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168
The derivatives of this equation versus time determine the CALM speed, acceleration and jerk trajectory:
13.3.11.2 Step movement
The step movement is a very blunt movement in which the motor is asked to go immediately from a position
to another. In such a movement, the speed, acceleration and jerk are infinite, therefore, no system is able to
perfectly perform it. A step movement is entirely defined by the final position x
This movement is generally only used to find the optimal values of the position and current loop regulators.
13.3.11.3 Trapezoidal movement
(For principle understanding - not used in the controller, S-curve
movement is preferred).
A trapezoidal movement is a movement whose speed trajectory
has a trapezoidal shape. There are three distinct zones. In zone 1,
a CALM (Constantly Accelerated Linear Movement) is used with a
positive constant tangential acceleration +a
no tangential acceleration (because the tangential speed is
constant). In zone 3, there is a negative tangential acceleration
(deceleration) –a
reach its aim without speed.
A trapezoidal movement is entirely defined by the length of the segment to reach (set up by the controller with
the POS command), the maximum tangential speed V
acceleration a
max
corresponds to the maximum of the curve and the tangential accelerations (+a
the three segments which make up the trapezium. The final segment length is given by the surface of the
trapezium.
Here are the equations found in a trapezoidal movement:
1
x t ( )
-- - a
=
2
v t ( )
=
a
0
Zone 1
a t ( )
=
a
0
j t ( )
=
0
Remark:
The maximum speed is not necessarily reached with a trapezoidal movement. In that case, we
have a triangular movement. This movement is optimal in time.
13.3.11.4 Rectangular movement
(For understanding principle - not implemented in the controller).
The rectangular movement is a special case of trapezoidal movement. Its speed trajectory has a rectangular
Chapter C: System functions
Operation & Software Manual
Direct Drives & Systems
1
2
x t ( )
-- - at
=
+
v
t
+
x
0
0
2
v t ( )
a t ( )
j t ( )
. Therefore, the mobile can slow down and
max
(ACC command). Those three values can be displayed on the speed trajectory graph. V
2
t
+
v
t
+
x
0
0
0
t
+
v
0
Zone 2
>
=
0
cst with a
0
with
x = position versus time
v
= initial speed
0
x
= initial position
0
=
at
+
v
0
=
a
=
constant
=
0
. In zone 2, there is
max
(given with the SPD command), and the tangential
max
x t ( )
=
v
t
+
x
0
0
v t ( )
=
v
=
cst
0
a t ( )
=
0
j t ( )
=
0
ETEL Doc. - Operation & Software Manual # DSC2P 903 / Ver. F / 3/6/05
to reach (STE command).
final
Speed
Zone 1
Zone 2
Zone 3
V
max
-a
+a
max
max
, 0, -a
) are the slopes of
max
max
Zone 3: same as zone 1 with a < 0
t
max
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