Does c2d function has some limitations? Not working properly

Hi all.

I have a continuous model and want to use c2d function to transfer it in discrete for further digital implementation in processor.

This is the part of the code:

Tsample = 1e-4;
H = tf([(2*pi*50)^2], [1 2*(2*pi*50) (2*pi*50)^2]);
Hd = c2d(H, Tsample, 'foh');

Depending on the Tsample I get different transfer functions, which is according to theory :)

But when I do comparison between continuous and discrete transfer function in Simulink I get different response (amplitude is different (red and green signal)). If I decrease Tsample more (e.g. 50e-6) amplitude difference gets even higher.

Answer 1

[Radha Krishna Maddukuri]

While the TF and ZPK representations are compact and convenient for display purposes, they are not ideal for system manipulation and analysis for several reasons:

• Working with TF and ZPK models often results in high-order polynomials whose evaluation can be plagued by inaccuracies.
• The TF and ZPK representations are inefficient for manipulating MIMO systems and tend to inflate the model order.

For more information and an example, please check the web link: Using the Right Model Representation .

So a fix for your particular example would be to use State-Space Representation instead of Transfer Function:

>> Tsample1 = 1e-4;
>> Tsample2 = 1e-3;
>> num = [(2*pi*50)^2];
>> den = [1 2*(2*pi*50) (2*pi*50)^2];
>> H = tf(num,den); 
>> sys = ss(tf(num,den));
>> Hd1 = c2d(sys,Tsample1,'foh');
>> Hd2 = c2d(sys,Tsample2,'foh');
>> bode(H,Hd1,Hd2);

Now you can see that using different sample times should still produce similar results.