Hello all, I hope you can help me with a question regarding an assignment I'm doing at the moment. I have had to design a lead controller in the time domain and then discretise it into into the z domain. That's all gone ok, but I've encountered a problem in trying to justify my choice of sampling period.

I am trying to measure the distortion between the sampled and continuous controller in MATLAB. From my notes, the formula is

\( D = \frac{1}{2n-1} \sum^n_n (y_0(nT) - y_T(nT))^2 \)

yo = output signal of the analogue controller
yt = output signal of a digital controller with sampling period T

I have both the analogue and digital controllers modeled as transfer functions in MATLAB. Does anyone have any ideas how to get their step responses into the above system?Unfortunately, I'm still in my early learning stages with MATLAB and I'd really appreciate any help.

 

In frequency domain: Input times Transfer Function equals Output.
In time domain: Input convolved with Transfer Function equals Output.
What seems to be the problem?

And if you know the Input, why the eF are you not using Nyquest Sampling Theorem to determine sampling period?