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Discrete Transfer Function

Purpose

Model discrete system as transfer function

Library

Control / Discrete

Description

pict

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

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.
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

Y (z)  n2z2 + n1z + n0
U-(z) =-dz2-+-dz-+-d-
         2     1    0

pict

where

bi  =  -di       for i < n
       dn1
bn  =  dn-
ai  =  ni - nndi for i < n
a   =  n    dn
 n      n

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.