Response of Proportional Plus Rate Control:

Derivative cannot be used alone as a control mode. This is since a steady-state input generates a zero outcome in a differentiator. The input signal it would receive is the error signal if the differentiator were used as a controller. As just elaborates, a steady-state error signal corresponds to any number of essential output signals for the positioning of the last control element. Thus, derivative action is combining along with proportional action in a manner such in which the proportional section outcome serves as the derivative section input.

Proportional plus rate controllers take benefits of both proportional and rate control modes.

As seen in below Figure, proportional action gives an output proportional to the error. The proportional action is slow if the error is not a step change, but is slowly changing.  Rate action, when added, gives quick response to the error.

Figure: Response of Proportional Plus Rate Control