Discrete to continuous

[kletze]

Added a function to convert discrete time LTI systems to continuous time LTI systems.
The function uses the inverse of the zoh-method. A mathematical derivation can be found for example on this page: https://studywolf.wordpress.com/tag/zero-order-hold/

[murrayrm]

I'm not sure this function is really needed. What's the use case where one wants to convert from continuous time to a (zero-order hold) continuous time model?

If we do include this, it needs to use python-control coding conventions and include unit tests (in the control/tests/ directory).

[sawyerbfuller]

thanks for the contribution!

I have not run into a need for this function but it has been suggested before in #294 , and it is available in Matlab https://www.mathworks.com/help/control/ref/dynamicsystem.d2c.html (but not, as far as I can tell, in scipy).

In addition to adding unit tests, I suggest moving this to being a method of the LTI class in lti.py because it applies equally to both ss and tf systems. and adding a function that calls that method. Please also see the example of lti.sample_system to see how to properly pass other system parameters like signal and system names.

[sawyerbfuller]

I just found that Harold has a cont2discrete method — see _undescretize in https://github.com/ilayn/harold/blob/main/harold/_discrete_funcs.py

might have some good ideas.

[ilayn]

Possibly my most useless spent week on a nerdy subject 😃 It is certainly possible but like Richard, I don't know what value it adds to anything. I just generalized this paper. Not that it makes it more useful but I was neck deep in IQCs so seemed simple enough. Didn't publish it but put it in harold instead. You can do arbitrary LFR connections between s and z in case needed.

The trick is to know how you ended up with that particular discrete model. Otherwise if you go --> zoh this way and tustin <-- this way, things get complicated very quickly.