inverted pendulum modelling in state space

Hi all, I'm modelling the behaviour of the inverted pendulum. I looked up this example: http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SimulinkModeling#2

I'm trying to remodel this example, so that I can control the pendulum only with the velocity of the cart. Is that even possible? (on the Matlab site it's the force applied to the cart that is control input). I was playing with state equations, but I didn't come up with anything. Could anybody help?

[Azzi Abdelmalek]

Can you precise what is your problem. What have you done so far?

[Daniel Moulin]

I have taken equation (10) and (11) from: http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SystemModeling

and I assumed that velocity (x') is my control input, so u=x'. I have also taken force applied to the cart F as a constant value (let's say 20N). In the model shown above F=u. But as I said I want to control the movement only with velocity. The next step, that I made was trying to differentiate the equations (10), (11) into state-space form and I obtained:

Now I'm not sure if that's correct, because I limited the range of the matrices and also I need x' as a state variable, because of the x'' that is in the equations (10), (11).