te System AVC Control GTAW orkplec FIGURE 104.3 Simplified gas tungsten arc welding setup time with addition of new training data. Finally, the neural network can calculate its results relatively quickly as the input data are only propagated once through the network in the application mode. The reader is referred to Andersen [1992] for a more thorough discussion of the neural network approach to weld process modeling. Andersen also presents a detailed comparison of neural network modeling to two nalytical models and a statistically based multidimensional parameter interpolation approach Control Practical considerations The easiest approach to controlling multiple weld process parameters can be realized if input variables can be found that affect only a single output quantity. If the output variable is affected by another input variable as well, then one may be the primary variable while the other may constitute a secondary feedback loop that is capable of controlling the output quantity by a relatively small amount with respect to the basic level set by the primary variable. For example, high-frequency pulsation of the current in GTAw may provide a means of controlling the depth of penetration over a small range without affecting the width of the weld bead. In this case the heat input, as determined by the voltage, current, and travel speed, would be the primary input variable Even for single-variable weld process control, nonlinearities in the process may call for an adaptive system to automatically adjust the parameters of the controller when the process parameters and disturbances are unknown or change with time. For example, Bjorgvinsson 1992] shows that a simple automatic voltage control AVC)system may be unstable over a wide range of current settings because of the variation of the arc sensitivity (voltage change per unit change of arc length) with current. A simplified schematic of an AVC system is shown in Fig. 104.3. The arc voltage(proportional to the arc length)is compared with a reference voltage in a simple position servo. If an error exists between the reference voltage and the arc voltage, the servo motor moves the welding torch up or down to reduce the error to zero. If K is the gain of the AvC motor drive system and K, is the arc sensitivity(,=dvarddLard), then the overall loop gain K is given by K=KK The closed-loop stability of the position control system is dependent on the loop gain and will obviously vary from its design setting if K, changes. Bjorgvinsson shows that for helium shielding gas, the arc sensitivity may vary by approximately a ratio over a current range of 15 to 150 A. In this case, for a standard proportional controller, the overshoot to a step input at 15 a is approximately 40% if the controller gain K, is fixed and set for optimum response at 150 A. Bjorgvinsson proposes a gain-setting adaptive controller(see Fig. 104. 4)to vary the controller gain in such a manner as to compensate for the changing arc sensitivity for all levels of welding current. Knowing the arc current, the adaptive controller uses information stored in a look-up table or computed from a mathematical e 2000 by CRC Press LLC
© 2000 by CRC Press LLC time with addition of new training data. Finally, the neural network can calculate its results relatively quickly, as the input data are only propagated once through the network in the application mode. The reader is referred to Andersen [1992] for a more thorough discussion of the neural network approach to weld process modeling. Andersen also presents a detailed comparison of neural network modeling to two analytical models and a statistically based multidimensional parameter interpolation approach. Control Practical Considerations The easiest approach to controlling multiple weld process parameters can be realized if input variables can be found that affect only a single output quantity. If the output variable is affected by another input variable as well, then one may be the primary variable while the other may constitute a secondary feedback loop that is capable of controlling the output quantity by a relatively small amount with respect to the basic level set by the primary variable. For example, high-frequency pulsation of the current in GTAW may provide a means of controlling the depth of penetration over a small range without affecting the width of the weld bead. In this case the heat input, as determined by the voltage, current, and travel speed, would be the primary input variable controlling the width and penetration, while the high-frequency pulsation would be the secondary variable capable of producing small corrections to the basic penetration depth. Even for single-variable weld process control, nonlinearities in the process may call for an adaptive system to automatically adjust the parameters of the controller when the process parameters and disturbances are unknown or change with time. For example, Bjorgvinsson [1992] shows that a simple automatic voltage control (AVC) system may be unstable over a wide range of current settings because of the variation of the arc sensitivity (voltage change per unit change of arc length) with current. A simplified schematic of an AVC system is shown in Fig. 104.3. The arc voltage (proportional to the arc length) is compared with a reference voltage in a simple position servo. If an error exists between the reference voltage and the arc voltage, the servo motor moves the welding torch up or down to reduce the error to zero. If Ka is the gain of the AVC motor drive system and Ks is the arc sensitivity (Ks = dVarc/dLarc), then the overall loop gain K is given by K = KaKs . The closed-loop stability of the position control system is dependent on the loop gain and will obviously vary from its design setting if Ks changes. Bjorgvinsson shows that for helium shielding gas, the arc sensitivity may vary by approximately a 5:1 ratio over a current range of 15 to 150 A. In this case, for a standard proportional controller, the overshoot to a step input at 15 A is approximately 40% if the controller gain Ka is fixed and set for optimum response at 150 A. Bjorgvinsson proposes a gain-setting adaptive controller (see Fig. 104.4) to vary the controller gain in such a manner as to compensate for the changing arc sensitivity for all levels of welding current. Knowing the arc current, the adaptive controller uses information stored in a look-up table or computed from a mathematical FIGURE 104.3 Simplified gas tungsten arc welding setup
ARC CONTROLLER AMPLIFIER VOLTAGE GAIN SETTING ADAPTIVE REVERSIBLE CONTROLLER MOTOR CONDITIONER VOLTAGE CONSTANT SUPPLY FIGURE 104.4 Gain -setting adaptive automatic voltage control. model of the arc to adjust K, in response to changes in K, such that the product K,K,=K is maintained constant independent of the current. The result is uniform closed-loop stability characteristics of the AVC system throughout the complete weld. This includes the up-slope period, when the current is varied from the low ar nitiation value to the nominal welding current, which is maintained until the down-slope period, when the urrent is brought back to a low value for termination of the arc. General Approaches to Multivariable and Adaptive Weld Process Control The welding process is generally nonlinear, and the different variables are normally coupled. If we can assume localized linearity, then adaptive control techniques can be used to change the controller characteristics in response to changes in the operating domain. To handle the multivariable control problem, we attempt to decouple the process input-output variables by appropriate controller design in order to reduce the system to a set of essentially noninteracting loops. Controller design can then be carried out using single-loop techniques. Necessary and sufficient conditions have been derived for decoupling a multivariable system. Unfortunately, the conditions are, in general, unlikely to be satisfied in practice because of model approximations, measurement uncertainties, parameter perturbations, and other causes. Therefore, system decoupleability may be inhibited by constant compensation techniques. In these situations, it is more appropriate to decouple the system in real time using an adaptive controller. It has been shown that such an adaptive controller can be expected to eventually achieve exact decoupling after the system parameters have converged A general multivariable adaptive direct weld process control system is shown in Fig. 104.5. It will frequently be the case that not all of the DwP that we wish to control can be directly sensed with available sensors. In this case, we may estimate the DWP(s) that we cannot measure and use the estimated values for feedback information. Control of these parameters will obviously not be any better than the model used to estimate nem. However, the model may be continuously tuned, i.e, calibrated, from both the IWP and those DWP that are directly sensed Cook et al. [1991] have described a multivariable weld process control system that makes use of a model to stimate one of two DWP(s)controlled. The system, shown in Fig. 104.6, was configured to accept weld bead width and weld penetration as its two inputs. The system used width sensing, but penetration was only available as an estimate from the forward process model acting in parallel to the actual process. Conventional time-base up-sloping/down-sloping was used for weld initiation and termination, so an inverse process model was use to provide initial weld IWP(s)(following up-slope)to the weld start sequencer. Referring to Fig. 104.6, the desired bead width and penetration are specified by the user as W. and Po, respectively. These parameters, as well as the workpiece thickness H, are routed to a neural network setpoint selector(inverse process model) c2000 by CRC Press LLC
© 2000 by CRC Press LLC model of the arc to adjust Ka in response to changes in Ks such that the product KaKs = K is maintained constant independent of the current. The result is uniform closed-loop stability characteristics of the AVC system throughout the complete weld. This includes the up-slope period, when the current is varied from the low arcinitiation value to the nominal welding current, which is maintained until the down-slope period, when the current is brought back to a low value for termination of the arc. General Approaches to Multivariable and Adaptive Weld Process Control The welding process is generally nonlinear, and the different variables are normally coupled. If we can assume localized linearity, then adaptive control techniques can be used to change the controller characteristics in response to changes in the operating domain. To handle the multivariable control problem, we attempt to decouple the process input–output variables by appropriate controller design in order to reduce the system to a set of essentially noninteracting loops. Controller design can then be carried out using single-loop techniques. Necessary and sufficient conditions have been derived for decoupling a multivariable system. Unfortunately, the conditions are, in general, unlikely to be satisfied in practice because of model approximations, measurement uncertainties, parameter perturbations, and other causes. Therefore, system decoupleability may be inhibited by constant compensation techniques. In these situations, it is more appropriate to decouple the system in real time using an adaptive controller. It has been shown that such an adaptive controller can be expected to eventually achieve exact decoupling after the system parameters have converged. A general multivariable adaptive direct weld process control system is shown in Fig. 104.5. It will frequently be the case that not all of the DWP that we wish to control can be directly sensed with available sensors. In this case, we may estimate the DWP(s) that we cannot measure and use the estimated values for feedback information. Control of these parameters will obviously not be any better than the model used to estimate them. However, the model may be continuously tuned, i.e., calibrated, from both the IWP and those DWP that are directly sensed. Cook et al. [1991] have described a multivariable weld process control system that makes use of a model to estimate one of two DWP(s) controlled. The system, shown in Fig. 104.6, was configured to accept weld bead width and weld penetration as its two inputs. The system used width sensing, but penetration was only available as an estimate from the forward process model acting in parallel to the actual process. Conventional time-based up-sloping/down-sloping was used for weld initiation and termination, so an inverse process model was used to provide initial weld IWP(s) (following up-slope) to the weld start sequencer. Referring to Fig. 104.6, the desired bead width and penetration are specified by the user as Wo and Po, respectively. These parameters, as well as the workpiece thickness H, are routed to a neural network setpoint selector (inverse process model), FIGURE 104.4 Gain-setting adaptive automatic voltage control
SYSTEM CONTROL DISTURB DISTURB PROCESS EQUIP WELDING WELD CONTRLRMCONTRLREQUIP PROCESS IwPs DWP ESTIMATED DWPs ESTIMATR DIRECTLY SENSED DWPs FIGURE 104.5 Multivariable adaptive weld process control system. -P]-CU Process FIGURE 104.6 Closed-loop weld process control system which produces the nominal travel speed, current, and arc length(vo, Io, and Lo, respectively). Arc ini and stabilization are controlled in an open-loop fashion by the weld start sequencer. Given the desired ment parameters, the typically initiated and established at a relatively low current, with the other equipment parameters set at some nominal values. Once the arc has been established, the equipment parameters are ramped to the setpoint values specified by the neural network. When the setpoint values have been reached, at time t=T, the closed-loop process control is enacted. As stated previously, the bead width from the process was monitored in real time, while a real-time penetration sensor was not used. Therefore, a second neural network(forward process model) is run in parallel with the process to yield estimates of the penetration. The measured bead width and the estimated penetration are subtracted from the respective reference values, processed through proportional-plus-integral controllers, and added to the final values obtained from the tpoint sequencer. When a workpiece thickness variation is encountered in the process, the system adjusts the current and the arc length accordingly to maintain constant bead geometry. To demonstrate the multivariable weld process control system Cook et al. report an experiment using mild teel for the workpiece material. Plates of two thicknesses, 3. 175 and 6.35 mm, were joined together, and a bead-on-plate weld using the nominal parameters(I=100 A, Larc=2. 54 mm, v=2. 54 mm/s)was made across the boundary between the plates, from the thicker section to the thinner one. The bead width and penetration e 2000 by CRC Press LLC
© 2000 by CRC Press LLC which produces the nominal travel speed, current, and arc length (vo, Io, and Lo, respectively). Arc initiation and stabilization are controlled in an open-loop fashion by the weld start sequencer. Given the desired equipment parameters, the arc is typically initiated and established at a relatively low current, with the other equipment parameters set at some nominal values. Once the arc has been established, the equipment parameters are ramped to the setpoint values specified by the neural network. When the setpoint values have been reached, at time t = T, the closed-loop process control is enacted. As stated previously, the bead width from the process was monitored in real time, while a real-time penetration sensor was not used. Therefore, a second neural network (forward process model) is run in parallel with the process to yield estimates of the penetration. The measured bead width and the estimated penetration are subtracted from the respective reference values, processed through proportional-plus-integral controllers, and added to the final values obtained from the setpoint sequencer. When a workpiece thickness variation is encountered in the process, the system adjusts the current and the arc length accordingly to maintain constant bead geometry. To demonstrate the multivariable weld process control system Cook et al. report an experiment using mild steel for the workpiece material. Plates of two thicknesses, 3.175 and 6.35 mm, were joined together, and a bead-on-plate weld using the nominal parameters (I = 100 A, Larc = 2.54 mm, v = 2.54 mm/s) was made across the boundary between the plates, from the thicker section to the thinner one. The bead width and penetration FIGURE 104.5 Multivariable adaptive weld process control system. FIGURE 104.6 Closed-loop weld process control system
were 3.6 and 0.9 mm, respectively, on the thicker plate. With the controller disabled (equipment parameters maintained constant), the bead width increased to 4.0 mm and the penetration increased to 1. 2 mm when the weld pool entered the thinner plate. with the controller enabled, the width and penetration were maintained the same on the thin plate as they were on the thick plate with only a slightly discernible transient. Intelligent Control Practical weld process control implementation, particularly with multivariable and adaptive control, involves a substantial body of heuristic knowledge concerning the weld process and the numerous constraints that are involved in its control. The role that intelligent control concepts can play is to provide a systematic approach to dealing with these constraints. For example, for a given set of material parameters, one may wish to control several geometrical parameters plus cooling rate for the GMAw process, while maintaining operation in the spray transfer mode of the process Because of the close coupling among the equipment, material, and geometric parameters, and because of the small latitude of permissible variation of one parameter once the others are specified, tight constraints on the control system will be necessary to achieve the desired process quality It will be desirable to specify degrees of control permitted over the various parameters in terms of a hierarchy of parameter importance. For example, while the wire feed rate has an influence on bead width in the gTaw process, it would not be desirable to allow the wire feed rate to be varied excessively as a means of controlling bead width. Further, the allowable variation of a given parameter, or parameters, may not be symmetrical about he desired set point. Again, for the GTAw process, an increase in current may be partially offset by an increase in travel speed, whereas a reduction in both parameters would tend to more rapidly force the geometrical parameters outside the desired range. Consideration of the process dynamics is also necessary, particularly for successful control during the initiation and termination phases of the overall welding operation. In addition to the hierarchical considerations referred to above, the time sequence and rate of change of each parameter should be considered. Intelligent control concepts may be used to handle these practical control issues in a formal and logical manner Conclusions Rapid advances have occurred in the development of sensors and in the development of both steady-state and dynamic models suitable for real-time weld process control applications. In combination with multivariable, daptive control theory methods, the tools are becoming available for significant progress in multivariabl direct weld process control. Long-range efforts will focus on combining process modeling and microstructural evolution modeling for eventual control of both macro and micro parameters. Defining Terms Direct weld parameters(DWP): A collection of parameters that characterize the weld in terms of the weld reinforcement and fusion zone geometry, mechanical properties, weld microstructure, and discontinui Electron beam welding: A welding process that produces coalescence of metals with the heat obtained from a concentrated beam composed primarily of high-velocity electrons impinging on the surfaces to be d Electroslag welding: A welding process that produces coalescence of metals with molten slag that melts the filler metal and the surfaces of the parts to be joine Gas metal arc welding(GMAW): A welding process that produces coalescence of metals by heating them ith an arc between a consumable filler metal electrode and the parts to be joined. The process is used with shielding gas and without the application of pressure Gas tungsten arc welding(GTAW): A welding process that produces coalescence of metals by heating them with an arc between a nonconsumable tungsten electrode and the parts to be joined. The process is used with shielding gas and without the application of pressure. Filler metal may or may not be used. c2000 by CRC Press LLC
© 2000 by CRC Press LLC were 3.6 and 0.9 mm, respectively, on the thicker plate. With the controller disabled (equipment parameters maintained constant), the bead width increased to 4.0 mm and the penetration increased to 1.2 mm when the weld pool entered the thinner plate. With the controller enabled, the width and penetration were maintained the same on the thin plate as they were on the thick plate with only a slightly discernible transient. Intelligent Control Practical weld process control implementation, particularly with multivariable and adaptive control, involves a substantial body of heuristic knowledge concerning the weld process and the numerous constraints that are involved in its control. The role that intelligent control concepts can play is to provide a systematic approach to dealing with these constraints. For example, for a given set of material parameters, one may wish to control several geometrical parameters plus cooling rate for the GMAW process, while maintaining operation in the spray transfer mode of the process. Because of the close coupling among the equipment, material, and geometric parameters, and because of the small latitude of permissible variation of one parameter once the others are specified, tight constraints on the control system will be necessary to achieve the desired process quality. It will be desirable to specify degrees of control permitted over the various parameters in terms of a hierarchy of parameter importance. For example, while the wire feed rate has an influence on bead width in the GTAW process, it would not be desirable to allow the wire feed rate to be varied excessively as a means of controlling bead width. Further, the allowable variation of a given parameter, or parameters, may not be symmetrical about the desired set point. Again, for the GTAW process, an increase in current may be partially offset by an increase in travel speed, whereas a reduction in both parameters would tend to more rapidly force the geometrical parameters outside the desired range. Consideration of the process dynamics is also necessary, particularly for successful control during the initiation and termination phases of the overall welding operation. In addition to the hierarchical considerations referred to above, the time sequence and rate of change of each parameter should be considered. Intelligent control concepts may be used to handle these practical control issues in a formal and logical manner. Conclusions Rapid advances have occurred in the development of sensors and in the development of both steady-state and dynamic models suitable for real-time weld process control applications. In combination with multivariable, adaptive control theory methods, the tools are becoming available for significant progress in multivariable, direct weld process control. Long-range efforts will focus on combining process modeling and microstructural evolution modeling for eventual control of both macro and micro parameters. Defining Terms Direct weld parameters (DWP): A collection of parameters that characterize the weld in terms of the weld reinforcement and fusion zone geometry, mechanical properties, weld microstructure, and discontinuities. Electron beam welding: A welding process that produces coalescence of metals with the heat obtained from a concentrated beam composed primarily of high-velocity electrons impinging on the surfaces to be joined. Electroslag welding: A welding process that produces coalescence of metals with molten slag that melts the filler metal and the surfaces of the parts to be joined. Gas metal arc welding (GMAW): A welding process that produces coalescence of metals by heating them with an arc between a consumable filler metal electrode and the parts to be joined. The process is used with shielding gas and without the application of pressure. Gas tungsten arc welding (GTAW): A welding process that produces coalescence of metals by heating them with an arc between a nonconsumable tungsten electrode and the parts to be joined. The process is used with shielding gas and without the application of pressure. Filler metal may or may not be used
Indirect weld parameters(IWP): A collection of parameters that establish the welding equipment setpoint values. Examples include voltage, current, travel speed, electrode feed rate, travel angle, electrode geom etry, focused spot size, and beam power. Laser beam welding(LBW): A welding process that produces coalescence of materials with the heat obtained from the application of a concentrated coherent light beam impinging on the surfaces to be joined Oxyacetylene welding: An oxyfuel gas welding process that produces coalescence of metals by heating them with a gas flame obtained from the combustion of acetylene with oxygen. The process may be used with or without the application of pressure and with or without the use of filler metal Thermit welding: A welding process that produces coalescence of metals by heating them with superheated liquid metal from a chemical reaction between a metal oxide and aluminum, with or without the application of pressure Variable polarity plasma arc welding(VPPAW): A welding process that produces coalescence of metals by heating them with a constricted variable polarity arc between an electrode and the parts to be joined (transferred arc)or between the electrode and the constricting nozzle(nontransferred arc). Shielding is obtained from the hot, ionized gas issuing from the torch as well as from a normally employed auxiliary shielding gas source. Pressure is not applied, and filler metal may or may not be added Related Topics 56.1 Introduction .66. 1 Generators References K. Andersen, Studies and Implementation of Stationary Models of the Gas Tungsten Arc Welding Process, MS Thesis, Vanderbilt University, 1992. K. Andersen, G. E. Cook, Y. Liu, D. S. Mathews, and M. D. Randall,"Modeling and control parameters for GMAW, short circuiting transfer, " in Advances in Manufacturing Systems Integration and Processes, D. A Dornfeld, Ed, Dearborn, Mich. Society of Manufacturing Engineers, 1989 R. J. Barnett, Sensor Development for Multi-parameter Control of Gas Tungsten Arc Welding, Ph D. Thesis, Vanderbilt University, 1993. J. B. Bjorgvinsson, Adaptive Voltage Control in Gas Tungsten Arc Welding, M.S. Thesis, Vanderbilt University, 1992 G. E. Cook," Feedback and adaptive control in automated arc welding systems, Metal Construction, vol. 13, no.9,pp.551-556,1981. G. E. Cook, Robotic arc welding: Research in sensory feedback control, IEEE Transactions on Industrial Electronics, voL. IE-30, no 3, Pp. 252-268, 1983 G. E. Cook, K. Andersen, and R J. Barnett, "Feedback and adaptive control in welding, in Recent Trends in Welding Science and Technology, S A. David and J M. Vitek, Eds, Metals Park, Ohio: ASM International, G. E. Cook, K. Andersen, R. J. Barnett, and J. E. Springfield,Intelligent gas tungsten arc welding control, " in Automated Welding Systems in Manufacturing, J. Weston, Ed,, Cambridge, England: Abington Publishing, 1991 T. W. Eagar, The physics and chemistry of welding processes, in Advances in Welding Science and Technology S. A. David, Ed, Metals Park, Ohio: ASM International, 1986, Pp. 291-298 J. E. Lancaster, The Physics of Welding, New York: Pergamon Press, 1986. Y. Liu, Metal Droplet Rate Control for Gas Metal Arc Welding, Ph D Dissertation, Vanderbilt University, 1991 R W. Richardson, A. Gutow, R.A. Anderson, and D F. Farson, " Coaxial weld pool viewing for process moni toring and control, Welding Journal, vol. 63, no 3, PP 43-50, 1984 M. E. Shepard, Modeling of Self-Regulation in Gas-Metal Arc Welding, Ph D Dissertation, Vanderbilt University, 1991 Y. C. Yi, Weld Pool Vibration Analysis in Gas Tungsten Arc Welding, M.S. Thesis, Vanderbilt University, 1991 e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Indirect weld parameters (IWP): A collection of parameters that establish the welding equipment setpoint values. Examples include voltage, current, travel speed, electrode feed rate, travel angle, electrode geometry, focused spot size, and beam power. Laser beam welding (LBW): A welding process that produces coalescence of materials with the heat obtained from the application of a concentrated coherent light beam impinging on the surfaces to be joined. Oxyacetylene welding: An oxyfuel gas welding process that produces coalescence of metals by heating them with a gas flame obtained from the combustion of acetylene with oxygen. The process may be used with or without the application of pressure and with or without the use of filler metal. Thermit welding: A welding process that produces coalescence of metals by heating them with superheated liquid metal from a chemical reaction between a metal oxide and aluminum, with or without the application of pressure. Variable polarity plasma arc welding (VPPAW): A welding process that produces coalescence of metals by heating them with a constricted variable polarity arc between an electrode and the parts to be joined (transferred arc) or between the electrode and the constricting nozzle (nontransferred arc). Shielding is obtained from the hot, ionized gas issuing from the torch as well as from a normally employed auxiliary shielding gas source. Pressure is not applied, and filler metal may or may not be added. Related Topics 56.1 Introduction • 66.1 Generators References K. Andersen, Studies and Implementation of Stationary Models of the Gas Tungsten Arc Welding Process, M.S. Thesis, Vanderbilt University, 1992. K. Andersen, G. E. Cook, Y. Liu, D. S. Mathews, and M. D. Randall, “Modeling and control parameters for GMAW, short circuiting transfer,” in Advances in Manufacturing Systems Integration and Processes, D. A. Dornfeld, Ed., Dearborn, Mich.: Society of Manufacturing Engineers, 1989. R. J. Barnett, Sensor Development for Multi-parameter Control of Gas Tungsten Arc Welding, Ph.D. Thesis, Vanderbilt University, 1993. J. B. Bjorgvinsson, Adaptive Voltage Control in Gas Tungsten Arc Welding, M.S. Thesis, Vanderbilt University, 1992. G. E. Cook, “Feedback and adaptive control in automated arc welding systems,” Metal Construction, vol. 13, no. 9, pp. 551–556, 1981. G. E. Cook, “Robotic arc welding: Research in sensory feedback control,” IEEE Transactions on Industrial Electronics, vol. IE-30, no 3, pp. 252–268, 1983. G. E. Cook, K. Andersen, and R. J. Barnett, “Feedback and adaptive control in welding,” in Recent Trends in Welding Science and Technology, S. A. David and J. M. Vitek, Eds., Metals Park, Ohio: ASM International, 1990, pp. 891–903. G. E. Cook, K. Andersen, R. J. Barnett, and J. F. Springfield, “Intelligent gas tungsten arc welding control,” in Automated Welding Systems in Manufacturing, J. Weston, Ed., Cambridge, England: Abington Publishing, 1991. T. W. Eagar, “The physics and chemistry of welding processes,” in Advances in Welding Science and Technology, S. A. David, Ed., Metals Park, Ohio: ASM International, 1986, pp. 291–298. J. F. Lancaster, The Physics of Welding, New York: Pergamon Press, 1986. Y. Liu, Metal Droplet Rate Control for Gas Metal Arc Welding, Ph.D. Dissertation, Vanderbilt University, 1991. R. W. Richardson, A. Gutow, R. A. Anderson, and D. F. Farson, “Coaxial weld pool viewing for process monitoring and control,” Welding Journal, vol. 63, no. 3, pp. 43–50, 1984. M. E. Shepard, Modeling of Self-Regulation in Gas-Metal Arc Welding, Ph.D. Dissertation, Vanderbilt University, 1991. Y. C. Yi, Weld Pool Vibration Analysis in Gas Tungsten Arc Welding, M.S. Thesis, Vanderbilt University, 1991