how to choose LQR
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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
4 commentaires
raja m
le 31 Juil 2014
There are some techniques to select value of Q and R in literature.please see to that............
Réponse acceptée
Shashank Prasanna
le 9 Fév 2013
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.
8 commentaires
Shashank Prasanna
le 9 Fév 2013
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
Plus de réponses (3)
Azzi Abdelmalek
le 8 Fév 2013
Modifié(e) : Azzi Abdelmalek
le 8 Fév 2013
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
5 commentaires
Shashank Prasanna
le 9 Fév 2013
shahad, you are trusting one or the other. I recon the model with no background is not of much value to anyone.
Fatma Yörük
le 21 Nov 2020
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.
2 commentaires
cmcm
le 9 Fév 2013
Modifié(e) : Azzi Abdelmalek
le 9 Fév 2013
4 commentaires
Azzi Abdelmalek
le 9 Fév 2013
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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