How to convert an equation from z-plane to w-plane in MATLAB

If we have an equation like G(z)=(2z^3-4.424z^2+3.3634z-0.8721)/(z^4-3.037z^3+3.425z^2-1.6935237z+0.3084332) how do we convert this to w-plane by using bilinear transformation z=(1+w)/(1-w)? Is there a single command or are a set of commands available?

Answer 1

[MA]

syms z w
G=(2*(z.^3)-4.424*(z.^2)+3.3634*z-0.8721)/((z.^4)-3.037*(z.^3)+3.425*(z.^2)-1.6935237*z+0.3084332);
GN=subs(G,z,(1+w)/(1-w))

Answer 2

[AaHi]

If you are working with an tf-values use following code:

T = 0.2;

NumG = [1]

DenG = [1 1 0]

Gs = tf(NumG, DenG)

Gz = c2d(Gs,T,'zoh')

%The stuff above to create the z-function out of a s-function

aug=[T,1]

Gwss = bilin(ss(Gz),-1,'S_Tust',aug);

%Use billingual transformation

Gw = tf(Gwss)

[Muhammad Talib Faiz]

Thanks a lot, helpful.

Answer 3

[Torsten]

help subs

Best wishes

Torsten.