add docs for sampled-data systems

[baggepinnen]

Work in progress

• Clocks TODO #1939

[AayushSabharwal]

Doesn't this make y lag x by one timestep? This would then imply that y(k+1) ~ x(k) which is not what the equation above says.

Basically, if x, y, u = [1.0, 1.0, 2.0] would the timeseries be[[1.0, 1.0, 2.0], [2.5, 1.0, 2.0], [3.75, 2.5, 2.0]] or [[1.0, 1.0, 2.0], [2.5, 2.5, 2.0], [3.75, 3.75, 2.0]]

I'm not very familiar with discrete-time modeling, so this may be some common misunderstanding I'm unaware of 😅

EDIT: If there's some tutorial/book for these kind of models I can go through that would be helpful, since the below examples also don't quite make sense to me

[baggepinnen]

Doesn't this make y lag x by one timestep?

Yes, the output x of this function is one step ahead of the output y, but y(k) does not lag x(k). Note how the comment mentions

The state x now refers to x at the next time step, while y refers to x at the current time step

Where next in x at the next time step is key. The returned value of the manually implemented function discrete_step is thus to be interpreted as the tuple

(state in next time step, current time output)

I'll commit a change to the comment to hopefully make this more clear

My goto book is usually "Computer-controlled systems" by KJ Åström, but I'm not sure if it would be particularly useful as a reference here.

[baggepinnen]

I hope this commit clarifies further? cbd9f59

[ChrisRackauckas]

@baggepinnen can something of this form be merged by the end of the day? It can continue to improve but we need something to go with the v9.

[baggepinnen]

This documents functionality that is not yet existing, in particular, the user interface for simulation is almost 100% missing and the MTK compiler is broken, JuliaSimCompiler is required, so I'd rather not merge any of it yet.

[ChrisRackauckas]

Okay then we'll v9 without this.

[ChrisRackauckas]

Build failed.