Civil Engineering Reference
In-Depth Information
be carried out off-line, prior to welding. Secondly, once the process has started, sensory feedback and
other available process information can be monitored in real-time and used to update the IWP which
control the welding equipment. These updates must be obtained on-line and the corresponding control
actions must be executed at a high enough rate to effectively control short-term transients of the process.
Controlling a multivariable system is not a trivial task without an adequate quantitative model. In the
case of arc welding, relationships between the various process inputs and outputs are not well defined.
Furthermore, the process variables are coupled (i.e., any given input parameter affects more than one
output parameter) and in general the welding processes are nonlinear (the output parameters are not
adequately described in terms of a linear combination of the input parameters and their time derivatives).
All of these facts add to the difficulty of designing a general controller for arc welding. Substantial research
has been carried out to mathematically model and control the GTAW process, as well as other arc welding
processes. Each welding process is primarily governed by specific control variables, as discussed in [12].
The available weld process models can be classified from either of two viewpoints. One classification
arises from the methods by which the models are derived, while the other is concerned with the ability
of the models to describe the dynamic behavior of the process as well as the static one.
In broad terms, weld process models are either derived from the fundamental physics of heat transfer,
or they are constructed from empirical data. The models derived from heat transfer physics frequently
assume that the arc can be modeled as a heat source of a given form (a point source, a disk-shaped source
of heat, etc.) and then the laws of heat conduction are applied to calculate the temperatures at various
points in the workpiece [65, 66, 69]. Of specific interest is the boundary at which the temperature equals
the melting temperature of the welded metal, i.e., the boundary of the molten weld pool. These results may
either be derived analytically or computationally to a varying degree. The analytical derivations usually
require significant simplifications, such as assuming that the welded workpiece is either infinitely thick
or of a specific shape, the thermal properties of the molten pool (e.g., heat conduction and density) are
homogeneous and the same as those of the solid metal, etc. As a result the analytically derived models
are usually fairly inaccurate when compared to the results of actual welding operations. On the other
hand they frequently offer some insight into the mechanisms of the welding process and they may
illustrate how the individual process inputs and outputs are related.
Computer solutions based on the physics of heat conduction can be made more accurate by including
some of the calculations omitted in the analytical simplifications. Finite-difference techniques and related
methods carry the computational solution of the heat equation to its fullest accuracy [21, 22, 20]. The
drawbacks of such approaches, however, are that they are computationally intensive (which usually
renders them impractical for real-time use) and they do not offer the insight into the interactions of
process variables that the analytical models may give.
An alternative to the physics-based models, discussed above, are the empirically derived models [13,
14]. These models may simply consist of one or more equations relating the process outputs to the process
inputs, and derived by obtaining a best fit of experimental data to the given equations. In such cases the
models are derived without any consideration of the underlying physics of the process. A number of weld
process models can be placed between the two extremes of pure physics-derived and empirical models.
Frequently, physics-based models are derived using the necessary approximations and then various
''empirical constants'' and other unspecified variables are tuned until the model adequately agrees with
experimental welding data. By the same token, empirical models frequently use pieces of general knowl-
edge of the process, derived from the underlying physics. Therefore, the physics-based and the empirical
models define the opposite extremes in approaches to weld modeling.
For the purpose of system control it is important to distinguish between static models and dynamic
ones. A static model describes the process in its steady-state, i.e., it does not consider short-term
transients of the process. A dynamic model, however, yields both the dynamic and the static responses
of the process, and thus it is more general. The lack of dynamic considerations is usually tolerable when
the initial setpoint values for the equipment parameters of the process are selected with the aid of a
model. Once the process has started, however, its dynamics must be adequately incorporated into the
control scheme. Some adaptive, dynamic control schemes for the GTAW process are discussed in [50].
