Hi . Im trying to design a LQR controller for the system below. but I don't know where to put the LQR Gain Block in the system . I know I have to remove the Fuzzy Controller Block and Replace it with LQR Gain , but I don't know how to do that , I mean I guess I need an Observable Matrix for that? can anyone help me pls ?
Dear Parham,
I suggest you to see links and attached file in subject.
-Design an LQR Servo Controller in Simulink - MATLAB & Simulink
https://www.mathworks.com/.../control/.../design-an-lqr-servo-cont...
-State-Space Control Design - MATLAB & Simulink - MathWorks
https://www.mathworks.com/.../control/state-space-control-design-...
-Linear quadratic regulator (LQR) controller design for DC motor speed ...
umpir.ump.edu.my/386/
-Vidéos
MATLAB/Simulink Differential Flatness LQR Controller
-Images correspondant à How to design a LQR Controller in simulink?
Best regards
Thanks , But none of them use Observer in their design. and My Main problem is that I dont know the output or the input of this model Im working on ! so I dont know where to put LQR Gain and Observer Gain in this !!!
Mohamed-Mourad Lafifi
Hi Parham,
For the unknown input and output of model i suggest you to see those links.
-Modelling, analysis and control of linear systems using ... - GIPSA-lab
https://www.gipsa-lab.grenoble-inp.fr/~o.sename/.../ME_auto.pdf
-(PDF) ESO Based LQR Controller for Ball and Beam System
https://www.researchgate.net/.../301744683_ESO_Based_LQR_Controller_for_Ball_and...
-State Feedback Optimal Controller Design for the Rotational ...
https://bib.irb.hr/datoteka/298662.MIPRO_Rastic_LQR_final.pdf
-Regulating Pressure in a Drum Boiler - MATLAB & Simulink ...
https://es.mathworks.com › Examples Home › Application Examples
-Control Tutorials for MATLAB and Simulink - Introduction: State-Space ...
ctms.engin.umich.edu/CTMS/index.php?...ControlStateSpace
Best regards
Hello Parham,
you could try to use the "Timed-Based Linearization Block" in simulink to obtain a state space representation of your system.
https://www.mathworks.com/help/simulink/slref/timedbasedlinearization.html
For sure before you need to identify system inputs and outputs. I think your scheme is representing only the system regulator since you are measuring an elevation through an encoder and producing a PWM to control a motor. You don't need this model but the model of the system you want to control that is the motor connected to the evelvator. Once you have implemented the process model in simulink and obtained it in state space you can design your LQR using the "lqr" command
in Matlab. The input to the regulator will be your system states that need to be estimated using an observer, but again you could tune it using the system in state space and the lqr command. If you need more help let me know.
Hope to be helpful!
Dear Parham
As Simone correctly said, if you have a valid model of the system in state space and you already select R and Q matrix of LQR, you can use "dare" or "care" or "lqr" MATLAB function to solve algebraic Riccati equation and finding LQR controller gain.
After finding the LQR gain in MATLAB, you can use a simple vector gain in simulink and set the LQR gain in it.
You can construct a simple Lunberger observer in simulink to estimate the state vector of the system based on model of system. So in each step, simulink finds state of system as input of LQR gain block.
Best Regard
Majid Shariat Simone Pozzoli Hi. thanks for your helpful advice. I've already designed my LQR controller and found it's gain as it is a 1x3 Matrix. what I can't really understand is that is the Observer also a Gain ? I mean is it the L gain we derive out of some pole placement method?, pls help!! and where to put them in the simulink model? I know that I have to delete the Fuzzy Controller there because I no longer need it. that PWM Scaling is the input and the Elevation (what I'm trying to control) is the output of the system. I have System's state matrices (A,B,C).
thanks.
Hello Parham,
to build your Luenberger observer you can use the pplace() command in Matlab. Usually this command is used to tune a pole placement regulator, placing the poles of A-BK, as in the LQR. You have to build an observer placing the poles of A-LC. Transposing everything we have A' - C'L' , so you can use the pplace command using matrices A' and C' to find a value for L', transposing the outcome of pplace you will find matrix L. Remember that the poles of the observer have to be faster enough.
To observer model is:
der(x)=Ax + Bu + L( y - Cx)
der(x)=(A - LC) x + [B L] [u ; y]
And the observer output is properly x, while u and y are the inputs.
A_obs=A-LC
B_obs=[B L]
C_obs=identity matrix of state dimension
D_obs=zeros(proper dimensions)
To incorporate your observer in simulink you can use a state space model with all the observer matrices which takes as input u and y and returns your state estimation. Be careful with vectors and matrices dimensions.
Best regards.
Dear Parham
In order to building Luenberger observers in Simulink, I propose you two variant methods:
1) Writing a Matlab function that gets both the input and output of plant and calculate system state,
then you can call this function through a Simulink block
2) constructing a Lunberger observer directly by Simulink block that simulate observer dynamic equation
Note that finding gain matrix of observer (L) has two different procedures for continuous and discrete time system
Regards
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