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XPS-Q8 Controller
much lower than static friction and would generally require less correction gain than
smaller moves. However, if Kp becomes too large, the mechanical system may begin to
overshoot (encoder position > SetpointPosition), and at some point, it may begin to
oscillate, becoming unstable if it does not have sufficient damping.
Kp cannot completely eliminate errors. However, since as the following error e,
approaches zero, the proportional correction element, Kp x e, also approaches zero and
results in some amount of steady-state error. For this reason other gain factors like Kd
and Ki are required.
Derivative Term
14.1.2.3
The Kd, or derivative gain, multiplies the differential between the previous and current
following error by the derivative gain value (Kd). The result of this gain is to stabilize
the transient response of a system and can also be thought of as electronic damping of
the Kp. The derivative acts as a gain that increases with the frequency of the variations
of the following error:
The result is that the derived term becomes dominant at high frequencies, compared to
the proportional and integral terms. For the same reason, the value of Kd is in most
cases limited by high frequency resonance of the mechanics. This is why a low pass
filter (cut off frequency = DerivativeFilterCutOffFrequency) is implemented in the
derivative branch to limit excitation at high frequencies. Increasing the value of Kd
increases the stability of the system. The steady-state error, however, is unaffected since
the derivative of the steady-state error is zero.
These two gains alone can provide stable positioning and motion for the system.
However to eliminate the steady state errors, an additional gain value must be used.
Integral Term
14.1.2.4
The Integral term Ki acts as a gain that increases when the frequency of the variations
of the following error decrease:
The result is that the integral term becomes dominant at low frequencies, compared to
the proportional and derivative terms. The gain becomes infinite when frequency = 0.
Even a very small following error will generate an infinite value of the integral term.
The advantage of the integral term is that it will eliminate any steady-state following
error. However, the disadvantage is that the integral term can reach values where the
corrector is saturated causing the system to become unstable at the end of a move and
cause the positioner to hunt or dither. To reduce this effect, two additional parameters
are included in the PID corrector to help prevent these instabilities, Ks and Integration
Time.
Ks
The saturation limit factor Ks permits users to limit the maximum value of Ki that is
applied to the total PID corrector output. The Ks saturation limit can be set between 0
and 1, a typical setting is 0.5. As an example, at a setting of 0.5, the maximum output
generated by the Ki term applied to the PID output would be 0.5 x the maximum set
output. However, if the Ki gain factor output is less than 0.5 x the maximum set output,
then the entire gain will be applied to the PID corrector. This maximum output is set
within the section MotorDriverInterface in the stages.ini using the parameters
AccelerationLimit, VelocityLimit or VoltageLimit. Refer to the Programmers manual
for more information on this function.
Integration Time
The IntegrationTime is used to adjust the duration for integration of the residual errors.
This can help in applications where large following errors can occur during motion. The
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XPSDocumentation V1.4.x (EDH0301En1060 — 10/17)
Motion Tutorial
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