PROPORTIONAL-DERIVATIVE (PD) CONTROL or anticipatory control or rate control (Transfer function for linear change in error)

PROPORTIONAL-DERIVATIVE (PD) CONTROL or anticipatory control or rate control (Transfer function for linear change in error)

This mode of control may be represented by

In this case, we have added to the proportional term another term,  

 

which is proportional to the derivative of the error.

The values of Kc and ��_D may be varied separately by knobs on the controller. Other terms that are used to describe the derivative action are rate control and anticipatory control.

 

The action of this controller can be visualized by considering the response to a linear change in error as shown in Fig.

This response is obtained by introducing the linear function e(t) = At into Eq.

Response of a PD controller to a linear input in error

For linear change in the input the output signal will vary as shown in the above figure.

For PI controller, output signal varies linearly with time.

For PD controller output signal takes a step change of amount AKcT_D and after that it varies linearly with a slope of AKc.

The effect of derivative action in this case is to anticipate the linear change in error by adding additional output AKcT_D to the proportional action.

Transfer function for linear change in error is given by,