Motion Control Topics ♦ Limited Jerk
Limited Jerk
Understanding LimitedJerk Movements
Limited-jerk movements are similar to normal Trapezoidal movements except that the user
may control the "gentleness" of the acceleration and deceleration ramps. This allows the user
to limit the "jerk" caused by the "instantaneous" acceleration of a Trapezoidal movement.
Typical applications where limited jerk is required:
−
lift
−
movement of heavy loads
As an example, the following chart shows the acceleration, velocity, and position curves for a
Trapezoidal movement from one position to another position. The sharp changes in
acceleration cause the motor to experience a "jerk" at the beginning and end of each velocity
ramp.
The following chart shows the same movement done using a Limited-jerk movement. Note
that the acceleration changes are no longer "instantaneous" and that the "corners" of the
velocity curve have become rounded. This will result in a smoother motor movement. It will
also require slightly longer to get to the desired target position because the motor takes
longer to accelerate to maximum acceleration.
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The user can control the "gentleness" of the acceleration ramp using 4 parameters:
JERKMIN
Acceleration ramp-up constant. This specifies the number of milliseconds
required to ramp the acceleration up from 0 to maximum acceleration.
JERKMIN2
Acceleration ramp-down constant. This specifies the number of milliseconds
required to ramp the acceleration down from maximum acceleration to 0 (i.e.
normally to constant maximum velocity). If set to 0, this will default to the same
value as JERKMIN.
JERKMIN3
Deceleration ramp-up constant. This specifies the number of milliseconds
required to ramp the deceleration up from 0 to maximum deceleration. If set
to 0, this will default to the same value as JERKMIN.
JERKMIN4
Deceleration ramp-down constant. This specifies the number of milliseconds
required to ramp the deceleration down from maximum deceleration to 0 (i.e.
normally to 0 velocity). If set to 0, this will default to the same value as
JERMIN.
These constants correspond to the "slopes" of the different portions of the acceleration
curve. This is shown in the chart below. When set to larger and larger numbers, the
acceleration and/or deceleration will become gentler and gentler as the ramps become
longer and longer. Note that the acceleration slope determined by the JERKMIN acceleration
ramp-up constant will be used whenever the acceleration is being ramped-up. It is not used
only to ramp-up from 0 to maximum acceleration. Similarly, JERKMIN2 is used whenever the
acceleration is being ramped-down, JERKMIN3 is used whenever the deceleration is being
ramped-up, and JERKMIN4 is used whenever the deceleration is being ramped-down.
Limited-jerk movements will not normally exceed the velocity and acceleration limits set for
the controller (e.g. limits set by the VEL, ACC, DEC, etc., commands). In the above chart, these
limits can be recognized by the "plateaus" in the acceleration curve. If the current velocity
and/or acceleration are outside these limits when the Limited-jerk movement is started, then
the movement is accelerated or decelerated as necessary to bring the movement within the
set limits.
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It is important to understand that for Limited-jerk movements, "acceleration" is defined as
"speeding up" in either direction (i.e. either forwards or backwards) and "deceleration" is
defined as "slowing down" in either direction. A result of this is that maximum velocity,
maximum acceleration, maximum deceleration, and the four JERKMIN values are all
independent of the direction of movement. This can have important consequences when a
Limited-jerk movement must "reverse" the direction of the motor, particularly when maximum
deceleration differs from maximum acceleration. In this case, the Limited-jerk movement will
ensure that the deceleration ramp flows smoothly into an acceleration ramp at exactly 0
velocity when the direction changes and without exceeding either the deceleration or
acceleration limits.
A Limited-jerk movement can be used in three different situations:
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1.
Stopping from the current velocity and acceleration (where the final position is not
important).
2.
Changing from the current velocity and acceleration to a specified constant velocity
(where the positions are not important).
3.
Moving from the current position (and the current velocity and acceleration) and stopping
at a specified position.
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Examples of LimitedJerk Movements
Stopping
In the following examples, maximum acceleration has been set to a value higher than
maximum deceleration so the motor can speed up faster than it can slow down. As well,
JERKMIN has been set smaller than JERKMIN2, JERKMIN2 smaller than JERKMIN3, and
JERKMIN3 smaller than JERKMIN4. This was done so that the various segments of the
curves can be visually distinguished in the charts. The four JERKMIN values have been labeled
simply J1, J2, J3, and J4.
The chart below shows a stopping movement that begins from a positive constant velocity.
The curve consists of a deceleration ramp-up segment (using JERKMIN3), followed by a
constant deceleration segment (at maximum deceleration), and finally a deceleration rampdown segment to 0 velocity (using JERKMIN4).
The chart below shows a stopping movement that begins from a positive velocity and a
positive acceleration. Since the initial acceleration is positive, the curve must start with an
acceleration ramp-down segment to 0 acceleration (using JERKMIN2). This will then be
followed by a deceleration ramp-up segment (using JERKMIN3), a constant deceleration
segment, and a deceleration ramp-down segment to 0 velocity (using JERKMIN4).
The chart below shows a stopping movement that begins from a negative velocity and a very
high deceleration. (It is a deceleration because the speed is slowing down.) However, because
the initial deceleration is so high, the motor is unable to stop without overshooting 0 velocity
and ‘coming back’.
So the curve starts with a deceleration ramp-down segment (using JERKMIN4) to slow the
deceleration as much as possible before reaching 0 velocity. At 0 velocity, the ‘deceleration’
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becomes an ‘acceleration’ because the direction has changed. Hence, the curve continues by
ramping-down the acceleration (using JERKMIN2) until it gets to 0 acceleration. The motor is
now at a constant positive velocity and so the curve will finish in the normal way with a
deceleration ramp-up segment (using JERKMIN3), a constant deceleration segment (very
short in this example), and a deceleration ramp-down segment to 0 velocity (using
JERKMIN4).
Changing to a Constant
Velocity
The chart below shows a movement that begins from a positive constant velocity and
increases its speed to a higher positive constant velocity. This curve consists of an acceleration
ramp-up segment (using JERKMIN), followed by a constant acceleration segment (at
maximum acceleration), and finally an acceleration ramp-down segment to constant velocity
(using JERKMIN2). Note that the deceleration JERKMIN3 and JERKMIN4 values are not used
because there is never any deceleration.
The chart below shows a movement that begins from a high positive constant velocity and
decreases its speed to a lower positive constant velocity. This curve consists of a deceleration
ramp-up segment (using JERKMIN3), followed by a constant deceleration segment (at
maximum deceleration), and finally a deceleration ramp-down segment to constant velocity
(using JERKMIN4). Note that the acceleration JERKMIN and JERKMIN2 values are not used
because there is never any acceleration.
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The chart below is similar to the previous example except that it begins with a positive
acceleration. In this case, the curve must start with an acceleration ramp-down segment
(using JERKMIN2). Once the acceleration reaches 0, then the curve can continue as before.
The chart below shows a movement that begins with a negative constant velocity and
changes direction to a positive constant velocity. The curve must start by slowing down the
speed so that it can ‘turn around’. Hence the curve begins with a deceleration ramp-up segment
(using JERKMIN3) until it reaches maximum deceleration.
The deceleration continues at maximum deceleration until it reaches 0 velocity. Note that
there is no deceleration ramp-down segment because the movement is not stopping. At
exactly 0 velocity, the direction reverses and the movement is now accelerating in the other
direction. But since maximum acceleration is higher than maximum deceleration for this
example, the curve is now able to include an acceleration ramp-up segment (using JERKMIN).
The curve finishes in the normal way with a constant acceleration segment and an
acceleration ramp-down segment to constant velocity (using JERKMIN2).
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Moving to a Specified
Position
The chart below shows a ‘normal’ movement from being stopped at one position and then
moving forward to stop at another position. The curve starts with an acceleration ramp to
maximum velocity. This portion of the curve will be similar to the first of the examples shown
in "Changing to a Constant Velocity". The curve is simply changing to a constant velocity where
the constant velocity is the maximum velocity.
Hence, the curve will consist of an acceleration ramp-up segment (using JERKMIN), a constant
acceleration segment at maximum acceleration, and then an acceleration ramp-down segment to
maximum velocity (using JERKMIN2). The movement then proceeds at maximum velocity until it
needs to start the deceleration ramp that will stop the movement at the desired position. The
deceleration ramp is identical to the first of the examples shown in "Stopping". The curve will
consist of a deceleration ramp-up segment (JERKMIN3), followed by a constant deceleration
segment (at maximum deceleration), and finally a deceleration ramp-down segment to 0 velocity
(using JERKMIN4) stopping at the desired position.
The chart below shows a typical ‘short’ movement where maximum velocity cannot be
reached. In this case, the curve ramps-up the acceleration (using JERKMIN) for as long as
possible. This may or may not reach maximum acceleration, depending on how far away the
target position is. There will then be an acceleration ramp-down (using JERKMIN2), followed
immediately by a deceleration ramp-up (using JERKMIN3). Again, depending on the target
position, there may or may not be a constant deceleration segment. The curve ends with a
deceleration ramp-down to 0 velocity at the target position.
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The chart below shows an example where the motor is initially moving in the ‘wrong’ direction
and must turn around and ‘go back’ to the target position. Since it must "turn around", the
curve starts with a deceleration ramp-up segment (using JERKMIN3) to maximum
deceleration.
This will slow the speed down until it turns around. Deceleration continues at maximum
deceleration until 0 velocity is reached and the direction reverses. At exactly this point, the
motor is now ‘speeding up’ but in the other direction. From this point, the curve is similar to a
normal movement to a target position, except that the whole curve is inverted because the
direction has changed. The curve will have an acceleration ramp-up segment (going
backwards), it may or may not have a constant acceleration segment, it will have an
acceleration ramp-down segment, it may or may not have a constant velocity segment, it will
have a deceleration ramp-up segment, it may or may not have a constant deceleration
segment, and finally it will have a deceleration ramp-down to the target position.
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