I recently had to deal with a power electronic system where I had to implement a dynamic model of a power converter in order to design a suitable controller for that converter. The control will be implemented on a DSP which reads in the digitize values (voltages and currents) from some ADCs. The plant itself consists of a PWM modulator and a 4th-order LC filter. Since ADCs and control are digital systems, I can describe them using the z-transform, whereas the LC filter is an analog system which I usually describe using the Laplace-transform.
The question which now arises for me is: should I discretize the time continuous transfer functions of the filter and work out the whole system dynamics using z-transform, or do I describe the digital controller in s-domain and describe the whole system as a time continuous system?
During my studies I always worked with Laplace transform. I heard that there is z-transform too, but I never really worked with it. This was usually working fine, however, in most of the papers I find the authors are using z-transform and I don't really know when I should use one or the other for mixed systems. As far as I know, it doesn't really play a role in which domain I work as long as the frequencies I'm concerned about are "low enough" compared to the sampling frequency of the system. Is this true?
Another problem I face: when I'm working with these dynamic models in s-domain in matlab and let the program calculate transfer functions, the models which result exhibit insanely high orders (e.g. order 100 for a system which should have order 7). I know that this is numerical issues and that most of those system poles are cancelled out by zeros laying extremely close to the poles. There is a matlab command ("minreal") which eliminates some of those pole-zero combinations but not all. Could I reduce this issue by switching into z-domain? If not: how trustworthy is the "minreal" command? Do I risk loosing important information if I apply this command on every transfer function?