# Thread: Representing y(t) correctly in a Simulink model

1. ## 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!

2. Originally Posted by coley0412
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!

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

3. 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!

4. Originally Posted by coley0412
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

5. 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.

6. Attached is the new model. Why do I only get a value of 10 no matter what I enter into the model???