Question

MatLab Simulink: S domain to Z domain?

Asked by: jhui

Hi~~ I having difficulty on using MatLab Simulink on converting a S domain transform function to Z domain~ I just wondor anyone have experience on this~

I get a transform function

H = tf([27.75 2.51675 0.5513 0],[4.2946e-8 0.00096105 6.4387 13587 2.6318e6 1.9954e5 4371])

                           27.75 s^3 + 2.517 s^2 + 0.5513 s
--------------------------------------------------------------------------------------
4.295e-008 s^6 + 0.000961 s^5 + 6.439 s^4 + 13587 s^3 + 2.632e006 s^2 + 199540 s + 4371

and wanna convert it into Z-domain by

>> Hd=c2d(H,0.0001,'zoh')
 
Transfer function:
6.27e-005 z^5 - 4.2e-005 z^4 - 0.0002297 z^3 + 0.0003141 z^2 - 8.462e-005 z - 2.049e-005
----------------------------------------------------------------------------------------
         z^6 - 4.497 z^5 + 8.211 z^4 - 7.753 z^3 + 3.97 z^2 - 1.037 z + 0.1067
 
Sampling time: 0.0001

The Step response looks fine in

step(Hd)

but I cannot obtain the result to put into Simulink using Discrete Transform Function Block?? which I have also set the sampling time to 0.0001 already~ Anyone have exp. this as well and can share your solution with me?

Thanks~

James.

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Asked On
2002-10-17 at 01:59:47ID20375387
Tags

domain

,

z

,

matlab

,

s

,

simulink

Topic

Math & Science

Participating Experts
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Answers

 

by: prashant_n_mhatrePosted on 2002-11-14 at 16:19:29ID: 7450925

Basically you want to store the numerator and denominator matrices.

Save the following function in a file 'stoz.m'

function [bz,az,zd]=stoz(bs,as,h,td)
%
%[bz,az,zd]=stoz(bs,as,h,td)
%     Convert s domain SISO transfer function to z domain.
%     It can deal with fractional dead-times.
%
%     bs    Zero polynomial
%     as    Pole polynomial
%     h     sample-time
%     td    time delay
%     bz    z-domain Zero polynomial (includes leading zeros for delay)
%     az    z-domain Pole polynomial
%     zd    Units of discrete time delays (represented seperately also);
%
x=td/h; k=fix(x); delta=td-k*h;
[phis,gams,deltas,omegas]=tf2ss(bs,as);
[phi,gam]=c2d(phis,gams,h);
 if delta > 0;
   [phi2,gam2]=c2d(phis,gams,delta);
   hd=h-delta;
   [phi3,gam3]=c2d(phis,gams,hd);
   b2=phi3*gam2;
   [bz1,az]=ss2tf(phi,gam3,deltas,omegas,1);
   [bz2,az]=ss2tf(phi,b2,deltas,omegas,1);
   bz=[bz1 0]+[0 bz2];
 else;
   [bz,az]=ss2tf(phi,gam,deltas,omegas,1);
 end;
 if k>0, bz=[zeros(1,k) bz];end;
   zd=k;
 return


Now define:


bs=[27.75 2.51675 0.5513 0]

as=[4.2946e-8 0.00096105 6.4387 13587 2.6318e6 1.9954e5 4371]

[bz,az,zd]=stoz(bs,as,0.0001,0)

This will give you bz and az matrices that you could use in simulink through workspace.

20120131-EE-VQP-002

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