ElmoMC SimplIQ Software Manual - Manual (Page 151)

SimplIQ Software Manual The Position Reference Generator
MAN-SIMSW (Ver. 1.4)
11-10
11.1.6 Position - Velocity - Time (PVT)
In a PVT motion the user provides the desired position and speed at selected time
instances. Between these specified times, the motion controller interpolates to obtain
smooth motion. The position and speed specifications are absolute, while the time
specification is relative.
A PVT motion can be referenced in absolute time by requiring it to start at a specified
time. The BT (Begin on Time) command is used to start a PVT motion exactly at a given
time, using a microsecond resolution.
The ability to relate PVT motions to absolute time makes them ideal for tightly-
synchronized multiple-axis motions. For an explanation of how to synchronize the
absolute time counters of multiple drives to the precision of a few microseconds, refer to
the Elmo CAN Implementation Manual.
Example 1:
The system should be at position 1000 and speed 100,000 counts/second at a given time,
and at position 1620 and speed 110,000 counts/seconds 6 milliseconds later.
The first point is specified by:
Position = 1000,
Speed - 100,000,
Time = (irrelevant to described motion, but relevant to the previous motion segment)
The second point is specified by:
Position = 1620,
Speed = 110,000,
Time = 6 msec
The time is defined in milliseconds, not in drive sampling times. The drive interpolates
the motion specification in order to calculate the desired position and speed at the
sampling instances, when it needs the information.
PVT implements a third-order interpolation between the position - speed data provided
by the user. For each motion interval, the user specifies the boundary positions and
speeds. Mathematically, the user provides the following data:
ƒ
Starting position and speed, denoted by P0 and V0, respectively
ƒ End position and speed, denoted by PT and VT, respectively
If t
0
denotes the starting time and T denotes the length of the time interval,
the position for t ∈ [t
0
, t
0
+ T] is given by the third-order interpolating polynomial:
P(t) = a(t – t
0
) 3 + b(t – t
0
) 2 + c(t – t
0
) + d
The speed is given by:
V(t) = 3a(t – t
0
) 2 + 2b(t – t
0
) + c