Circuit states

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Hi folks,

 

I was thinking to a dynamic programming application today and figure out that I do not really understand a basic concept in electrical circuit. My question is why do we choose capacitor voltage and inductor current as circuit states and then formulate the circuit in state space based on these states. In other words, we solve the linear state equations as .x_p=Ax+Bu where x_p is the derivative of state and x is the state. 

Can we choose capacitor current as state? oh I think because then what would be the derivative of capacitor current? The second order derivative of its voltage, right? so it can not come in the form of the matrix? Is it the reason?

If I am not binded to this form, can I choose power of elements as circuit states?

Last Edited: Wed. Mar 11, 2015 - 02:35 AM
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Inductor and capacitor have long been considered "duals" of each other.

 

Part of the dual relationship is that where one has a derivative relationship, the dual has an integral relationship. That is one of the reasons why they are defined in the way that they are. They could, of course be defined differently, but that (integral for one, derivative for the other) has come to be the accepted way of stating their current-voltage relationships.

 

Jim

 

 

 

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Last Edited: Thu. Mar 12, 2015 - 08:45 PM