User`s manual

16-8 Motion Mate™ DSM314 for Series 90™-30 PLCs User's Manual – January 2001 GFK-1742A
16
Interpolation and Smoothing
One CAM key feature is the interpolation scheme used to define the CAM profiles. The following
is a reprint of a section from the CAM Editor help system. It is included in this section to not only
introduce these important concepts, but also to encourage you to explore the CAM Editor on-line
help for additional information.
The CAM editor employs spline polynomial interpolation to define regions of a profile that fall
between user-defined points. This approach reduces the memory required for profile storage on the
target motion module while providing accurate and smooth motion trajectories. Without this
interpolation scheme, a large number of data points, thus a large amount of memory, would be
needed to define each profile.
A CAM profile is defined with a minimum number of actual data points. After these points are
defined they are grouped into sectors; a profile is composed of one or more sectors. For each sector,
you specify the curve-fit order (1, 2 or 3). The higher the order the smoother the curve-fit. The
curve-fit order is the order of the polynomial curves used to define the regions of the sector not
specified by user-defined points. Unique curve-fit polynomial coefficients are generated for each
segment of a sector (that is, between each pair of user-defined points). The coefficients of the
polynomials are calculated to include the user-defined points and to match the slope of the profile
on either side of a user-defined point (except for 1
st
order sectors).
The polynomial curves for a position profile are described by the following function:
Y(X) = A
n-1
(X
n
-X
n-1
)
3
+ B
n-1
(X
n
-X
n-1
)
2
+ C
n-1
(X
n
-X
n-1
) + Y
n-1
Where:
Y = slave position value for a master position X.
X
n-1
= master position value at point n-1.
A
n-1
, B
n-1
, C
n-1
= curve-fit coefficients at point n-1.
Notes
•
For a given master position X, that lies between X
n-1
and X
n
, the coefficients A, B and C
are selected for the point corresponding to X
n-1
.
•
For a second order curve-fit, the A coefficient is always zero, and for a first order curve-
fit, both the A and B coefficients are always zero.