Control of inverted pendulum

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AG
AG 2019-11-18
回答： AG 2019-12-5
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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回答（2 个）

M
M 2019-11-18
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.
https://scholar.google.com/scholar?hl=fr&as_sdt=0%2C5&q=state+estimator&btnG=
https://scholar.google.com/scholar?hl=fr&as_sdt=0%2C5&q=LQR+controller&btnG=
In the simulink example, the state space estimator is implemented with a discrete time state space equation:
https://mathworks.com/help/simulink/slref/discretestatespace.html
And the LQR block is simply a matrix gain. You can find details about lqr in matlab here:
https://mathworks.com/help/control/ref/lqr.html
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M
M 2019-11-20
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 2019-11-22
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 2019-12-5
No one could help me?
Thank you very much!

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