D link

D-link in the structure diagram

D-link as a symbol

A D-element is an LZI - transmission element in control technology , which has a differentiating transmission behavior, i. H. the value of the output variable depends on the rate of change of the input variable.

The associated functional relationship in the time domain is

${\displaystyle y(t)=K\cdot {\dot {u}}(t)}$,

so that the complex transfer function in the image area takes the form

${\displaystyle G(s)=K\cdot s}$

Has. Here, K, K> 0, denotes the transfer constant or the gain factor of the D-element.

The D element is only considered theoretically, since a Dirac pulse occurs in the step response . In the real system, a D element is always associated with a delay. In addition, the impulse response is not causal.

Bode diagram

The D link is . Therefore, the following applies to the amplitude and phase response in the Bode diagram : ${\displaystyle G(j\omega )=Kj\omega }$

${\displaystyle |G(j\omega )|=K\omega }$

${\displaystyle \varphi (\omega )={\frac {\pi }{2}}}$

The amount characteristic is therefore a straight line that increases with 20 dB / decade and has the value K _dB at ω = 1 . Due to the linear slope of the gain, an ideal D-element has an infinitely high gain for infinitely high frequencies, which cannot be represented by a real system. The phase characteristic is a constant 90 °.

Bode diagram of a D-link (K = 2)

Step response

The step response of the D element is described by , where stands for the delta function. ${\displaystyle h(t)=K\delta (t)}$ ${\displaystyle \delta (t)}$

Locus

The locus ( ) of the D-element runs on the positive imaginary axis from the point zero for opposite . ${\displaystyle 0\leq \omega \leq \infty }$ ${\displaystyle \omega \to \infty }$ ${\displaystyle \infty }$

Locus of a D-link for positive frequencies

See also

• Regulator
• P element
• I-link
• PT1 element
• PT2 element
• PID controller
• Dead time element