Multiplexed and distributed control of automated welding - IEEE ...

Multiplexed and Distributed Control of Automated Welding Charalabos C. Doumanidis

lthough modem sensor technology and control algorithms have enabled in-process regulation of arc welding, classical single-torch actuation methods provide only a few welding conditions that can be modulated in real time to control multiple weld geometry characteristics. To decouple the procesr dynamics and simultaneously control thermal characteristics of the weld, mul-

A

The author is with Tufts University, Depurrnietit Engineering, Medfor-d, M A 0215.5.

August 1994

r---

of

Mechuriicd

tiple virtual heat inputs are implemented by rapid periodic reciprocation (timesharing) of the single torch on the weld surface. Dynamic analytical, numerical and linearized experimental process models are developed for the design of adaptive MIMO control systems of both geometrical and thermal characteristics, and their performance is tested in rejecting disturbances and following setpoint changes. To maximize the range of achievable weld features, a continuous heat distribution and temperature monitoring on the entire weld surface is finally adopted. The necessary vector-scanning trajectories of the torch are regulated

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13

Wle I Representative Control Systems in Welding Research Literature Control

Inputs

Outputs

Sensor

Remarks

GTAW

pulse-step

current

backbead radiation

photoelectric

On-off control

1977

PAW

analog

voltage

penetration estimate

backbead ion. voltage

Various materials

Vroman-Brandt 4

1978

GTAW

P-PI, analog computer

velocity

pool width @ fixed distance

line scan camera

Problems with delays and nonmin. phase

BoughtonRider-Smith

5

1978

Pulsed GTAW

On-off, P

current, velocity

backbead width, topside width

photocell

Full penetration, partial penetration

Chi-Yin-Gao

6

1980

PAW

PWM

voltage

backbead radiation

photoelectric

Keyhole PAW

Hunter-BryceDoherty, Cook

73

1980

GMAW

weld fillet, penetration

several

Estimated penetration

1980

SAW

Researchers

Ref

Year

Method

1974

3

Smith, Bennett Gladkov et al.

Model

2nd order

static empirical

openlclosed several loop

~

~

Nomura et al.

9

~

on-off

current

backbead width

arc light intensity 4 IR photosensors

Full penetration, disturbance rejection

~

Domfeld-Tomizuka-Langari

10

1982

GMAW

2nd order wl2 zeros

MRAC

velocity

backbead temperature

infrared

Measurability, causality, identification

Hardt-GarlowBates. Weinert

11.12

1985

GTAW

nonlinear thermal

linear PI

current, velocity

pool cross section

optical backbead temperature

Full penetration, n-(T identification

suzuki

13

1987

GTAW

2nd order empirical

adaptive deadbeat

current, velocity

backbead width

optical

Full penetration

Doumanidis

14

1988

GMAW

analytical,

heatIR pyrometry affected camera zone and cooling rate

Timeshared multitorch configuration

exper

multivariabl double adaptive torch power

MiyachiMasuhuchi

15

1989

GTAW

numerical

open-loop

lateral torch power

distortion, root gap

stylus profilometer Laser interferomtr.

Large process delays

Hale

16

1989

GMAW

2nd order empirical

nonlinear slidingmode

velocity, wirefeed

bead width and height

active optical (Laser)

Partial penetration

Song

17

1991

GMAW

analytical

multivariabl velocity, wirefeed adaptive

width & backbead temperature

optical and IR On-line penetration pyrometer estimator

Masmoudi

18

1992

GTAW

numerical

multivariabl weaving, adaptive current

pool and HAZ width

infrared pyrometer

Weaving amplitude modulation

Cook, Banerjee, Einerson, Cho, Richardson

19-23

1992

GTAW GMAW

empirical, 1inear, neural nets fuzzy logic

width, penetration, cooling rate, fill

infrared pyrometry coaxial vision

Under development

___

several

GTAW Gas Tungsten Arc Welding SAW Submerged Arc Welding

14

I E E E Control Systems

in real time by a distributed-parameter control strategy, integrated to the weld design software for flexibility in production. f

I Q

Actuation Limitations in Welding Process Mechanized and robotic welding is now commonplace in industrial practice, for its well-known econotechnical advantages over manual methods. These include increased productivity and quality of the welds, as well as health and safety benefits for the welder. However, the replacement of the human operator by a welding robot is not without problems, since the elimination of the human senses and judgement deprives mechanized welding of the superior flexibility and adaptability of manual control, especially in handling process variations and disturbances. It is the purpose of in-process welding control systems to compensate for these essential functions, or even surpass them by incorporating feedback of welding characteristics, which are unobservable to humans, such as infrared temperature measurements. Furthermore, modem control systems modulate the welding Fig. 1. GMA welding geometrical arrangement. conditions in real time according to rigorous, sophisticated algorithms, thus insuring superior control authority and process per- work of their suitability for in-process control, by introducing formance. modifications such as the multiple virtual torch configuration. The developments in the field of in-process welding control These actuation schemes will take specific advantage of autohave been dramatic in the last two decades. With the exception mated welding, and are not necessarily implementable by the of seam tracking guidance systems, which are not examined human operator. Finally, the spatially continuous, uniform nature because they relate only marginally to the nature of the process of the respective inputs (heat distribution) and measured outputs itself, most representative research efforts in this area are listed (surface temperatures) will reformulate their regulation in the in Table I [1]-[23]. As it appears clearly, the availability of distributed-parameter control domain. complex nondestructive sensor technology permits real-time measurement of an increasing number of weld characteristics, to insure a complete description of the weld quality and productivWELD BEAD WIDTH AFTrR POSITIVE VE,LOClTY STEP. ity. Also, the progress in dynamic modeling of the welding process, through various analytical, numerical, and empirical models, provides the basis for designing high-performance, multivariable control systems for the regulation of these welding outputs. Of course this must be done by in-process modulation of the welding conditions (i.e., inputs), ensuring decoupled con.0°7 .005 trol of the process outputs through real-time measurement and -20. -15. -12. -8. -4. 0 0 4. 8. 12. 15. 20. 24 feedback of the latter [24]. Unfortunately, as indicated on the TIME ( S ) table, modem automated welding actuation techniques did not WELD BEAD DEPTH AFTER POSITIVE VELOCITY STEP. ,0041 evolve much from the traditional manual methods of torch ma,0037 nipulation, and they currently provide only a limited number of ,0033 manipulatable welding conditions for process control. This is the E ,0029 case for all industrial techniques, including shielded metal arc ,0025 welding (SMAW), which employs a consumable length of metal .0021 electrode coated with protective fluxes to avoid oxidation of the .0017 melt, as well as gas metal arc welding (GMAW), using continu-15:lZ. -9. -6. -3. 0 0 3. 6. 9 12. 15. 18. TIME (S). ous feed of consumable electrode wire from a reel and a separate WELD POOL HEIGHT AFTER POSITIVE VELOCITY STEP. inert gas (e.g., argon) supply for protection, or gas tunsten arc ,0040 welding (GTAW), employing a permanent (nonconsumable) ,0038 tungsten electrode for autogenous fusion of the weld material A ,0030 under inert gas shielding. 0020 The purpose of this article is to illustrate these fundamental ,0015 actuation limitations, which stem from the nature of the welding ,0010 process and cannot be relaxed by sensing or control improve-20. -15 -12 -8. -4. 0.0 4. 8. 12. 15. 20. 24. ments. These will be attributed to the spatially localized, nonuniTIME (S). form character of the welding inputs (such as torch velocity, wirefeed rate, etc.) as well as outputs (such as bead width, cooling rate), which leads to a lumped-parameter formulation of their Fig. 2. Step responses of the weld geometry ajter a torch velocity -: E,xperimental data. - - -: modeling and control strategies. This analysis will eventually change jkom 1,=6 to J O mmls. Analytical model. - . - . -: Linearized model. propose the redesign of modem welding techniques in the frame,~~~

, ~

-

August 1994

1-

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Geometry Modeling of the Weld In Table I it can be noticed that the regulated welding characteristics can be classified in three distinct categories: weld bead geometry characteristics microstructureand material properties residual stresses and distortion. Undoubtedly most of the in-process welding control systems regulate geometrical characteristics of the weld bead, because of their dominant influence on the mechanical properties of the joint, as well as the availability of real-time optical measurement methods (e.g., for bead width) and estimation models (e.g., for bead penetration). For partial penetration butt GMAW of mild steel plates, this bead geometry is illustrated in Fig. 1, and can be described by three lumped welding outputs: the pool width w, penetration depth d,and reinforcement height h. These must be controlled in-process by modulating three welding inputs: the torch power Q, velocity v and wirefeed rate f . The controller design will be based on a hybrid analytical as well as on a dynamic experimental process model. Analytical Model In the solid region, the conduction temperature field T resulting from the heat influx from the “fingered”poo1,can be obtained by superposition of two partial fields, generated by two fictitious Gaussian heat distributions on the surface and centerplane of the weld. Under the quasi-stationary (Rosenthal) assumptions of constant process conditions, the composite field T is:

k=inf

0

Experimental Model Besides the hybrid analytical model above, the design of a geometry control system is based on a linearized dynamic experimental model, derived by off-line process identification in the neighborhood of the nominal welding conditions. Starting at this operating point, positive and negative step changes are imposed separately to each one of the welding inputs, i.e., the torch power Q , velocity v and wirefeedf, as summarized in Table 11. The respective experimental transients of the welding outputs, Le., the bead width w and height h, are measured optically,and the penetration d is measured by off-line longitudinal sectioning [16]. Fig. 2 shows these step responses of w, d, and h during test #3, obtained by unfiltered and filtered measurement, by the analytical model, and by a linearizedfirst order model fittedto the experimental data, and expressed in the form of transfer functions:

L

where To is the preheat temperature, D the plate thickness, p,c,a the density, heat capacity and thermal diffusivity of the material, and (nl,ol),(n2,02)thepartial efficiencies and distribution radii of the two components of the heat input pair. In automated welding, where the process conditions are constantly adjusted by the controller, this expression applies in its differential (Green’s function) form. The calculated temperatures at points Ty and Tz adjoining the pool width w and depth d can be used for their estimation, by interpolation of the solidus isotherm Tm. In the weld pool cross section, the two flow streams can be described by scalar state variables, i.e., their total masses mi, average velocities vi and equivalent temperatures Ti. The evolution of these stream states is govemed by the respective scalar mass, momentum and energy balances, which take into account the stream interactions as well as the boundary effects at the solid and the surface interface. Changes of the pool width w and depth d due to melting or solidification depend on the local states of streams 1 and 2, respectively, while the bead height h can be determined by a mass balance of the molten reinforcement. Last, the GMAW torch effects are modeled by a Gaussian surface distribution of heat, momentum, and mass from the consumable electrode, and partitioned to the two streams 1 and 2 according to the position r of their interface as follows:

16

where the torch efficiency n and distribution are identified in-process through temperature measurements at points Ty and Tz. A detailed description of this integrated real-time model is given in [25].

where the time constants t and gains K are tabulated in Table 11. In the absence of overshoot effects in the experimental responses, this first-order modeling simplifies the controller design relative to higher-order models in [25]. These individual transfer functions can be assembled into a 3x3 transfer matrix. The analytical model can also be made to match the responses of the linearized one at the steady state by a slight recalibration of its parameters (n,o), indicating an apparent alteration of the torch characteristics after the step. Multiple Torch Configuration As indicated by the gains K in Table 11, such a 3 input x 3 output weld geometry system is completely coupled, since each of the modulated welding conditions (Q,vfi affects substantially although through each of the geometrical characteristics (w,d,h), widely different transient dynamics, Le., time constants t. The performance of such a welding system under closed-loop control is effectively improved by adopting welding inputs of uniform nature, configured so as to exert a selective (i.e., decoupled) influence on certain welding outputs [ 141. Since the torch power Q in Table I1 exhibits the smallest parameter alterations for positive and negative deviations from the nominal conditions, and thus approaches linearity in its effects, multiple torch systems at various arrangements and with independently modulated

IEEE Control Systems

Table I1 Identification Tests for the Analytical Model and Dynamics of the Linearized Model

1

1

Variable vorf Power

2.5 kW

3.0 kW

0.75

Width w KU 2.12

2

Power

2.5 kW

2.0 kW

0.78

1.83

3

Velocity

6 “/s

10“/s

0.6

-0.75

4

Velocity

6 mm/s

4“/s

1.4

-1.7

5

Wirefeed

600idmin

800irdmin

0.95

0.026

Test #

From

To tiv

power can be used for lumped welding control. Alternatively, multitorch configurations can be regarded as an in-process implementation of preheating or postheating process stages, which are usually practiced off-line to obtain the necessary weld bead penetration without excessive metallurgical effects in a limited heat affected zone. Such a 3x3 welding system for bead geometry control in longitudinal welding of open cylindrical shells (Fig. 3) employs nonconsumable lateral torches Q2 and a backbead torch Q3 in addition to the primary GMAW torch Ql. The secondary torches Q2 and Q3 have a preferential effect on streams 1 and 2 in the weld pool respectively (Fig. l),thus providing decoupled control of the width w and penetration d. These are estimated by the analytical model through temperature measurements Ty and Tz, respectively, by a line scanning IR camera, which also measures the bead height h directly. Since such multitorch configurations involve the complexity and cost of multiple independent power sources as well as potential interference between the torches, a single heat source can be timeshared (Le., multiplexed in time) by rapid repetitive reciprocation on the weld surface, so as to imitate the effect of multiple torches [ 141. In the example of longitudinal GTAW of the cylindrical shells in Fig. 4, both the torch power Q(Q and its motion v( Y) relative to the workpiece are modulated to supply a continuous circumferential heat distribution q(y) providing the lumped heat inputs Ql and Q2 (virtual torches):

Depth d

0.52

1.67

0.82

Height h KI, -0.22

0.57

1.74

0.69

-0.17

0.4

-0.30

0.8

-0.15

1.2

-0.32

0.7

-0.24

0.65

,0094

0.4

,0042

Kd

td

1

~

~

th

-

where L is the distance and T the transition time between Ql and Q2. Notice also that the modulated rotation of the workpiece to implement the double-torch arrangement enables the periodic measurement of temperatures T,.and Tz by a single spot pyrometer. For GTA welding of stainless steel pipes in Fig. 4, the width w and depth d of the bead can be regulated through the directly measurable temperatures and T- respectively. For a maximum bead width wd, the temperature Tyd at this distance must by specified as less or equal to the solidus temperature of the material Tnl,while for full penetration of the shell the temperature Tzd must be specified higher that Tm.For this 2-input (Q1,Qz) x 2-output ( TJZ) system, the parameters of the linearized dynamic model

ry

are identified as before and collected in Table 111. Notice that the small values of Kz for Q2 indicate an almost decoupled effect of the secondary heat input on temperature T,.in the width direction, as expected. This model forms the basis for the design of a 2x2 adaptive thermal controller in the following sections.

Thermal Modeling in Welding

mI Line Scan IR Camera

~~

Fig. 3. Multitorch welding and thermal line scan sensing ofan open cylindrical shell.

August 1994

Besides weld bead geometry, thermal characteristics such as the final microstructure and properties of the material as well as the residual stresses and distortion of the joint are important weld quality descriptors. In particular, nucleation of certain undesirable equilibrium material phases requires regulation of the heat affected zone isotherm Th, while the formation of nonequilibrium structures is characterized by the centerline cooling rate at a critical temperature Tcr. In the previous section it was realized that the few lumped welding inputs of the GMAW and GTAW processes (Q, v,j) were barely sufficient for regulation of the basic geometric welding outputs (w,d,h).If thermal characteristics of the weld are to be controlled simultaneously to the geometrical ones, the introduction of additional inputs (virtual torches), implemented by time multiplexing of a nonconsumable torch, and positioned so as to cause decoupled effects becomes the only feasible approach. In the GMAW arrangement of Fig. 5, a secondary trailing torch Q2

17

Numerical Simulation The computational simulation of the thermal field in arc welding [14] integrates the transient conduction equation (Fourier) in discrete time steps t and space elements s, using an explicit Eulerian finite difference formulation:

Pyro

v/Y\

AS2

Q2 I

To encompass the solidus Tm and the heat affected zone (HAZ) T h isotherms, the model

Fig. 4. Multiplexed virtual torch welding and temperature measurement of an open cylindrical shell. ( a )Geometrical arrangement and pipe rotation. ( b )Modulation of torch power; velocity and heat distribution.

Test ~

Input

From

To

Temperature T,

Temperature T,

I

Qi

2.5 kW

3.0 kW

421

3.58

KZ 316

3.86

2

Qi

2.5 kW

2.0 kW

445

3.81

402

4.23

3

Q2

500W

600W

173

2.10

23

5.15

4

02

500W

400W

722

2.61

21

6.20

Ky

fv

follows the primary Ql along the centerline, located so as not to affect the heat affected zone (HAZ) width HZ, and thus provide decoupled control of the cooling rate CR [14]. This secondary torch can be considered as an in-process implementation of a postheating (annealing) or multipass cycle. Open-loop laser preheating as well as lateral [ 151 and weaving [ 181torches have also been 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 a specified value HZd, the peak temperature Tp observed along a sideline at distance HZd from the centerline can be controlled to the HAZ isotherm temperature Th. Again, the cooling rate CR can be substituted by the temperature drop Td that it causes during one sampling period of the controller, to the centerline point at the critical temperature Tcr. The two temperature outputs Tp and Td are measured directly in-process by line scans af an IR pyrometry camera along the sideline and centerline respectively, and regulated through the heat inputs Ql and Q2, implemented through torch reciprocation as in Fig. 4. The design of a thermal control system will be based on a dynamic numerical simulation of the temperature field, as well as on a linearized experimental model as before.

18

Ti(x+_As,yfAs,zfAs;t) - 6T(x,y,z,t)

tz

uses a fine and a coarse grid, respectively, which follow the motion of the heat source (Fig. 6). It can also handle multiple torches with arbitrary heat distributions, and the basic butt welding arrangement can be easily extended to more general configurations. The simulation provides for initial preheat and convective-radiative heat transfer from the boundaries, as well as temperature-dependent material properties and latent transformation effects. Also, the thermal convection in the pool is accounted for by equivalent anisotropic conduction through directional conduction coefficients. The torch efficiency and distribution parameters (n,o) are calibrated experimentally. The simulation also generates temperature and phase field section maps, as well as temperature hill and isotherm section contours and 3D surfaces.

Experimental Model Starting at the nominal conditions, a linearized model of the thermal dynamics is again derived by experimental positive and negative step perturbations of the heat inputs Ql and Q2, and formulated through delayed first order transfer functions of the welding outputs Tp and Td:

I

I

01

02

Y

I

Fig. 5. Input-output definition of the thermal system.

f E E E Control Systems

Q1

I

where Y=[T, TzlTor[TpTdITisthe vector of welding outputs and d are their respective delays. _V is an augmented state vector including current and n previous values of the outputs Yas well as current and m previous values of the inputs Y=[Qi Q21T, where m and n are the degrees of the numerator and denominator polynomials of the respective transfer functions. The parameter matrix 0,initially estimated from the values in Tables I11 and IV, is updated by a recursive adaptation law, based on the orthogonal projection of the state vector Yon its measured error:

02

grid

I

Large grid

Fig. 6. Arrangement of the numerical simulation.

The experimental transients for butt GMAW of mild steel plates during test #1, together with the calibrated numerical simulations and the linearized model responses are shown on Fig. 7. The parameters of the transfer functions are again determined through fitting of the linearized transients to the experimental data, and collected in Table IV. Notice the decoupled effect of the secondary heat input Q2 on the temperature drop Td, as well as the improved linearity and similarity of dynamic parameters, attributed to the adoption of thermal outputs (Tp,Td) and heat inputs (Qi, Q2) of uniform nature. 1-1.029

1

Lumped Adaptive Control System

-g.

For both the geometrical and thermal weld-

880.

where y is the adaptation gain and 6 the sampling period. If the delays d and orders m and n of the system dynamics are known, and the sampling period 6 is long enough to cover the measurement, computation and process delays or nonminimum phase effects, then the ARMA equation is invertible and forms the basis of a stable deadbeat control law. Given a set of desired outputs &, this equation can be solved for the necessary welding inputs y in the vector 45, on the basis of the estimated parameters 0 (t): Solve for g ( t ) : Yd(t+d)= O(t)._V(t). It can be shown that this multivariable adaptive strategy ensures the boundedness of inputs II and outputs Y, the convergence of parameters 0 and asymptotic tracking of the specified output values &.The original algorithm [26], [27] was modified

PRIMARY HEAT INPUT POSITIVE STEP RESPONSES.

-70. I

p

0

1

-80.

ing models of Tables I11 and IV, respectively,the Y -85. 4a 860. K differences in the values of the dynamic parame-90. ters for positive and negative step of the same 840. -95. input variable, as well as the variations of the 820. -100. torch parameters ( n , o ) ,indicate the nonlinearity 0. 5. 10. 15. 20. 25. 30. 0. 5. 10. 15. 20. 25. 30. of the welding process. Because of thermal drift TIME (S). TIME (S). of the material properties, the process is also nonstationary (time-varying). Additionally, many disturbances in the welding geometry, Fig. 7. Step response of the thermal system after a heat input changefrom Qi=2.5 to ambient conditions and process characteristics 3 kW 000:Experimental data. -: Numerical simulation- - . -:Linearized model. are reflected as intemal parameter alterations. All these effects call for in-process identification and adaptation of the control system to the paController Welding PID Process - a rameter uncertainty, as well as robustness to Filter r+ & Actuator unmodelled welding dynamics. Other require'Parameters 8 ments include closed-loop stability in welding ranges of practical interest, satisfactory time perParameter Cformance and suitability of the MIMO control strategy to the input-output structure of the Temperature linearized model. Measurement Secondary Y loop The experimental process models can be written in a discrete-time, autoregressive moving average (ARMA form as:

p

I

- -

I Y(t+d) =

August 1994

I

O.x(t)

Fig. 8. Adaptive thermal welding control system.

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to include saturation of the welding inputs with antireset windup to avoid bum-through, lack of fusion and excessive porosity of the weld. Also, the adaptation gain y is modulated in-process to avoid singularities and optimize the numerical conditioning of the deadbeat control law. Finally, a second external feedback loop with feedforward filters is employed to smooth the deadbeat effects and improve the closed-loop performance (Fig. 8).

1580 1560

0

5

15

10

20

1700

0

5

Time (s)

Time (s)

10 15 Time (s)

20

Time (s)

Fig. 9. Closed-loop responses of output temperatures Ty, Tz and heat inputs QI, Q2 after a velocity disturbance v=6 to 5 m d s .

OUTPUT RESPONSES TO A STEP COMMAND. 890. 880. 870.

-.

-

860. 850. 840. 830. 820.

5 ?L

a

g p

-70. -75.

-80. -85. -90. -95. -100.

TIME (S).

TIME (S).

ESTOAS

2850. 2800. 2750. 2700.

5 8

E:;

6

2550. 2500. 0. IO. 20. 30. 40. 50. 60. TIME (S).

650. 600. 550. 500. 450. 400. 350. 300. 250. 0. IO. 20. 30. 40. 50. 60. TIME (S).

Fig. 10. Closed-loop responses ofoutput temperatures Tp, Td, and heat inputs Qi,Q2 after a change of the reference setpoint. 000: Experimental data. -: Numerical simulation. - . - . -:Linearized model.

Closed-LoopWelding Performance As already explained, the bead cross section geometry in GTA welding of cylindrical stainless steel shells (Fig. 4) can be described by the temperatures TJ and Tz adjoining to the maximum width and penetration locations. These are regulated in process through the virtual heat inputs Ql and Q2of the timeshared torch, according to the multivariable adaptive strategy above. The closed-loop behavior of this geometry control system in rejecting process disturbances is tested when the welding velocity is suddenly reduced from the nominal 6 “ I s to 5 m d s , thus initiating an increase of the weld pool size, and the respective transients are shown in Fig. 9. The numerical simulation, adapted and employed as a butt GTAW process model under feedback control, matches well the experimental model responses of the temperature outputs. However, the modeling imperfections are manifested as differences between the steady-state values of the required heat inputs after the disturbance transients. Despite these deviations, the effects of the torch deceleration are completely rejected by the adaptive controller. In the same way, the thermal characteristics of the HAZ and cooling rate in robotic GMAW of mild steel plates can be controlled via the equivalent peak and drop temperatures ( Tp,Td) through the multiplexed torch powers (QI,Q2) of Fig. 5 , by a similar 2x2 adaptive deadbeat controller. The responses of the resulting closedloop system are assessed during a step reference command to the specified Tpd, Tdd (Fig. 8), cor-

Table IV Identification Tests for the Dynamic Parameters of the Linearized Model I

I

I

I

I

Temperature Tp

Temperature Td

To 1 I

KP

I

I

2.5 kW

Q1 I

3.0 kW

tP

0.239

I

2.57

dP

Kd

0.50

0.0340

I

I

2

Qi

2.5 kW

2.0 kW

0.250

2.72

0.55

3

Q2

500w

I .0 kW

0.0008

0

4

42

500 W

0.0 w

0.0028

0

20

‘

dd

td

4.55

0.96 I

~

0.0439

4.05

1.06

0

0.0405

3.75

0.14

0

0.0421

2.52

0.34

I E E E Control Systems

responding to a wider, steeper temperature hill on the weld surface, and plotted in Fig. 10. Again, the numerically simulated transients of the outputs and the responses of the linearized model match the experimental behavior of the feedback system, al-

-50.

though static differences between the model predictions appear as deviations of the respective heat inputs at the steady state. Despite this, the desired reference temperatures are eventually obtained exactly in all cases. The range of achievable welding output setpoints (Tpd,Tdd) of this thermal system can be determined by numerical simulation, and it is depicted in Fiq 11, as a mapping of the unsaturated heat input pairs U=[Ql Q2] to the resulting steady state temperature [TpTdlT. The feasible reference setpoints are inside outputs the envelop line. Although the slopes of the two constant-input curve families generally denote a coupled input-output dependence, the angles between the curves indicate the preferential effect of Ql on Tpand Q2 on Td, as expected. The high total power end of the reachable area corresponds to a single flattened temperature hill on the weld surface, thus resulting in a coupled, limited control authority, while the low power end corresponds to two widely separated peaks of the temperature hill, resulting in decoupled, more efficient regulation.

r(m)=

-100.

-150.

Distributed-Parameter Welding Control

I

Y a

2n k

-200.

600.

700.

800.

900.

1000

TPEAK (K).

Fig. 11. Simultaneous control range of temperatures Tp and Td by the heat inputs QI and Q2.

A

Robot

Ah.

I( 1

/\\\TorchAHeat

Control

Trajectories

1

Measurements

Fig. 12. Implementation and trajectories of distributed welding system with IR feedback.

August 1994

Since Fig. 11 indicates that specification of a desired setpoint (Tpd,Tdd) outside the enveloped region in not achievable by this welding process, it is evident that lumped heat inputs from distinct virtual torches Qi, Q2 allow independent variation of the welding outputs in a limited controllable range. Moreover, localized thermal measurements on the weld surface enable the estimation of limited observable intemal weld characteristics, such as the bead penetration, HAZ width, etc. Both limitations stem from the lumped, concentrated actuation and sensing techniques inherent in the welding process, and they are clearly not a consequence of the open or closed-loop control method. As already realized, carefully arranged configurations of multiplexed virtual torches and spot temperature measurements enable decoupled control of multiple distinct weld features through reshaping of the thermal field in the welded parts. However, a broad-range regulation of the total thermal distribution in the workpiece is needed for combined control of structure, properties and stress conditions of the material. Thus, a generalization of the ideas above suggests a continuous heat distribution on the entire accessible weld surface, with its intensity independently modulated at each boundary location. Similarly, the estimation of the intemal thermal field necessitates full surface measurements during the process. Such a distributed-parameter formulation of welding modeling and control insures maximal flexibility in identification and regulation of all weld quality and productivity measures simultaneously. As before, the distributed heat actuation in welding can be implemented by repetitively scanning the weld surface with a single torch and by modulating its thermal power as a function of its position, so as to mimic a continuous spatial distribution. This scanning motion can be performed in a raster fashion, i.e., by periodical sweeping of a static orthogonal pattem on the weld surface and by adjusting the heat input for each raster element. Rather, a vector scanning technique will be employed, in which the torch follows dynamically controlled trajectories on the surface to implement the specified heat distribution. This technique is more energy efficient and less demanding in terms of bandwidth of the welding equipment. The method is illustrated in Fig. 12, where a GTAW torch is cycled in a fast repetitive motion pattem along longitudinal sideline paths at various dis-

21

tances from the centerline of the butt weld. The torch power Q(t) is adjusted and its trajectory X ( t ) , Y(t) is modulated by coordinated motion of the workpiece by the servodriven table and the torch by the high-speed robot, so that the desired heat distribution q(X, Et) is implemented. The temperature field on the weld surface T(x,y;t) is monitored by an IR pyrometry camera with a servoed mirror scanner. Fig. 13 compares these temperature fields measured on the top surface for conventional and scanned GTAW of thin (3 mm) stainless steel plates, under identical process conditions (arc length 3 mm, voltage 15 V, current 100 A, inert gas Ar-2%02 flow of 0.4 Ids). The travel speed in the traditional technique was 3 “/s, while the average velocity of the torch reciprocation in the scanning method was 120 m d s . Clearly scanned welding results in a more uniform longitudinal temperature distribution, with smooth transverse thermal gradients. This temperature hill generates an elongated weld puddle with controlled melt solidification, and a heat ffected zone with regulated cooling rates.

TRAD. WELD MEASURED FIELD

T(x,y,z;t:X,Y,~)is the temperature of the (x,y,z) point at time t because of a unit heat input from the torch at point (X, Y,O) at time 7,and h is the surface convection coefficient, then: m

1

T(x,y,z;f:X,Y,Z)=

k=-- 8pc[xa(t-r)13”

- ( x - X ) ~+ (y-Q2

I-

+ ( ~ - 2 k - D ) ~2 h ( t - ~ )

4a(t-z)

PCD

In longitudinally uniform welding, in which the process conditions (including part geometry, fixturing, material preheat, and ambient conditions) do not vary along the centerline, this threedimensional Green’s function is reduced to a two-dimensional The resulting longitudinally invariant temperafield T(y,z;t:Y,T). ture field applies to certain industrially important cases such as straight plates, pipe girth, and flange welding. Also for thin, fully penetrated welded plates, the Green’s field will be one-dimensional Tcy;t:Y,~)(Fig. 14). Because of the linearity of this thermal problem, the heat distribution q ( X ,Y;T) on the weld surface will produce a temperature field T(x,y,z;t)by superposition: T(x,y,z;t)= T(x,y,z:O)

+

f $(x,y,

T(x,y,z;t:X , Y , T ) . ~ ( X , Y , dXdY.dz T)

0

SCAN WELD MEASURED FIELD

which simplifies to a single time integral convolution for a timeshared heat input q(X(T),Y(T);T) from a single torch. Notice that the numerical simulation already developed can also be used as a distributed temperature field model for additional flexibility in handling realistic thermal conditions and for improved accuracy with nonlinear heat transfer phenomena. Distributed-Parameter Estimation and Control For real-time estimation of the temperature field, a computationally efficient quasilinear, adaptively-weighted superposition technique is used, as it combines the advantages of the analytical,

2500

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

These thermal effects result in a favorable metallurgical structure in the weld, and consequently superior mechanical properties of the weld joint. Distributed-Parameter Modeling In the literature, the mathematical (functional operator) analysis of distributed-parameter systems [28]-[32] has failed so far to provide useful control design tools for practical manufacturing processes. Useful modeling insight to the thermal distribution is provided by an analytical conduction solution for the temperature field, derived using Green’s function analysis 1341. If

22

2000

I

THERMAL DISTRIBUTION ACROSS THIN S.S. PLATE

I

k0.5~

Timet=0.5.1.1.5...5s

1

I -

1 2 3 4 y Distance from Centerline (m)

1

5

xlO-3

Fig. 14. Temperature field T(y;t) generated in (I thin stainless steel plate 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-process thermal observer is necessary in direct real-time parameter identification, and it is based on a two-dimensional convolution of the Green’s temperature field similar to the previous equation. However, rather than determining the Green’s function analytically, this is computed off-line under realistic process conditions by the numerical simulation, calibrated so as to match the experimental measurements on the part surface. Also, instead of calculating the Green’s function values in real time, these are stored in a 3-D look-up table for various surface distances of the torch, depths in the plate and elapsed times. In-process convolution of these data needs only to consider numerically signifi-Lant components (Le., from neighboring and recent heat inputs) to the desired level of accuracy. Although this quasilinear superposition applies strictly to limited ranges of welding conditions, the thermal process nonlinearities are smooth and locally

r -

I

Fig.15. Trajectory Y ( X ) andpower Q(X)control based on the error e(x,y)of the temperature field T(x,y)from the specified Td(x,y)for a flange weld.

linearizable in wide ranges through appropriate adjustment (weighting) of the heat distribution q in the equation above. The simplicity and spatial-temporal decoupledness makes this method well suited for efficient parallel computation of only the necessary thermal field values. Instead of the deadbeat control law used previously, a more efficient strategy for vector modulation of the torch motion is developed on the basis of direct specification of a desired thermal distribution. Planning of the torch trajectories is based on a specified temperature field Td(x,y,z;t),determined by computational simulation through optimization of some welding performance criterion. Altematively, if a satisfactory pilot weld can be produced experimentally in the laboratory by some welding technique, its surface temperature field is measured by thermographic pyrometry, recorded as a function of time and specified as Td in order to be reproduced by the distributed welding control system. In both cases, if e is the deviation (error) of the in-process measured temperature field T from the desired Td,then the torch is driven along the locus Y ( X )of the transverse maxima of this error surface e (Fig. 15). The heat input per unit length q(X,Y(x);t)required to determine the torch power Q(t) is a linear (e.g., PID), but can also be any nonlinear functionfof this local error: Thermal error: e(x,y,z;t) = Td(x,y,z;t) - T(x,y,z;t) Trajectory Y(X):de/dy(X,Y(X),O;t)= 0

August 1994

Heat input q(X):q(X,Y(X);t) = f[e(X,Y(X),O;t)] and Q = q( X ,Y f X );t)dX Torch power & speed:Q(t) = Q/dt and X(t) = Q(t)‘l/Q where 1 and dt are the length and duration of a single reciprocation of the torch. Analogous trajectory control can be obtained if, instead of specifying Td to regulate HAZ-related characteristics, the cooling rate aT&t is set for nonequilibrium structure control, or the thermal gradient VTd to describe residual stresses or thermal distortion.

Advantages of Distributed Welding As already explained, distributed parameter control of the thermal field in welding provides comprehensive in-process regulation of the final weld bead geometry, microstructure, and properties of the material, as well as residual stresses or joint distortion. Thus, it can be used for optimization of lumped welding quality or productivity measures, such as the static and dynamic strength of the weld, fracture toughness, geometric tolerances corrosion and oxidation resistance, or any weighted combination of these indices. The scanning torch actuation on the weld surface can implement any arbitrary heat distribution, including conventional single-torch or multiple virtual torch arrangements, and temperature sensing on the entire weld surface provides all necessary measurements for estimation of intemal characteristics, such as the bead cross section. As a result, distributed welding yields superior control and observation authority in the broadest possible operating ranges, and decouples the timelspace dependence of the lumped actuation and sensing in classical welding. Experimental investigation of these beneficial effects is currently in progress (Fig. 12). These advantages of multiple virtual torch and distributed welding techniques have been obtained primarily through the redesign of conventional welding methods, i.e., modification of their process configuration so as to take advantage of modem control and estimation strategies. Indeed, distributed welding differs from traditional techniques currently practiced in industry both in spatial distribution and in process evolution over time. Classical welding is a localized, serial process [35], i.e., the thermal field and the weld bead are developed sequentially in time, in longitudinal increments. In contrast, distributed welding is a parallel process, since the weld is heated and the bead is deposited simultaneously in the longitudinal direction, in progressive cross-sectional increments. Thus it can provide a longitudinally invariant thermal field, with several advantages in process speed and efficiency, improved linearity of the welding dynamics, elimination of preheating and postheating requirements, as well as weld bead defects associated with starting and extinguishing the torch. Last, the multiplexed virtual torch and distributed welding control and estimation methodology analyzed in this article is directly interfaceable to the product and process design software, by sharing the same geometric modeling descriptions of objects and motions. The part geometry, the material and process conditions are typically developed on a computer-aided design (CAD) system, and transferred to the controller design software. This will retum to the geometric modeling environment, the optimal process schedule and the scan trajectory descriptions for the actuator and the sensor. It will also provide estimates of the performance indices and suggest modifications of the part geometry and process conditions, such as the fixturing areas on the

23

surface. This interactive redesign of the thermal process will be aimed at the optimization of its control and observation authority, by combining the product and control system design procedures in an integrated fashion, with the concomitant benefits for the production and quality of industrial welding.

References [ l ] C.J. Smith, “Self-adaptive control of penetration in tungsten inert gas weld,” Advances Weld. Proc., pp. 272-282, 1974.

[ 191 H.S. Cho, “Application of AI to welding process automation,” in Proc. ASME JapaniUSA Symp. Flex. Auto., July 1992, pp. 303-308.

[20] G.E. Cook, K. Andersen, and R.J. Barrett, “Computer-based control system for GTAW,” in Proc. ASME JapunlUSA Symp. Flex. Auto., July 1992, pp. 297-301. [21] P. Banerjee and B.A. Chin, “Front side sensor based dynamic weld penetration control in robotic GTAW,” in Proc. ASME JapanlUSA Symp. Flex. Auto., July 1992.

[Z] A.P. Bennett, “The interaction of material variability upon process requirements in automatic welding,” Advances Weld. Proc., 1974.

[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 in GMAW,” in Proc. ASME JupanlUSA Symp. Flex. Auto., July 1992.

[3] E.A. Gladkov, A.I. Akulov, A.V. Petrov, 0.1.Sokolov, and.4.N. Aleksandrov, “An automatic stabilizer of penetration in plasma welding with a penetrating arc,” Weld. Prod. U.S.S.R. vol. 24, pp. 26-27, Nov. 1977.

[23] R.W. Richardsn and C. Conrardy, “Coaxial vison-based control of GMAW,” in Pmc. ASME JapaniUSA Symp. Flex. Auto., July 1992.

[4] A.R. Vorman and H. Brandt, “Feedback control of GTA welding using puddle width measurement,” Welding J., pp. 742-746, Sept. 1978.

[ 5 ]P. Boughton, G. Rider, and E.J. Smith, “Feedback of weld penetration in 1978,” Adisances Weld. Proc. pp. 203-209, 1978. [6] Y. Chi, D. Yin, and Y. Gao, “Closed-loop control of weld penetration in pulsed 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 arc welding process,” Dev. Mech. Auto. Robot. Weld., pp. 37-49, 1980.

[8]. G.E. Cook, “Feedback and adaptive control to process variables in arc welding,” De\: Mech. Auto. Robot. Weld., pp, 321-329, 1980. [9] H. Nomura, Y. Satoh, K. Tohno, Y. Satoh, and M. Kuratori, “Arc light intensity controls current in SA welding system,” .I. Welding Metal Fab., pp. 457-463, Sept. 1980. [lo] D.A. Domfeld, M. Tomizuka, and G. Langari, “Modelling and adaptive control of arc welding processes,”Meus. Control Batch Manufact., pp. 53-64, Nov. 1982. [ l l ] D.E. Hardt, D.A. Garlow, and J.B. Weinert, “Amodel of full penetration arc welding for control system design.” Trans. ASME J . Dyn. Sysf., Meas. Control, vol. 107, pp. 40-46, Mar. 1985. [I21 B.E. Bates and D.E. Hardt, “A real-time calibrated thermal model for closed-loop weld bead geometry control,” Trans. ASME J . Dyn. Syst., Meas. Control, p. 25-33, Mar. 1985. [ 131. A. Suzuki. D.E. Hardt, and L. Valavani, “Application of adaptive control theory 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 of heat affected zone and cooling rate during arc welding,” Welding J . , vol. 69/5, pp. 186s-l96s, May 1990, [15]. H. Miyachi, “In-process control of root-gap changes during butt welding,” Ph.D. thesis, Dept. of Mechanical Engineering, M.I.T., 1989. [16] M. Hale, “Multivariable geometry control of welding,” presented at ASME Winter Ann. Meet., Symp. Manufact. Proc. Modeling Control, Dec. 1990. [17] J.B. Song and D.E. Hardt, “Multivariable adaptive control of bead geometry in GMA welding,”presented at ASME WAM Symp. Welding, Dec. 1991. [18] R. Masmudi and D.E. Hardt, “Multivariable control of geometric and thermal properties in GTAW,” presented at 3rd ASM Conf. Trends Welding Res., Gatlinburg, TN, June 1992.

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[24]. J.L. Schiano, J.H. Ross, and R.A. Weber, “Modeling and control of puddle geometry in gas-metal arc welding,” in Proc. 1991 Amer. Control Cons., Boston, MA, 1991. [25] C.C. Doumanidis, “Weld bead geometry control based on lumped pool modeling,” Trends Weld. Res., presented at 3rd Conf. ASM Int., Gatlinburg, TN, June 1992.

[26] G.C. Godwin, P.J. Ramadge, and P.E. Caines, “Discrete-time multivariable adaptive control,” IEEE Trans.Auto. Confro/,vol. AC-25, pp. 449-456, June 1980. [27] C.E. Rohrs, L. Valavani, M. Athans, and G. Stein, “Robustness of adaptive control algorithms in the presence of unmodelled dynamics,” IEEE Trans. Auto. Control, vol. AC-30, pp. 881-889, Sept. 1985. [28] N.K. Bose, Multidimensional Systems, Theory and Applications. New York, NY: IEEE Press, 1979. [29] J.L. Lions, Optimal Control of Systems Governed by Partial DifSerential Equations. New York, N Y Springer-Verlag. 1971,

[30] M. Delfur, A. Bensoussan, and S.K. Mitter, Linear Irrfirrite Dimensional Sysrems. Cambridge, MA: M.I.T. Press, 1983. [311 J.R. Partington and K. Glover, “Robust stabilization of delay systems by approximation of coprime factors,” Sysr. Contra/ Lett., vol. 14, pp. 325-31, Apr. 1990. [32] T.T. Georgiou and M.C. Smith, “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 distributed parameter 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,” ASME Manufacf. Rei:,. to be published.

Charalabos Doumanidis received the diploma in mechanical engineering from the Aristotelian University of Thessaloniki (1983), the M.S. degree from Northwestem University (1985), the Ph.D. degree from the Massachusetts Institute of Technology (1988), and worked as a Postdoctoral Research Associate at the Laboratory of Manufacturing and Productivity, M.I.T. (1989). He is currently Assistant Professor of Mechanical Engineering at Tufts University, and his research interests include thermal manufacturing process modeling and control, and biomedical instrumentation. He is a member of ASME, ASM, SME, and IASTED.

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