maxon motor control
EPOS Positioning Controller
EPOS Application Note: Interpolation Position Mode
4
maxon motor control
Edition December 2008 / Subject to change
2
Interpolated Position Mode
2.1
Explanations to the Interpolated Position Mode
Introductory analogy:
In a company a department manager must convert the department goals into clear tasks for his coworkers. It is to
be considered that often the individual tasks stand to each other in close interdependency. Thus each department
manager is glad, if he has capable coworkers, who are able to solve their tasks already on basis on substantial
data. For the quality of such a solution it is in particular important that it:
1.
is factually correct, i.e. it does not have to be controlled again,
2.
is finished in time and
3.
was reached efficiently.
The functionality
Interpolated Position Mode values up the positioning controller EPOS2 to such a “capable
coworker” in a superordinated drive system. This thesis is described in the following text.
In a drive system normally several axes must be moved after the guidelines of a central controller. This can take
place in the way that each local axis controller receives the next target position in real time – i.e. in time and at the
same time to each sampling instance –. This strategy has the advantage that the local controller need only little
intelligence. However, the central controller must compute target positions for every sampling interval and has to
communicate the data to every local controller in real time.
In the sense of the introductory analogy it would be favorable, if only few, but substantial points of the driving
profiles have to be regarded. Besides it would be desirable, if the corresponding data have to be communicated to
the local controller not necessarily at the same time but only in time. Both goals can be reached by
interpolation
and
data buffering.
The central controller decides first which points of the local trajectories are substantial for a synchronized total
movement. Then each relevant point of the local trajectories is supplemented with the corresponding velocity and
time, i.e. triples of the kind (position, velocity, time = PVT) are formed. These triples are then transferred to the
associated axis controllers in time. Each local controller possesses a buffer in order to take up these data. The
buffer of the
EPOS2 covers 64 locations for triples. The transfer of data to the EPOS2 is in time, if always the buffer
contains at least 1 and at the most 64 new triples.
The local position regulation works at the
EPOS2 with a sampling rate of 1 kHz. I.e., there are 1000 target positions
per second necessary in real time. These target positions are computed in the
EPOS2 by means of interpolation.
Each triple forms a base point with the abscissa
time and the two ordinates position and velocity. Two triples
therefore deliver two abscissas and four corresponding ordinates, so that an interpolation polynomial of third order
can be computed unambiguously between the two base points. This computation as well as the evaluation of the
polynomial in the local sampling clock takes place on basis of simple arithmetic and is efficiently carried out by the
EPOS2.
The endpoint of the polynomial [n] forms the starting point of the polynomial [n+1] Therefore it is sufficient to
indicate only the relative time in a data triple, i.e. the length of the time interval. Concretely with the
EPOS2 the time
distance of two base points can be selected between 1ms and 255ms. This interval length can be adapted by the
central controller to realize the desired total movement.
With the goal that all controllers in the drive system refer to the same time base, the central controller initiates
periodically a time check. This time synchronization takes place with the
EPOS2 via the SYNC time stamp
mechanism.
