LQR Error about controllability

Question

Usman Shahzad 2012-12-2

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评论：嘉俊黄 2022-3-21

Hi everyone,

I am doing some work on LQR controller for time variant system. My problem is that by choosing the weights Q and R some of my states get worked but some does not. MATLAB gives the error that:

The "lqr" command failed to stabilize the plant or find an optimal feedback gain. To remedy this problem:

1. Make sure that all unstable poles of A are controllable through B (use MINREAL to check)

2. Modify the weights Q and R to make [Q N;N' R] positive definite (use EIG to check positivity).

My question is how i can remove this problem as [Q N;N' R] is sure positive definite and my system is controllable as well.

thanks

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Muhammad Ali 2014-11-2

I am facing the same problem as Usman suggested. Please someone answer the queries. Thnx

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Answer 1

Ursula 2013-5-24

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编辑：Ursula 2013-5-24

在 MATLAB Online 中打开

Hi,

I have the same problem. The error message appears, although my system is controllable, and my [Q N;N' R] is positive definite. If I want to get the controller with pole placement, Matlab says:

The "place" command could not place the poles at the specified locations.
Probable causes include:
* (A,B) is nearly uncontrollable
* The specified locations are too close to each other.

The specified locations are at -1, -2, -3, ... -59, and there is no other result, if I increase the space between the desired poles.

My System is of 59th order. The maximum value of Matrix A is 3e+006 and the Controllability Matrix of (A,B) has maximum value of 3e+120. Is this maybe a numerical problem, and how can I solve it?

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Sam Chak 2022-3-21

Hi @嘉俊黄 (Mr. Wong)

You are advised to post a new question on the LQR design problem that your are facing, on the grounds that the users have been inactive since 2013. Most likely, you won't get any useful response from them.

If there is no sensitive information, it is preferrable to show the State Matrix

, the Input Matrix

, and the weights

,

in the cost function.

Thanks for considering this advice.

嘉俊黄 2022-3-21