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An example of how the response overshoot can be improved
with a proper rate action setting is depicted in the following
graphic.
PID TRANSFER FUNCTION
The transfer function of a PID control is as follows:
Kp + Ki/s + s Kd = Kp (1 + 1/(s Ti) +s Td)
with Ti = Kp/Ki, Td = Kd/Kp,
where the first term represents the proportional action, the
second is the integrative action and the third is the deriva-
tive action.
Proportional action can be set by means of the Proportional
Band (PB). Proportional Band is expressed in percentage of the
input range and is related to Kp according to the following:
Kp = 100/PB.
