Derive 6 Help with Laplace Transforms

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Discussion Overview

The discussion revolves around using Derive 6 software to solve for the closed loop gain A/B of a control system using Laplace Transforms. Participants are exploring how to apply Derive 6 to this problem, which involves evaluating transfer functions and algebraic substitutions.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant expresses a desire to learn how to use Derive 6 for solving closed loop gain problems, indicating that future problems will be more complex.
  • Another participant suggests that if the user understands how to find the closed loop transfer function, it can be solved through substitution, providing a general formula for H_cl.
  • A later post acknowledges confusion and attempts to clarify the question, emphasizing the need to evaluate the closed loop gain of the loop C/R using the Laplace operator s.
  • Another participant reiterates the importance of algebraic substitution and provides a formula for the closed loop transfer function, indicating that it involves substituting the appropriate expressions for F(s) and R(s).

Areas of Agreement / Disagreement

Participants generally agree on the method of using algebraic substitution to find the closed loop transfer function, but there is no consensus on the specific steps to be taken using Derive 6, and some confusion remains regarding the initial question.

Contextual Notes

Limitations include the lack of access to the circuit attachment mentioned, which may contain critical information for solving the problem. There are also unresolved details regarding the specific steps in Derive 6 and the definitions of the transfer functions involved.

BIGEYE
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I am new to Derive 6 and Laplace Transforms. Is it possible to solve the closed loop gain A/B of the attached loop using Derive 6. If it is possible, can someone guide me through the steps using Derive, as the problems that lie ahead will be much more complex, and I want to use Derive in the future.

TIA
 

Attachments

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Not sure I'm fully understanding what you're asking, but assuming you underdstand how to find the closed loop transfer function in general then it's just a matter of substitution.

That is, H_cl = F/(1+F R)

Where F = Ka Km / (s (1+ sT)) and R = Ki in the example you post.
 
Let me try again!

I made a complete balls of that question, everything was wrong. Let me try again, I have to evaluate the closed loop gain of the loop C/R, using the laplace operator s.
The correct circuit is attached.
I can do this problem manually, but it is very tedious and easy to amke a mistake. I want to know how this can be done using Derive 6, if someone can show me the steps.

TIA
 

Attachments

  • OC1.JPG
    OC1.JPG
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Well I can't yet see that attachment becasue it's still pending approval but I hope you understand the basic concept here. All you need is simple alegraic substitution, that's it!

It's trivial to show that the closed loop transfer function is F(s)/(1+ F(s)*R(s)). Where F(s) is the transfer function of forward block and R(s) is the transfer function of the feedback block (and * is just normal multiplication). So just subst in the appropriate expressions for F and R, it couldn't be much simpler.
 

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