ETEL Doc. - Operation & Software Manual # DSC2P 903 / Ver. F / 3/6/05
Chapter C: System functions
Operation & Software Manual
Direct Drives & Systems
169
shape. It is very blunt because motor speed moves from 0 to v
max
suddenly at the beginning and from v
max
to
0 at the end. A motor cannot move exactly over this speed trajectory because it would imply infinite acceleration
and deceleration. This type of movement can be used for very small movements at high speed. The rectangular
movement is entirely defined by the position to reach (POS command) and by movement speed (SPD
command).
A rectangular movement equation is very simple because it only has one zone with constant speed.
13.3.11.5 S-Curve movement
The S-Curve movement is even smoother than the
trapezoidal movement because it can avoid infinite
jerk (derivative of the acceleration). This
movement avoids as much as possible the shocks
in the machine and increases mechanical parts in
motion and bearings lifetime. But, with the same
maximum speed, acceleration and final position,
the motor's S-curve movement will last longer than
a trapezoidal movement.
Here are the equations of the S-Curve movement:
As the S-curve movement uses 3
rd
degree equations, it needs one more parameter than the trapezoidal
movement to be defined. This parameter is called
jerk time
which is programmed with the JRT command and
defines the additional time (number of times of sti (refer to
) that the S-Curve movement will last with respect
to a trapezoidal movement.
Example:
If a movement of 10cm takes 0.5 seconds with a trapezoidal profile, the same movement will last 20 x 166.67
µ
s
for the DSC2P/DSC2V or 20 x 500
µ
s for the DSCDP, DSCDL and DSCDM longer if a jerk time of 20 [sti] is
programmed, so the total time will be: 0.5s + (20x166.67
µ
s) = 0.503s for the DSC2P/DSC2V or 0.5s +
(20x500
µ
s) = 0.51s for the DSCDP, DSCDL and DSCDM.
Caution:
If a very big jerk time is used, the maximum programmed speed will not be reached.
Remark:
A S-curve movement without any jerk time is equal to a trapezoidal movement.
x t
( )
vt
=
x
0
+
v t
( )
v
cst
=
=
a t
( )
0
=
j t
( )
0
=
t
Speed
v
max
Z
one 1
Z
one 2
Z
one 3
Z
one 4
Z
one 5
Z
one 6
Z
one 7
Zone 1
x t
( )
1
6
---
=
j
0
t
3
1
2
---
a
0
t
2
v
0
t x
0
+
+
+
v t
( )
1
2
---
j
0
t
2
a
0
t v
0
+
+
=
a t
( )
j
0
t a
0
+
=
j t
( )
j
0
cst with j
0
0
>
=
=
Zone 2
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
=
j t
( )
0
=
Zone 3: same as zone 1 with j < 0
Zone 4:
x t
( )
v
0
t x
0
+
=
v t
( )
v
0
cst
=
=
a t
( )
0
=
j t
( )
0
=
Zone 5: same as zone 3 with a < 0
Zone 6: same as zone 2 with a < 0
Zone 7: same as zone 1 with a < 0
Содержание DSC Series
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