Dear Researchers,
I have to build a Kalman filter in Simulink based on linearized model of a system using state space block. The linearization of a system occurs at every one hr. and the matrices A,B,C,D are updated. As far as the Simulink is concerned it doesn't update these matrices (defined as global variables) in state space block every time the linearization happens. I was wondering if there is any other way to implement this. Note that this filter has to run with Simulink's run-time as it then sends state estimates to controller.
Thanks in advance!
Probably the easiest way that I think of is to use a 'Matlab function block'. This function block is similar to writing your mfile, the only difference being that it can be used in your simulink block. Your individual system matrices can be updated by whatever logic you are applying to these matrices.
Hope this works.
Hi Niraj
you can make state space block that has inputs for A, B, C, D like follow picture
Dear Niraj,
You could take a look at the set_param command, which updates variables of a Simulink block. You could run it after every linearization to update the state space block in your Simulink model with the new A, B, C, and D matrices.
You could bulid a s-function, which will be implemented in a certain period. So, you can update your A, B, C and D in the function, and output the new value of A, B, C and D to the other blocks.
If I'm following you, you may try the Linear Matrix Inequality viewpoint. This would allow you to consider a set of n systems (Ai, B, C, D, i=1,...n) equivalently to a single time-varying system (A(t),B,C,D) where A(t)={A1,A2,...,An}. The later will form a convex hull which may allow you to have a single structure for all your cases.
Thanks a lot all of you for your answers and time. The solution given by @René works only when the matrices don't change their dimension over time. In my case, as I am trying to build a Kalman filter on linearized system (linearized every 60 sec) and then reducing the order, the dimension of A,B,C,D matrices changes every time new linearization happens online. So may be solution given @Luo could work but I am not expert in that. @Ricardo I have very little knowledge of LMI formulation, but I will still try to look in to this perspective.
Consult:
http://web.mit.edu/braatzgroup/33_A_tutorial_on_linear_and_bilinear_matrix_inequalities.pdf
http://www.dcsc.tudelft.nl/~cscherer/lmi/notes99.pdf
http://www.mathworks.com/help/releases/R13sp2/pdf_doc/lmi/lmi.pdf
I hope it helps...
Use 4 integrators and define the initial values of A,B,C,D in them. Give the changes of A,B,C,D as derivative signals to the inputs of integrators.
If the dimension of the set S={A,B,C,D} is changing then you may also try the hybrid dynamical systems approach. From what you say, it seems you have to define first your set of systems, say, Si={Ai,Bi,Ci,Di}, i=1,2,..., n (fix your n). Once with this set defined, what it seems to me is that you have this set Si in the direct trajectory of the feedback loop diagram. Depending of the system you are dealing with at a moment, you have to choose the control law which corresponds to each of them. So, define a logic table or switch (consult details in Simulink) to commute among the corresponding controllers Ci, i=1,2,...,n you need to apply to each Si. I think your problem is rather decision-logic-based than another thing. You may consult:
http://www-inst.cs.berkeley.edu/~ee291e/sp09/handouts/book.pdf
Have you reviewed the Lookup table and the Logic and Bit Operations options in Simulink? It seems you may switch among your systems...
Hi Ricardo,
Thanks for the detailed answer but in my case I can't pre-defining the set as the system develops over the time and hence I always have to linearize it at new equilibrium points to update the kalman filter and the MPC controller.
In that case, you may know the limits of the entries of your matrices? Say, if A=[a1 a2;a3 a4], with 1
Dear Dr.,
I hope all is well with you, I make a simple a SIMULINK block shows how to build a 1st order dynamic system with dynamic parameters.
the implemented system is:
dx/dt=-parameter*x+u
y=x
this mean that A=[parameter], B=[1], C=[1],D=[0]
https://wameedhmuc.wordpress.com/how-to-solve-a-state-space-model-in-simulink-with-abcd-matrices-that-are-updated-regularly-over-fixed-time-intervals/
Define the initial values of A,B,C and D in the initial conditions of 4 integrators. Use an Embedded function (MATLAB function) to define the update rules in it. In fact, the update rule determines the changes applied to A,B,C, and D. This changes should be defined as outputs of the Embedded function. Its inputs are the outputs of the 4 integrators.
Let’s first analyze the system response when c = 0.5. Define the A, B, C, and D
matrices in the m-file. A sample code is shown below
k=2;
m=1;
c=.5;
A=[0 1;-k/m -c/m];
B=[0;1/m];
C=[1 0];
D=[0 0;0 0];
sim('mass_spring_dam');
t=sim_u.time;
u=sim_u.signals.values;
y=sim_y.signals.values;
25. We can actually use variables in all the simulink blocks provided that they are
defined in the Workspace before the model is run. Now change the parameters of
the State-space block to match the matrices that you defined in the m-file. The
state space block should like similar to then click on state space block and file with A,B,C,and D
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