Writing Output in State Space Form: RLC Circuit Example

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Discussion Overview

The discussion revolves around the representation of output in state space form for an RLC circuit, specifically addressing the challenges when the output is not a direct combination of state variables. Participants explore the implications of using state space representation in electrical engineering contexts.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how to represent the output 'voltage across resistor' in the form y=cx+du when it is not a combination of state variables.
  • Another suggests using phasor equivalents and deriving the transfer function to convert it to state space form, which would allow for identifying the A, B, C, D components.
  • A participant expresses uncertainty about explaining the output equation y=cx+d when the output seems to be merely a combination of state space variables.
  • A newcomer mentions the necessity of expressing all variables as state space variables to utilize state space form, referencing a specific chapter from a textbook for context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to represent the output in state space form, and multiple competing views regarding the approach to take remain evident throughout the discussion.

Contextual Notes

There are limitations regarding the assumptions made about the relationships between state variables and outputs, as well as the dependence on specific definitions and contexts within the RLC circuit analysis.

Who May Find This Useful

Individuals interested in electrical engineering, particularly those studying circuit analysis and state space representation, may find this discussion relevant.

asad1111
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the general form of state space output is y=cx+du which means that output is linear combination of state variables and inputs my question is can we write output in this form when our output is not combination of state variable for example in rlc circuit state variables are vc and IL now if we want to take output 'voltage across resistor' how can we represent it in form y=cx+du
 
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Use the phasor equivalents for the circuit (capacitors = 1/sC and inductors = sL) and figure out the transfer function of your circuit (Vo/Vi). Then convert the transfer function to state space form and you will be able to break out the A, B, C, D parts.
 
okay but how will you explain it to anybody by looking at output equation y=cx+d when output is merely combination of state space variables
 
I'm a total newbie on this, but from what I've read, you need to express all variables as a state space variable if you want to use them in a state space form. For example, when you want to incorporate an excitation system into a SMIB model, you have to express the variables of the excitation system as a function of state variables. (Kundur Chapter 12) But like a said I'm a total newbie.
 

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