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Math Help - Representing y(t) correctly in a Simulink model

  1. #1
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    Representing y(t) correctly in a Simulink model

    Hi, I am trying to simulate the following equation:
    \frac{dy(t)}{dt}=0.2*\frac{y(t-tau)}{1+y^{10}*(t-tau)} -0.1y(t)
    with y(0) = 1.5

    A model is attached. I think it is close but I'm not sure I have represented the y(t) or the time delay correctly. Can anyone help me troubleshoot it?

    Thanks so much for any help!

    Representing y(t) correctly in a Simulink model-chs_model.pdf
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by coley0412 View Post
    Hi, I am trying to simulate the following equation:
    \frac{dy(t)}{dt}=0.2*\frac{y(t-tau)}{1+y^{10}*(t-tau)} -0.1y(t)
    with y(0) = 1.5

    A model is attached. I think it is close but I'm not sure I have represented the y(t) or the time delay correctly. Can anyone help me troubleshoot it?

    Thanks so much for any help!

    Click image for larger version. 

Name:	chs_model.pdf 
Views:	30 
Size:	9.4 KB 
ID:	19745

    You seem to have applied the gain 0.2 twice. Also I'm not sure (or rather I am sure) you have set up the initial conditions correctly.

    There also seems to be confustion between y^{10} * (t-\tau) and (y(t-tau))^{10}

    CB
    Last edited by CaptainBlack; November 18th 2010 at 02:43 AM.
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  3. #3
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    Ok I have fixed the gain error and the initial condition error but I believe the y^{10} * (t-\tau) term is still incorrect. I'm guessing what I currently have is the second term you have listed above. I am unsure how to fix this as there are no t terms in the formula. How can I get the 10 to apply to the y only? Thank you for looking at the model!
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by coley0412 View Post
    Ok I have fixed the gain error and the initial condition error but I believe the y^{10} * (t-\tau) term is still incorrect. I'm guessing what I currently have is the second term you have listed above. I am unsure how to fix this as there are no t terms in the formula. How can I get the 10 to apply to the y only? Thank you for looking at the model!
    Somewhere you have a problem specification, what exactly does that say?

    CB
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  5. #5
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    Hmm a problem specification? I'm not sure I understand but I am given the equation I wrote above and I have to simulate it. It seems I don't have one of the terms in the equation exactly right. I am given the time delay and that has been incorporated into the transportation delay block. Once the model is running I just change the step size a few times to demonstrate the sensitivity of the system. That is all the information I am given.
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  6. #6
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    Attached is the new model. Why do I only get a value of 10 no matter what I enter into the model???
    Attached Thumbnails Attached Thumbnails Representing y(t) correctly in a Simulink model-chs_model.pdf   Representing y(t) correctly in a Simulink model-chs_eqn2.pdf  
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