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Discrete Transfer Function

Purpose

Model discrete system as transfer function

Library

Control / Discrete

Description

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The Discrete Transfer Function models a discrete time-invariant system that is expressed in the z  -domain:

Y(z)   n zn +⋅⋅⋅+ n z + n
---- = -n-n--------1----0-
U(z)   dnz  + ⋅⋅⋅+ d1z + d0

The transfer function is displayed in the block if it is large enough, otherwise a default text is shown. To resize the block, select it, then drag one of its selection handles.

Parameters

Numerator coefficients
A vector of the z   term coefficients [nn ...n1,n0]   for the numerator, written in descending order of powers of z. For example, the numerator z3 + 2z   would be entered as [1,0,2,0].
The output of the Transfer Function is vectorizable by entering a matrix for the numerator.
Denominator coefficients
A vector of the z   term coefficients [dn ...d1,d0]   for the denominator, written in descending order of powers of z  .
Note  The order of the denominator (highest power of z  ) must be greater than or equal to the order of the numerator.
Sample time
The time interval between samples. See also the Discrete-Periodic sample time type in section Sample Times.
Initial condition
The initial condition vector of the internal states of the Transfer Function in the form [xn...x1,x0]  . The initial conditions must be specified for the controller normal form, depicted below for the the transfer function:

          2
Y-(z)= n2z--+-n1z +-n0
U (z)   d2z2 + d1z + d0

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where

       -di
bi  =  dn        for i < n
bn  =  d1-
        n   nndi
ai  =  ni - dn   for i < n
an  =  nn

For the normalized transfer function (with nn = 0   and dn = 1  ) this simplifies to bi = di   and ai = ni  .

Probe Signals

Input
The input signal.
Output
The output signal.