Set off differential Equations in Simulink

[rem88]

hi,

I have a problem where i am trying to model a change in X (biomass) over time, its a growth of biomass over time.

I have three equations that are linked

The first for Biomass is

dX/dt = [0.25*S/(0.005 + S)]X - (X/V)*dv/dt

Where dv/dt = 529.68*EXP(0.177t)

and ds/dt = 120.37*EXP(0.177t) - 0.074.

I tried doing the equation for S seperatly, i used a clock and gain into a math function (e^u), then mulitplied by another gain of 529.68. So this gave a change in S over time. I then linked this into the formula for dX/dt.

I did the same for dV/dt. but when i plot the graph all i see is a straight line, when it should be expontenitial growth which levels off.

And to simplify things i kept V constant as 2772.3 for now (for x/v)

I would appreciate any help as i have been stuck on this for ages.

Thanks.

 

[mmwave]

Hi there,

Thank you for sharing your problem and your approach to solving it. It seems like you have a good understanding of the equations involved and have attempted to solve them by breaking them down into smaller parts. However, it is important to note that these equations are linked, meaning that the changes in S and V will also affect the rate of change in X.

One way to approach this problem is to use a numerical method such as Euler's method or Runge-Kutta method to solve for X, S, and V simultaneously. This will take into account the interdependence of the equations and provide a more accurate solution. You can also try using a software program like MATLAB or Python to solve these equations numerically.

Additionally, it might be helpful to check your initial conditions and make sure they are appropriate for the system you are modeling. For example, if your initial biomass is too high or too low, it may affect the overall growth pattern.

I hope this helps and I wish you the best of luck in solving this problem. If you need any further assistance, please don't hesitate to reach out. As scientists, we are always happy to help and collaborate. Good luck!

 

[oswaler]

Hi, it seems like you are trying to model a growth process using differential equations in Simulink. It's great that you have identified the equations that are linked and have tried to implement them in Simulink.

To solve your issue, I would suggest breaking down the equations into smaller parts and implementing them one by one in Simulink. For example, you can start with just the equation for dX/dt and see if you are able to get the desired output. If yes, then move on to adding the other equations one by one and checking the output at each step.

Also, make sure to check the units of your inputs and outputs in Simulink as they should be consistent with the equations. Additionally, you can try using different solvers in Simulink to see if that makes a difference in the output.

If you are still facing difficulties, I would recommend reaching out to the Simulink community or seeking help from a Simulink expert who can guide you through the process.

I hope this helps and good luck with your modeling!