Rational Discrete Time Element (G(z))¶

The G(z) element is the general implementation of a linear discrete time transfer element. It is the counterpart to the analog G(s) element and is also known as digital controller.

A real time computer program must be causal, i.e. for computing the new output value y(kT), one can only use the input values u(kT), u(kT-T), ... From that is concluded that the order of the denominator must be greater or equal to the order of the numerator.

Functions

m ≤ n; m ≤ 31;

a_n≠0; n ≤ 31;

The meaning of the initial values is depicted by the matrix representation of the state equations:

;