RLC Series Circuit: State Equations

  • #1
Dustinsfl
2,281
5
Using the capacitor voltage and the inductor current as states, write the state equations for the RLC series circuit shown in the figure.

mc8hQL5.png


We can write that . I am not sure with what it wants when it says to write it as states.
 
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  • #2
Shouldn't it be I think when they say "state", they mean that the DE should be in that unknown variable. So if is the state variable, write the DE with as the unknown function.
 
  • #3
dwsmith said:
Using the capacitor voltage and the inductor current as states, write the state equations for the RLC series circuit shown in the figure.

mc8hQL5.png


We can write that . I am not sure with what it wants when it says to write it as states.

In electric egeneering are called states of a network somewhat is related to the 'energy' contained in the reactive elements, i.e. the voltage across a capacitors and the current in inductors. In Your case the network has two states, i.e.the two unknown variables are and . The equation governing the network are...





Kind regards

 
Last edited:
  • #4
I have determined my state transition matrix as

Then

What is and .
Additionally, I have that

where , , and .

The solution has

Therefore, where does this come from?

If we take the Laplace Transform of , we end up with the factor . That is, we have

but that still leaves the question where does come from?
 
Last edited:

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