Modelling ODE in Simulink when input multiplied by ouput

Hi, so I have this hysteresis equation of a battery, this equation will be combined with other ODE (which could be easily modelled with transfer function) to generate a battery model

where h is the output and i is the input, sgn is the sign of i(t), and the rest are constant. I had tried to make a laplace transfer function and it is not working because the input multiplied by output (h multiplied by i). How can I model this equation in simulink? Could I make this equation in a discrete block and combine with continoues block at the same model?

Thank you

Answer 1

[Ghazwan]

What you are looking for is available here

https://www.youtube.com/watch?v=_bzQ1Ws28cg

Answer 2

[Sam Chak]

Hi @aizo zeo

The given ODE cannot be modeled in the Laplace transform sense because it is a non-affine system due to the product term .

However, it can be modeled in continuous-time using the fundamental blocks like the following:

• Constant for and M
• Abs for
• Sign for
• Add for
• Product for multiplying , , and
• Integrator for integrating the right-hand side of the ODE, and to specify the initial value.