Define State space in simulink for pendulum inverted

Hello, I am studying inverted pendulum in Matlab following this link: https://www.mathworks.com/help/control/examples/control-of-an-inverted-pendulum-on-a-cart.html

But I don't understand the block State Space in simulink and I will explain why...

When you double-click on this block you will see this image:

We can see that matrix A is 2X2, B is 2X1, C is 1X2 and D is 1X1. But when I look the state space form for this problem, this is what I found:

We can see that the size of them are different... for example The first image, the matrix A is 2X2 and the second image is 4X4. Thinking about it, I image that state space program is using just the theta variable and it's not using the position variable... (correct this part is I am wrong!)

How did they define the variables form state space block?

Cheers,

Answer 1

[Sebastian Castro]

Two different things!

The 4-state system you provided are the system equations for the inverted pendulum on a cart. In the model you shared, these dynamics are modeled with Simscape Multibody blocks instead of mathematical equations.

The 2-state system in the Simulink screenshot, as its block name suggests, is a controller. The matrices in this system will be tuned by that example to control the physical system.

- Sebastian