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Control of inverted pendulum

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AG
AG on 18 Nov 2019
Answered: AG on 5 Dec 2019
Hello everyone,
I'm playing with the Inverted Pendulum example : openExample('simulink_general/penddemoExample') in Command Window. I'm trying to understand which control theory stays behind the state space estimator and the choice of LQR parameters.
I don't find anything similar in literature, can anyone help me, please?

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Answers (2)

M
M on 18 Nov 2019
I don't find anything similar in literature
LQR algorithm with state estimator is very common and you can find plenty of examples in the literature.
In the simulink example, the state space estimator is implemented with a discrete time state space equation:
And the LQR block is simply a matrix gain. You can find details about lqr in matlab here:

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AG
AG on 18 Nov 2019
Dear M,
thank you for your reply and please excuse me, I don't explained well my problem. The meaning of "I don't find anything similar in literature" is referred on the Simulink example. In particular I can't find an answer to these questions:
Why A matrix is 0? Why B matrix is 1/Ts? Why D matrix is not set to 0?
Thank yoy very much!
M
M on 20 Nov 2019
I did not look into details but it looks like the matrices inside the estimator block come from a linearization of the functions that model the cart + pendulum. I guess the linearization is made around the vertical position.
AG
AG on 22 Nov 2019
Its look like we use the information of cart position and angle sensor "as is", the meaning of A=0 is that we don't consider the previous state but I don't understand why. If I linearize the generic model of a inverted pendulum on a cart I must use the general model where A is a 4x4 matrix and not 2x2.

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AG
AG on 5 Dec 2019
No one could help me?
Thank you very much!

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