I have a state space model: A is 4X4 matrix B is 4X1 vector, C is 4X5 matrix and I am using Kalman filter and LQ-controller. The model have 4 state and 5 output, the controller give of course 4 K-values (gain), because of 4 states. I understand how this kind of design works when it is about SISO system and understand the math behind it. But how this design works with MIMO, I mean if I multiply the output of a model ( C and possible D matrixes) so there is 2 or three output (control input) the K-values will be different, why? how Kalman have combined them?
Dear Ali,
Note: Matrix C can not have this dimension unless Ct, because because n = 4(nb. of sate) and m = 5(nb of output), dim of C equal to 5x4.
Also i suggest to you application's exemple of MIMO Kalman and LQ Controller, please look at links and attached files in topics.
- Operations Research and Decision Aid Methodologies in Traffic and ...
https://books.google.dz/books?isbn=3662035146
- Features - Control System Toolbox - MATLAB - MathWorks
https://www.mathworks.com/products/control/features.html
- Optimal Control Systems
https://books.google.dz/books?isbn=0849308925
- Linear Systems: Optimal and Robust Control
https://books.google.dz/books?isbn=1420008889
-Dynamics and Control of Chemical Reactors and Distillation Columns: ...
https://books.google.dz/books?isbn=1483298906 -
Best regards
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