State space model with disturbance
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@Paul If I have a system x_dot= [500 0;0 0.1]x+[50;0]u+[0 0.001]d and y= [0 1]x. So I want to make an LQR controller but my problem with the disturbance term and how can I deal with it?
2 个评论
Sam Chak
2022-4-4
Do you have the knowledge about the disturbance d?
Is the disturbance d bounded?
Try providing these info before @Paul comes.
回答(2 个)
Sam Chak
2022-4-5
I refer to the state-space system from another post that you opened in the link:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/952904/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/952909/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/952914/image.png)
where u is the controller, and w is the unmatched bounded disturbance that you mentioned above.
If the unmatched disturbance w is measuarable, then the proposed controller u is given by
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/952919/image.png)
where ζ and Ω are the two control parameters to be determined. Note that ζ is damping ratio and Ω is the undamped natural frequency of the control system.
If you let the autotuner to design the Linear Quadratic Regulator (LQR) for you and obtain the gains
, then you can apply
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/952924/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/952929/image.png)
Try it and show the result to see if it works or not.
4 个评论
Sam Chak
2022-4-6
Can you confirm if the following LQR u?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954290/image.png)
Can you confirm which of the following disturbance
is true?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954295/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954300/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954305/image.png)
where
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954310/image.png)
The lsim() function can take multiple inputs, but the first input
and the second input
are fed into different "systems". You can find the desired output using the superposition principle if it holds.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954315/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954320/image.png)
Else, can you consider using the more direct approach with the ode45() method to feed in the LQR u and the disturbance w?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954325/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954330/image.png)
with initial condition
, and
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954335/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/954340/image.png)
另请参阅
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