Definitions
27
4 Definitions
4.1 Uncompensated
gain
The maximum stable gain (with a safety margin) that can be used to compensate the position error without
the use of the lead and lag filters.
4.2 Acceleration
feedback
A high proportional gain is desirable for a high disturbance rejection and better precision (smaller steady
state error).
To allow a higher proportional gain, feedback from the acceleration acts as an electronic inertia which
pushes the upper limit for the proportional gain.
Furthermore, this does not interfere with any other control that may be added later (filters, etc). Thus you
will be able to start at the point where you first have to tune the gain, only this time your upper limit is
higher.
4.3 Dynamic
integrator
To be able to increase the proportional gain, an acceleration dependent, rate-varying lag that prevents
windup is used.
One might expect that a higher gain and lag term would induce a high overshoot, but the dynamic
integrator peels off the effect of integration (lag) as the target is approached. When the target is hit, the
effect of integration (which would have induced the overshoot) is eliminated. Once stationary again, the
effect of the integrator is re-applied. Consequently, it is possible to have
very
high gains leading to a high
precision and high disturbance rejection.
To summarise, the integration is applied when needed and cancelled (gradually) when it is not needed
(and becomes undesirable).
4.4 Velocity
feed-forward
Velocity feed-forward helps reduce the following error and increase the responsiveness of the system,
consequently reducing overshoot due to delay.
It is particularly useful for short moves used with a relatively high acceleration.
This can be seen as a gain on the error that is proportional to the velocity profile which is high at constant
speed and gradually increases during acceleration and decreases during deceleration.
Too much gain on velocity feed-forward will result in a higher overshoot for the system’s response.
