Omron SYSMAC CP Series Instruction & Reference Manual page 301

Derivative Action (D)
Proportional action and integral action both make corrections with respect to the control results, so
there is inevitably a response delay. Derivative action compensates for that drawback. In response to a
sudden disturbance it delivers a large manipulated variable and rapidly restores the original status. A
correction is executed with the manipulated variable made proportional to the incline (derivative
coefficient) caused by the deviation.
The strength of the derivative action is indicated by the derivative time, which is the time required for the
manipulated variable of the derivative action to reach the same level as the manipulated variable of the
proportional action with respect to the step deviation, as shown in the following illustration. The longer
the derivative time, the stronger the correction by the derivative action will be.
PID Action
PID action combines proportional action (P), integral action (I), and derivative action (D). It produces
superior control results even for control objects with dead time. It employs proportional action to provide
smooth control without hunting, integral action to automatically correct any offset, and derivative action
to speed up the response to disturbances.
CP1E CPU Unit Instructions Reference Manual(W483)
Derivative Action
Step response
Deviation
0
Manipulated
0
variable
PD Action and Derivative Time
Ramp response
Deviation 0
Manipulated
0
variable
Td: Derivative time
Step Response of PID Control Action Output
Step response
0
Deviation
Manipulated
0
variable
Ramp Response of PID Control Action Output
Ramp response
Deviation 0
Manipulated
0
variable
2 Instructions
PD action
P action
D action
PID action
I action
P action
D action
PID action
I action
P action
D action
2
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