Trapezoidal S-Curve Acceleration - Advanced Micro Controls Inc. SMD23E2 User Manual

C M
ALCULATING OVE
S-Curve Acceleration Equations (continued)

Trapezoidal S-Curve Acceleration

Figure R3.4 shows the speed profile of a move during its acceleration phase. The figure shows the desired
trapezoidal S-curve acceleration in red along with the equivalent constant acceleration in blue. The equivalent
constant acceleration is equal to the change in speed divided by the time it takes to achieve the change in
speed. This is the value that would have to be used if the Acceleration Jerk parameter was left at zero and we
will use this information to calculate the S-curve acceleration and the value of the Acceleration Jerk Parame-
ter.
Programmed
Speed
s
Starting
Speed
t=0
In this example, the period of constant acceleration is 50% of the acceleration phase.
Trapezoidal S-Curve Deceleration
a
s
a
c
t/2
t/4
Figure R3.5 Trapezoidal Acceleration
This means that a trapezoidal S-curve acceleration profile that is has a period of constant acceleration equal to
half of the total phase time, requires its programmed acceleration value to be 4/3 that of the constant acceler-
ation value used to achieve the same speed in the same amount of time.
48
P
ROFILES
Constant
Acceleration
Trapezoidal S-curve
Acceleration
Time
t
Figure R3.4 Move Profile Example
Speed is equal to acceleration multiplied by the time it is applied.
This is shown graphically in figure R3.5 as the area of the blue
rectangle. In order for the Trapezoidal S-curve acceleration to
Constant
reach the same speed in the same amount of time, the area of the
Deceleration
polygon must equal the area of the rectangle.
Time
t
3t/4
S = Programmed Speed – Starting Speed
speed
Acceleration =
time
s
a =
t
a t a t
s s
------ - + ------ - = a t Area of polygon = Area of rectangle
c
2 4
2a t a t
s s
--------- - + ------ - = a t
c
4 4
3a t
s
--------- - = a t
c
4
4
-- - a
a =
s c
3
ADVANCED MICRO CONTROLS INC.
SMD23E2 and SMD24E2 User's Manual
SMD
Acceleration
acceleration
jerk = Jerk Parameter (J) =
time
a
j =
t
100j
a
Ja
j =
100