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AN2350 Datasheet(PDF) 28 Page - STMicroelectronics

Part # AN2350
Description  Guidelines for the control of a multiaxial planar robot with ST10F276
PDF  41 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

AN2350 Datasheet(HTML) 28 Page - STMicroelectronics

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Control algorithm
AN2350
28/41
gradually ramp-up the motor velocity, until it reaches the desired speed and then, gradually
ramp-down it until it stops after the task is complete, as shown in Figure 21:
Figure 21.
Example of trapezoidal velocity profile
The trapezoidal velocity profile is analytically expressed as follows:
where t1 is the time slot for the ramp-up, t3 is the total time for the execution of the entire
trajectory, and
is the time slot during which the end effector moves at desired
speed vc (also called the cruising speed).
Integrating it respect to the time, it is possible to obtain the function that describes the space
covered in the workspace.
The time t1 can be obtained from the knowledge of the cruising speed and the acceleration
a (that represent the known parameters)
and the total time t3 can be obtained from the distance smax between the start point and the
stop point as follows:
Motor
Speed
Time
Start
Accelerate
Cruising speed
Decelerate
Stop
t1
t2
t3
⎪
⎩
⎪
⎨
⎧
<
≤
−
+
−
−
−
<
≤
<
≤
=
3
1
3
1
3
1
3
1
1
)
(t
)
(
)
(
t
t
t
0
)
(
t
t
t
t
t
t
a
v
t
t
t
v
at
t
v
c
c
)
(
t
1
3
2
t
t
−
=
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
<
≤
−
+
−
+
−
+
+
−
−
<
≤
+
<
≤
=
3
1
3
2
1
3
1
3
2
1
1
3
1
3
1
2
1
1
2
)
(t
)
t
-
a(t
2
1
)
(
at
2
1
)
2
(
)
(
t
at
2
1
)
t
-
(t
t
t
0
2
1
)
(
t
t
t
t
t
t
t
v
t
t
v
t
t
t
v
at
t
s
c
c
c
a
v
c
=
1
t
1
max
3
1
3
3
max
t
)
(
s
t
v
s
t
v
t
v
t
s
c
c
c
+
=
⇒
−
=
=



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