/sci/ - Science & Math » Thread #11650106

7KiB, 251x173, state-space.png

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Anonymous Fri 08 May 13:02:07 2020 No.11650106 View Reply Original Report

Quoted By: >>11654270

When given a set of ODE's 'or' a single second-order equation: when do you rewrite the system as "State space" and when do you write it in "State space standard form"?

As" state space" doesn't necessarily imply the standard matrix notation, correct?

Anonymous

Anonymous Fri 08 May 2020 21:06:45 No.11651402 Report

Quoted By:

Bump for interest.

Anonymous

Anonymous Sat 09 May 2020 11:14:26 No.11653009 Report

Quoted By:

One last desperate try, because I'm also interested.

Anonymous

Anonymous Sat 09 May 2020 13:00:46 No.11653142 Report

Quoted By: >>11653145

Your terminology is not standard so if you want an answer you are going to have to define "state space standard form".

State space is just the set where the solutions can take values in, so a single first order ODE has state space on the real line, a system of n 1st order ODE has state space on R^n. Sometimes you can be fancy and have stuff like periodic variables so the pendulum equation has a state space of a cylinder (R x S^1). So the state space is just something that is there, not a way a system can be written in.

Anonymous

Anonymous Sat 09 May 2020 13:03:14 No.11653145 Report

Quoted By:

>>11653142
Ignore that shit in the second part, I was getting mixed up with phase space

Anonymous

Anonymous Sat 09 May 2020 13:51:13 No.11653220 Report

Quoted By:

State Space is general, the one in your pic isn't unique. It is, however, the standard, so you can represent your ODE's in that way with well known methods of analysis like yielding the transfer function directly from A, B, C, D matrices. I would say you can find better state space forms for some equations but it doesn't compensate for the time you'll spend developing new formulas.

Anonymous

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Anonymous Sat 09 May 2020 14:45:46 No.11653328 Report

Quoted By:

I remember taking this class, and five years later I still don't understand the state space method.

t. controls engineer

Anonymous

Anonymous Sat 09 May 2020 20:50:51 No.11654270 Report

Quoted By:

>>11650106
You can rewrite any linear set of ODEs in any state space form you want, whenever you want. If you're confused as to why there's more than one form, that's because the state space representation isn't unique. Some forms are more convenient for algebraic manipulation in some contexts, but you can use whatever form you want.

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