Operation & Software Manual
168
Direct Drives & Systems
Chapter C: System functions
ETEL Doc. - Operation & Software Manual # DSC2P 903 / Ver. F / 3/6/05
with x = position versus time
v
0
= initial speed
x
0
= initial position
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
final
to reach (STE command).
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 accelea
max
. In zone 2, there is
no tangential acceleration (because the tangential speed is
constant). In zone 3, there is a negative tangential acceleration
(deceleration) –a
max
. Therefore, the mobile can slow down and
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
max
(given with the SPD command), and the tangential
acceleration a
max
(ACC command). Those three values can be displayed on the speed trajectory graph. V
max
corresponds to the maximum of the curve and the tangential accelerations (+a
max
, 0, -a
max
) are the slopes of
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:
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
x t
( )
1
2
---
at
2
v
0
t x
0
+
+
=
v t
( )
at v
0
+
=
a t
( )
a
constant
=
=
j t
( )
0
=
Speed
Zone 1
Zone 2
Zone 3
V
max
+a
max
-a
max
t
Zone 1
x t
( )
1
2
---
a
0
t
2
=
v
0
t x
0
+
+
v t
( )
a
0
t v
0
+
=
a t
( )
a
0
cst with a
0
0
>
=
=
j t
( )
0
=
Zone 2
x t
( )
v
0
t x
0
+
=
v t
( )
v
0
cst
=
=
a t
( )
0
=
j t
( )
0
=
Zone 3: same as zone 1 with a < 0
