I’ve been trying to implement LQR with state-observer in real-time. Since, I couldn’t manage to implement it using MATLAB real-time workshop, I had to write the C code for LQR and state observer. However, it seems like the C code isn’t working at all and I can’t get my head around it. My first question is, when I design my state-feedback matrix and observer matrix in MATLAB before using it in my C code, do I have to design them (K and L) in discrete-time. I appreciate if someone can give me some advice how to implement LQR+observer in real-time using either MATLAB or C, as I don’t really know why I keep getting issues with implementation.
Best regards
I would suggest that you design the LQR with the observer using Matlab's inbuilt functions (e.g. "LQR", "place" and others) in the continuous time. Then, once you are able to verify that the observer and controller work correctly, you do the same but now in the discrete time. Choose a sampling frequency at least 10 times higher than the bandwidth of your closed-loop. Once you are happy with the simulation results, you can implement the LQR+observer code in a Matlab script and check that it works correctly. The real-time workshop should be able to run this code as well but if you really want to implement it in C, you can do it as well but it will only add complexity at the time of debugging.
Thanks heaps Enrique! I design state-feedback matrix and observer matrix in MATLAB using LQR command and I am able to stabilise my system. Then, I design the discrete time state-feedback matrix and observer matrix, but this time using dlqr command in MATLAB. However, when I use MATLAB to implement it, it gives me runtime error, so I had to write the C code by myself. The C code works, but I am not able to stabilise my system. I'm not sure if the there is something with the design of K and L in discrete time using dlqr command. I have the same problem with implementing sliding mode controller in realtime.
I think I didn't explain it correctly. Obviously you get the run-time error because you are using the real-time workshop. I would suggest that _before_ you test your controller with the real-time workshop, you test it outside that environment to be sure that the controller+observer perform as intended. You could make a frequency analysis(?). _Then_ you can move ahead and run it in the real-time workshop.
Alternatively, you could try to stabilize the plant with a simpler controller (which you are 100% sure it works even though the performance is poor) in the real-time workshop to investigate whether it is a wrong general setting in the real-time workshop or a wrong implementation of the controller? Hope it helps...
Amid Noshadi, How do you implement your controller algorithm in C? Could you right it here?
If your controller worked in the continuous time, it may work when you implement it in real-time, if the closed-loop bandwidth were 10 to 30 slower than the sampling frequency. Did you check that?
You can design and simulate the LQR using Matlab and for real time you can embed it into arduino mega.
Looks like you have been given some good advice already, just wanted to add a few suggestions.
There are typically two ways to implement a control law like this, directly as a discrete time filter, or as a continuous time filter which you solve using a numerical integration scheme, such as the Euler or Runge-Kutta method. The last method is what is standard in for example Simulink if you try to solve a continuous time filter there, and will typically be a more computationally demanding.
I would suggest using a discrete time implementation, but you have to make sure you are using gains that are suitable for discrete time, as already mentioned. Newer versions of MATLAB has the 'dlqr', 'lqrd', and 'kalmd' functions, that might be useful for this.
Also, you can run your C code as a so-called S-function inside Simulink. This can be very useful in debugging your code. Set up your model of the system as a regular LTI system block, and your LQR and observer implemented in C in an S-function block.
Hope this helps...
I think if you develop a code for LQR in Lab VIEW you will be able to interface with real time set up.
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