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Proportional-Derivative control is useful for fast response controllers that do not need a steady-state error of 0. Proportional controllers are fast. Derivative controllers are fast. The two together is very fast. Below is a review.
Proportional Action[1]Proportional action provides an instantaneous response to the control error. This is useful for improving the response of a stable system but cannot control an unstable system by itself. Additionally, the gain is the same for all frequencies leaving the system with a nonzero steady-state error. Derivative Action[2]Derivative action acts on the derivative or rate of change of the control error. This provides a fast response, as opposed to the integral action, but cannot accomodate constant errors (i.e. the derivative of a constant, nonzero error is 0). Derivatives have a phase of +90 degrees leading to an anticipatory or predictive repsonse. However, derivative control will produce large control signals in response to high frequency control errors such as set point changes (step command) and measurement noise.In order to use derivative control the transfer functions must be proper. This often requires a pole to be added to the controller (this pole is not present in the equations below).
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