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.
