how to choose LQR

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cmcm
cmcm 2013-2-8
评论： manohar sahu 2022-11-8
hello everyone i am trying to use LQR controller i simulate my system and have my A and B matrix ,, used theme in m-file and use the lqr function to control this system,,, is there any way to know what is the right value for Q and R ?? i try a lot of values for them but the results give me 2 positive values and that is wrong, all values must be negative depending on the choice of the Q and R. so is there any way make me know what is the right values for them instead of try and error ? please help
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raja m
raja m 2014-7-31
There are some techniques to select value of Q and R in literature.please see to that............
Jose Almeida
Jose Almeida 2015-6-20
Can you reference some literature? Thank you

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采纳的回答

Shashank Prasanna
LQR always returns a stabilizing feedback gain.
Are there 1 or 2 eigen values that are always show up positive?
You most likely have an uncontrollable mode in your system. As Azzi mentioned you have to just try different weights, choosing Q and R is part art, part science.
If you can provide the state space (A,B,C,D) for your plant, it would be useful.
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Shashank Prasanna
Shashank Prasanna 2013-2-9
yes,
You have a negative feedback and this is not LQR Servo. You have to be careful with convention. LQR 'ALWAYS' returns a stabilizing gain matrix, as long as all modes are controllable. This is by construction. LQR does not care about your outputs i.e. C and D and it stabilizes the closed loop plant with the feedback gain K that gives you good properties at the plant input u
cmcm
cmcm 2013-2-9
thank you soooo much for your notes ... that was a mistake from me that i did not notice the sign ... all my problem was about sign :) thanx again

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Azzi Abdelmalek
Azzi Abdelmalek 2013-2-8
编辑：Azzi Abdelmalek 2013-2-8
There is no systematic method to choose Q and R. You can start with
Q=eye(n) % n: number of states
R=eye(m) % m: number of inputs
Simulate your system in closed loop, then try to adjust your weighting coefficient Q and R. You have just to know, that more the weighting parameter is great, more the weighted signal is minimized.
You have to know, also, that you will need to insert integrators, if you want to correctly control your system
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Shashank Prasanna
Shashank Prasanna 2013-2-9
shahad, you are trusting one or the other. I recon the model with no background is not of much value to anyone.
cmcm
cmcm 2013-2-9
ok am sorry i will post it

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Fatma Yörük
Fatma Yörük 2020-11-21
There are some optimization methods to find the best Q and R so that you achieve your desired performance. Most literature uses GA or PSO algorithms for it. However, some comparisons with the descent algorithm takes also part in. So, rather than the trial and error, trying to develop some optimisation-based algorithms might be more proper way.
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Victory Friday
Victory Friday 2022-1-31
Please can you help me with one of the pso for A and RN matrix
manohar sahu
manohar sahu 2022-11-8
Can you please let me know how to implement pso for lqr controller

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cmcm
cmcm 2013-2-9
编辑：Azzi Abdelmalek 2013-2-9
clear all;
gi=1;
% initial condition
a=2.9975;
b1=0.034025;
b2=0.034025;
b3=0.5606;
b4=-b3;
Am =[ 0 1.0 0 0 0 0;
0 0 -a 0 0.0000 0;
0 0 0 1.0 0 0;
0 0 0 0 0 0;
0 0 0 0 0 1.0;
0 0 0 0 0 0];
Bm =[ 0 0;
0 0;
0 0;
b3 b4;
0 0;
b1 b2];
Cm=[1 0 0 0 0 0;0 0 1 0 0 0;0 0 0 0 1 0];
Dm=[0 0;0 0;0 0];
Ai = Am;
Ai(7,5) = 1;
Ai(8,1) = 1;
Ai(8,8) = 0;
Bi = Bm;
Bi(8,2) = 0;
co=ctrb(Ai,Bi);
rank(co)
unc=length(Ai)-rank(co)
Q = diag([0 0.05 0 0 2 1 1 0.001]);
R = 50*diag([1 1]);
K = lqr( Ai, Bi, Q, R );
disp( ' ' )
disp( 'Calculated LQR controller gain elements: ' )
K
eig(Ai+Bi*K)
CMD_RATE_LIMIT = 45.0 * pi / 180;
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cmcm
cmcm 2013-2-9
why ???
Azzi Abdelmalek
Azzi Abdelmalek 2013-2-9
Shahad, explain what you want to control. What are your references? And you can't control 3 output with 2 inputs, unless you want them to tend towards zero.

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