LIBRARY ı6ıul 0) - Cranfield University

where y is the dependent variable, xi (i=1,2, k)
..., are the regressor variables, ß; (j=0,
1,2, k)
..., are the regressor coefficients and c, a random error with zero mean.
The regressor coefficients are estimated through using the least squares
method, by which the sum of square errors is minimised. The full description of the
multiple linear regression method can be found in references 167 and 173 and will not
be repeated here.
The regressor variables can assume the form of non linear-functions in such a
way that a non-linear curve may be fitted to the experimental points [refs. 167,173].
For example, a multiplicative model, as shown in equation (2.35), can be transformed
to the form of equation (2.34) by applying logarithms to both sides, as shown in
equation (2.36) [ref. 51].
y= aoxI'x2'... xk'
(2.35)
log(y) = log(ao) +a1 log(x, ) + a2 log(x2)+... +a, t log(xk) (2.36)
where ai (i=0,1, ..., k) are constants.
When building a model, a compromise must often be made between the
simplicity of the model and the accuracy of the result of the analysis. This requires
making decisions about which physical variables are important and should be included
in the model [ref. 51].
In prediction oriented problems, the inclusion of variables that don't contribute
to the regression model inflates the error of prediction [ref. 51]. It is better to exclude
from regression variables that are not statistically significant or that are known from
previous/practical experience not to have an influence on the process output.
However, deleting too many variables could lead to "underfitting" and including too
many variables to "overfitting" [ref. 51].
2.6.5 Adaptive control
To adapt means to change a behaviour to conform to new circumstances. An
adaptive controller is a controller that can modify its behaviour in response to changes
in the dynamics of the process and the disturbances [ref. 174]. This implies that linear
constant parameter regulators are not adaptive [ref. 174].
In robotic welding, the term adaptive control is used in a wide sense to
characterise the ability of the system to adapt to the changing environment based on
the information provided by sensors (see section 2.6.1). Two main control aspects can
be identified [ref. 11]: a) the control of position and orientation of the welding torch
relative to the joint (i. e. seam tracking); and b) the control of the welding process
variables during welding (i. e. in process control) in such a way to adapt the process to
unexpected situations such as presence of gap, variation in plate thickness, etc.
Seam tracking is based on sensing the torch-to-joint relative position and
feeding it back to the robot controller in order to correct the torch path. Various
sensing techniques are available and have already been discussed in section 2.6.1.3.
The controller simply commands the robot movement in such a way that it can track
the weld joint.
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