Fig. 8.32: Ramps with smoothing: Red =Actual speed; Grey = Actual position
8.3.6 Interpolation
If there is no analytical description available for a function, and only individual points
are known instead, it will not be possible to evaluate the function at just any point.
Fig. 8.33: Known points
MOOG
ID
No.:
CB40859-001
Date:
02/2018
MSD Servo Drive - Device Help
185
8 Motion profile
By using a suitable interpolation method, the function’s values between known
points can be estimated. This is termed an interpolation problem. There are a
number of solutions to the problem; the user must select the appropriate functions.
Depending on the functions chosen, a different interpolant is obtained.
Interpolation is a type of approximation: The function under analysis is precisely
reproduced by the interpolation function at the interpolation points and at the
remaining points is at least approximated. The quality of approximation depends on
the method chosen. In order to estimate it, additional information above the function f
is required. Even if f is not known, this is usually obtained naturally: The limitation,
consistency or differentiation capacity can frequently be assumed.
8.3.6.1 Linear interpolation
Fig. 8.34: Linear interpolation
Here two given datum points f
0
and f
1
are connected by a line. To n+1 differing
datum point pairs there is exactly one n-th order interpolation polynomial, which
matches at the specified interpolation points.
