Discrete Time Integrator (Iz)¶

There are several methods to implement a discrete time integrator. SimApp uses a trapezoidal approximation to transform an ideal time continuous integrator to its discrete time counterpart.

Functions

Polygonal approximation:

State equation:

Transfer function:

Step response

Magnitude and phase response

Polar plot

The discrete time integrator can also be derived from the analog implementation of the bilinear transformation:

Transfer function of the analog integrator is

Bilinear Transformation:

Replacing s in G(s) by the bilinear transformation yields G(z)