boston, MA, 1991.[25] C.C. Doumanidis, Weld bead geometry control based on lumped poolmodeling, Trends Weld. Res., presented at 3rd Conf. A SM Int., Gatlinburg,TN, June 1992.[26]G.C. G odwin, P.J. Ramadg e, and P.E. Caines, Discrete-time multivari-able adaptive control, IEEE Trans. uto . Confro/, ol. AC-25, pp. 449-456,June 1980.[27] C.E. Rohrs, L. Valavani, M. Athans, and G. Stein, Robustness ofadaptive control algorithms in the presence of unmodelled dynam ics, IEEETrans. Auto. Control, vol. AC-30, pp. 881-88 9, Sept. 1985.[28] N.K. Bose, Multidimensional Systems, Theory and Applications. Ne wYork, NY: IEEE Press, 1979.[29] J.L. Lions, Optimal Control of System s Governed by Partial DifSerentialEquations. New York, N Y Springer-Verlag. 1971,[30]M. Delfur, A. Bensou ssan, and S.K. Mitter,Linear Irrfirrite DimensionalSysrems. Camb ridge, MA: M .I.T. Press, 1983.[3 11 J.R. Parting ton an d K. Glover, Robust stabilization of delay system s byapproximation of coprime factors, Sysr. Contra/ Lett. , vol. 14, pp. 325-31,Apr. 1990.[32] T.T. Georgiou and M .C. Sm ith, Robust stabilization in the gap metric:Controller design for distributed plants, Trans. Aufo. Control, vol. 37, pp.1133-43, Aug. 1992.[33] H. Ozbay, H-infinity optimal controller design for a class of distributedparameter systems, Inr. J. Conrrol, vol. 5 8 , no. 4, pp. 739-782, 1993.[34] H.S. Carslaw and J.C. Jaeger, Conduction of Hear in Solids. London,U.K.: Oxford Press, 1959.[35] D.E. Hardt, Real-time process control: limits to progress, A S M EManufac f .Rei:,. to be published.

Charalabos Doumanidis received the diploma inmechanical engineering from the Aristotelian Uni-versity of Thessaloniki (1983), the M.S. degreefrom Northwestem University (1985), the Ph.D.degree from the Massachusetts Institute of Technol-ogy (198 8), and worked as a Postdoctoral ResearchAssociate at the Laboratory of M anufacturing andProductivity, M.I.T. (1989). He is currently A ssis-tant Professor of M echanical E ngineering at TuftsUniversity, and his research interests include ther-

mal manufacturing process modeling and control, and biomedical instrumen-tation. He is a member of ASME, ASM, SM E, and IASTED.

24 IEEE ControlSystems

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