Can I implement a spatial derivative in a simscape custom component?

I have an equation based off of two variables M and H. At some point in my equations I need to take the spatial derivative of H with respect to M like this: dM/dH. Then dM/dH is set equal to some expression that is also dependent on M and H. So think of it like the equation is dM/dH = x;

In a simscape custom component I can set a time based derivative dH/dt = x; How would I implement a spatial derivative in a custom component? I'm a little confused at the math because neither is based on time, but the simulation is always changing time and has a numerical solver that is time based. These derivatives are not dependent on time at all.

Answer 1

[Rollin Baker]

The beginning of your question is a bit unclear. You mention you want to take the derivative of H with respect to M, but you then go on to say you want to find dM/dH, which is actually the derivative of M with respect to H. For the purposes of answering your question, I will assume you mean to find dM/dH.

You say you have some equation that relates M and H. You will need to solve for M in this equation. Then you will have a function M(H). You can then find dM/dH by simply taking the derivative of this equation with respect to H. If you were trying to find dH/dM, just do the same process, but solve for H instead of M.

While the simulation is time-based, there is no requirement that you actually use the time measurements for anything. You can just create new vectors to represent the values that H and M are dependent on inside the "variables" or "parameters" section of the custom component.

Below I've linked a few documentation pages on the sections of Simscape components that may be relevant to you:

https://www.mathworks.com/help/physmod/simscape/lang/variables.html

https://www.mathworks.com/help/physmod/simscape/lang/parameters.html

Good luck with writing your custom component,

Rollin