c2d transformation from s domain to z domain
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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.
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Aquatris
2024-2-19
编辑:Aquatris
2024-2-19
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.
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)
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