P element

P element in the structure diagram
P-element as a symbol

As P-member is referred to a LZI - transmission member in the control engineering , which is a proportional having transmission characteristics. The associated functional relationship in the time domain is

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

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

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

Has. Here, K, K> 0 denotes the transfer constant or the gain factor.

Bode diagram

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

${\ displaystyle | G (j \ omega) | = K}$
${\ displaystyle \ varphi (\ omega) = 0}$

The amount characteristic is therefore a straight line at a distance of K dB from the 0 dB line. The phase characteristic is a constant 0 °.

Bode diagram of a P element (K = 2)

Step response

The step response of the P element describes a unit step with step height K.

Step response of a P element (K = 2)

Locus

The locus ( ) of the P element lies for all ω on the positive real axis at point K. ${\ displaystyle 0 \ leq \ omega \ leq \ infty}$

Locus of a P element (K = 2)