ElmoMC SimplIQ Software Manual - Manual (Page 163)

SimplIQ Software Manual The Position Reference Generator
MAN-SIMSW (Ver. 1.4)
11-22
11.1.7.1 Interpolation Mathematics
PT implements a third-order interpolation between the position data points provided by
the user.
Let T = m * T
s
where:
T
s
is the sampling time of the position controller. The parameter WS[28] reads T
s
.
T is the sampling time of the PT trajectory.
m (system parameter MP[4]) is the integer parameter that relates T
s
and T.
For m = 1, no interpolation is required. For m > 1, there are certain sampling instances of
the position controller for which the path command must be interpolated, using a third-
order polynomial interpolation.
The user provides position points P(k), k = 1…N.
The drive calculates the speeds V(k), k=1…N for points P(k), k=1…N as follows:
ƒ
If k is an ordinary point inside the path:
T 2
) 1 k ( P ) 1 k ( P
) k ( V
− − +
=
ƒ If k is the first programmed point in the path:
T
) k ( P ) 1 k ( P
) k ( V
− +
=
ƒ If k is the last programmed point in the path:
T
) 1 k ( P ) k ( P
) k ( V
− −
=
For each motion interval, four requirements must be satisfied:
ƒ
Start position
ƒ End position
ƒ Start speed
ƒ End speed
These four requirements exactly suffice for solving the third-order interpolating
polynomial.
Example:
Consider the position controller reference signal P(t) - sin(2π * 10t)
where t is the time in seconds.
The controller sampling time is 200 microseconds and the path is programmed with a
data point once per MP[4] = 50 controller sampling times (10 milliseconds). The PT
reference points are depicted as circles in the following graph. The path interpolated by
the drive is shown as a solid line.