## Derivative Control

When derivative control is applied the controller senses the rate of change of the error signal and contributes a component of the output signal that is proportional to a derivative of the error signal. Thus:

It is important to remember that the controller where Td is a time rate constant.

It is important to remember that if the error is constant there is no corrective action with derivative control. In practice, derivative control is never used on its own. The response curve has therefore been deliberately omitted from Fig. 8.17.

Figure 8.19 demonstrates the response of derivative control to sinusoidal error inputs. The output is always in a direction to oppose changes in error, both away from and towards the set point, which in this example results in a 90° phase shift. This opposition to a change has a fast damping effect and this property is very useful in combination with other modes of control which will be discussed later.

Table 8.2. The effect of controller gain (Kc) on band width of a proportional temperature controller

Measured temperature

Pressure output (psig) at Kc= lpsig/r

Pressure output (psig) at Kc = 2 psig/1"

Table 8.2. The effect of controller gain (Kc) on band width of a proportional temperature controller

Measured temperature

Pressure output (psig) at Kc= lpsig/r

Pressure output (psig) at Kc = 2 psig/1"

 35° 15 " 