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## The derivative lag element (DT1 element)

This element has a step response which initially contains a step and then decreases exponential to zero with a characteristic time constant as shown in Figure 4.13.
Figure 4.14 shows an example of such a system; a simple high pass filter. The differential equation of this circuit is

which can be written as

Applying the Laplace transform one obtains the transfer function

 (4.41)

The generalised notation of the element is

 (4.42)

For constructing the Bode plot one starts with the frequency response

 (4.43)

which on substituting gives

 (4.44)

From Eq. (4.44) it follows that

and

 (4.45)

After some calculations the phase response can be shown to be

 (4.46)

Comparing Eq. (4.45) with Eqs. (4.38) and (4.41) shows that the magnitude characteristic of the element can be obtained by adding the corresponding curves of a element and a D element. The same also holds for the phase response . With this information the curves of the frequency response characteristics and of the Nyquist diagram can be simply constructed according to Figure 4.15.

Next: The 2nd-order lag element Up: Some important transfer function Previous: The proportional plus derivative   Contents
Christian Schmid 2005-05-09