Civil Engineering Reference
In-Depth Information
patterns are trained into the network. A multi-level neural network structure with non-linear activations
can store knowledge and attain a higher level feature abstraction. Back propagation of errors during
training using a learning rule is used to create relations in the network. As this knowledge is stored in
the connections, it can be utilized readily in on-line classification. More detail on neural networks can
be found in Rummelhart and McClelland (1986).
Despite all the advantages of neural networks, this approach has severe restrictions and limitations for
use in real-time estimation. The number of training cases needed to bound the set of possible solutions
for the grinding process parameter may not be practical (or even known) with grinding. Training data
are dependent on the particular setup in grinding, and are not usually known
a priori
. Also training of a
back-propagation network can take thousands of repetitions to generalize and complete learning to an
acceptable error level. Thus, the training set size and learning cycles may be too large to be practical.
Linear networks may be trained adaptively but cannot produce results significantly different from linear
RLS methods. Therefore, neural network methods are not examined for real-time, multi-sensor estimation
in grinding.
Based on these attributes the approach taken for the development of real-time multi-sensor techniques
to improve the estimate of the grinding model parameter is generally limited to the recursive techniques
including a windowed Kalman filter and recursive least squares with a forgetting factor (RLS-FF).
Optimizations of RLS-FF and Kalman Filters
Window size variation is critical for the estimation techniques used in adaptive control of precision
grinding systems, and a key metric to determining the appropriate window size is the displacement error
covariance. The window size represents a trade-off between accuracy and timeliness of the data. If the
window is too large, the data can be old and less useful. If the window is too small, the statistical variances
due to noise are too large. Depending on the sensor sampling rate and the process variation spectrum,
there should be a preferred sampling window balancing the timeliness of sensor data and a meaningful
statistical representation of process. Thus, if the frequency content of the input data increases, it is
speculated that relatively smaller windows are required to have a minimal estimation error.
Similar effects are expected for the both the Kalman filter and RLS-FF technique. In the RLS-FF
estimation scheme smaller forgetting factors (larger discounting with time) are needed where higher
frequency content is important in the parameter estimation, much like the shorter windows for the
windowed Kalman filter.
For multi-dimensional systems, there are several inputs and outputs, one for each axis. Cross-coupling
of the inputs and outputs can occur. For example, if the desired outputs of a two-dimensional system
are force and velocity, an increase in force on one axis may slow the velocity of the other axis. Treatment
of two-axis systems with cross coupling can be found in Jenkins, Kurfess, and Dorf (1996). The system
described in that research utilized one axis to control velocity while the other axis provided force
regulation. This approach is applicable to traverse grinding. For plunge grinding using only a single axis,
multiple axis coupling is not an issue.
3.5
Control
To control the grinding process means to control the position, feed velocity, and normal force, as these
process measures relate to the quality of the final ground part in terms of dimensional accuracy, surface
finish, and mitigation of damage, respectively. Currently, industrial grinding systems only control the grind-
ing process in terms of position and velocity. Limitations in modeling, control, and computer hardware
have impeded the progress of force control in grinding.
Generally fixed-gain controllers (such as PID-type controllers) are preferred for applications because
of their simplicity in implementation. These controllers are easily tuned using simple approaches. Many
commercial motion control applications for position and velocity loops have self-tuning programs using
Ziegler-Nichols tuning or other algorithms. However, many processes or systems vary sufficiently to limit
