s-Domin or z-Domain - What to Use for Mixed systems 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?
First choice :

Convert the Laplace transform of your process to the Z-domain using the ZOH method as it models your DAC. In your case, your DAC is a PWM. 

Second choice :

Work in the Laplace domain but take in account the delay due to your PWM, which should be T/2 where T is your PWM period. To model the delay, you can use the Padé approximation.

I personnaly used the second technique. It was easier, more intuitive. But both techniques will work.

For the numerical issues :
The order of your transfer function might get large when including the controllers, I used minreal too, but you can convert your tranfer functions to ZPK, this solves many of the numerical issues you might have.

Edit : As Tim Wescott mentioned in the comments. The ZOH modelization is accurate when using a real DAC. Not so for a PWM. It's better off to work in the s-domain and try to model the delays (sampling, PWM, computation, etc.) as accurately as possible.