Block diagrams to transfer functions

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Discussion Overview

The discussion revolves around the conversion of a block diagram into a transfer function, specifically focusing on the formulation of closed-loop transfer functions. Participants are examining the correct expressions for the transfer functions involved in feedback systems.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes a closed-loop transfer function as $$\frac{\frac{HLG}{1+HL}}{1 + \frac{HLG}{1+HL}} = \frac{KK_f}{s^2J + (KK_f + a)s + KK_f}$$ based on their definitions of G, H, and L.
  • Another participant corrects this by stating that the transfer function for the inner feedback loop should be $$\frac{H(s)}{1 + H(s) L(s)}$$ rather than the proposed form.
  • A subsequent post reiterates the correction and requests clarification on why the initial formulation was incorrect.
  • A further response explains that the forward path transfer function appears in both the numerator and denominator of the closed-loop transfer function, while the feedback path transfer function does not.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there is a correction of the initial claim regarding the formulation of the transfer function, but the discussion remains open regarding the implications of this correction.

Contextual Notes

There are unresolved assumptions regarding the definitions of the transfer functions G, H, and L, as well as the specific context of the feedback system being analyzed.

Dustinsfl
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Homework Statement


I am trying to write a block diagram as a transfer function.

hINLD1J.png


Homework Equations





The Attempt at a Solution


Let ##G = \frac{1}{s}##, ##H = \frac{K}{Js + a}##, and ##L= K_f##. Then wouldn't the closed loop transfer function be written as
$$
\frac{\frac{HLG}{1+HL}}{1 + \frac{HLG}{1+HL}} = \frac{KK_f}{s^2J + (KK_f + a)s + KK_f}
$$
I only ask because the book has it as
$$
\frac{K}{s^2J + (KK_f + a)s + K}
$$
and I don't see how that was obtained.
 
Last edited:
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The transfer function for your inner feedback loop is \frac{H(s)}{1 + H(s) L(s)}, not \frac{H(s) L(s)}{1 + H(s) L(s)}.

I think that should sort it out.
 
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milesyoung said:
The transfer function for your inner feedback loop is \frac{H(s)}{1 + H(s) L(s)}, not \frac{H(s) L(s)}{1 + H(s) L(s)}.

I think that should sort it out.

Can you explain why that is?
 
Dustinsfl said:
Can you explain why that is?
It's an easy mistake to make. The transfer function in the forward path appears in both the numerator and denominator of the closed-loop transfer function but the transfer function in the feedback path does not:
http://en.wikipedia.org/wiki/Closed-loop_transfer_function
 

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