c2d transformation from s domain to z domain

I have a s- domain equation and want to convert it to z domain.....but i will be using variables in my TF instead of values for those variables...how to convert this? I am asking this since c2d requires numeric values rather than unknown variables.

Answer 1

[Aquatris]

For forward Euler method, plug in s = (z-1)/T where T is your sampling time

For backward Euler method, plug in s = (1-z^(-1))/T where T is your sampling time

You can use symbolic toolbox or hand calculate the resulting transfer functions.

There is a nice lecture slide from MIT on this topic here.

Simple example;

s = tf('s'); % create s domain variable
sysC = 100/(s^2 + 2*0.1*10*s + 100); % continous time system

T = 1e-3; % define sampling rate
z = tf('z',T); % create z domain variable

z_forward = (z-1)/T; % forward euler method
sysD_forward = 100/(z_forward^2 + 2*0.1*10*z_forward + 100); % forward euler method discretization

z_backward = (1-z^(-1))/T; % backward euler method
sysD_backward= 100/(z_backward^2 + 2*0.1*10*z_backward + 100);% backward euler method discretization

bode(sysC,sysD_forward,sysD_backward)