How to solve this system of differential equations in Simulink ?

I have to solve the following system of differential equations in Simulink. I have attached what I have done. I think there must be something wrong with the block diagram that I built, but I cannot figure out what. The independent variable is the time. ms, mu, cs, ks, ku, cu are constants. y is the road which I gave to the Simulink model as input using 1-D LookUp Table block.

From which:

It is a 2-DOF system coressponding to a vehicle. It has been obtained using the laws of motion.

I cannot figure what it is wrong with the diagram I created. Below is an example of why I am saying this. In the left picture is the kind of graph for SWS I would like to obain. In the right picture is what I actually get. It looks like, at the beginning, the SWS I obtain is ok, but afterwards, it is constanlty very close to 0, and it is not oscillating anymore like in the right picture. I guess there might be something wrong with input road (the y - 1DLookUpTable). Note, also, that the range is completely different. In the left image i goet values up to 300, while in the right image I get values of 10 to the power of -4.

Answer 1

[Amit Dhakite]

Hi Patrausanu Andrei,

As per my understanding, you are not able to solve the system of equations in the simulink model. In you model, you have considered y and y_dot as the same entity. However, y and y_dot are different.

Kindly try to correct the equations and modify the Simulink model.

For more information you can refer to: https://www.mathworks.com/help/simulink/ug/model-a-differential-algebraic-equation.html

[Patrausanu Andrei]

Hi, Amit! Yes, you are right. I know about this issue, but for me, it's not clear how to obtain y_dot, since y represents the input (y_dot being the first order derivative of y). For the rest of variables in similar situations, I followed the principle presented in the tutorial you provided. Nevertheless, could you help me, please, with a hint or explanation on how to do that ?

I tried this out, but it's not working either.