Dear colleagues,
Kindly support me in finding the best efficient way to identify MIMO transfer function matrix of an HVAC system whose block diagram is attached. I can get an accurate responses for various inputs values applied on the input ports.
What is remaining for me is to identify the transfer function matrix to enable me applying INA multi variable control technique
The two inputs I have are the voltage of the blower fan and the mass flow of the refrigerant in the refrigeration cycle, while the outputs are the temperature of the zone (air-conditioned space) and the temperature of the mixed air entering the air handling unit
I am familiar with using the system identification toolbox of MATLAB to identify the SISO transfer function but I seriously face trouble in how to find the transfer function matrix of 2-inputs 2-outputs.
Kindly advise and support.
Regards
Basim Touqan
Hi,
If you use the MATLAB system identification toolbox, the procedure has no differences for SISO and MIMO. However, you should use "iddata" command to define the dataset as MIMO.
Bests
Thank you sir for your valuable answer, I would highly appreciate if you elaborate more on how to do so, the model i am looking for is 2 x 2 transfer matrix.
I attach here in the simulink block diagram of the whole plant, how may i start to establish the above mentioned matrix , what ideas do you have?
Thanks & regards,
Basim Touqan
Dear Basim Touqan,
I suggest you to see links and attached files on topic.
https://fr.mathworks.com/help/ident/ug/dealing-with-multi-variable-systems-identification-and-analysis.html
https://fr.mathworks.com/matlabcentral/answers/75742-identification-of-miso-mimo-models-based-on-transfer-functions-poles-multiply-contained-in-result
https://vsip.info/advanced-control-using-matlab-4-pdf-free.html
https://www.bib.irb.hr/699199/download/699199.2000-Parameter-Identification-of-Transfer-Functions-Using-MATLAB.pdf
Chapter Multivariable Control by Transfer Function Matrix
Best regards
Dear Mr. Lafifi, I highly appreciate your interaction and valuable answer.
Actually I have passed through your suggested documents, and still unable to find what I need.
I am very familiar with the control techniques that can be applied on SISO and MIMO systems, the only problem is that i am still not sure how to obtain the transfer function matrix ( 4 elements) of the block diagram I attached before. I need the transfer functions in Laplace representation.
Dear Basim,
Is it within your reach the representation in the state space of your system (MIMO), if yes so the thing becomes trivial simply apply the algebraic equation in the case where the system is proper namely D=0 :
C 1 / [sI-A] B = G(s) = Y(s) / U (s), then you can check the identification of each element of the transfer matrix.
Regards
Thanks Mr. Lafifi, I think I can manage to jot down all the state equations and obtain the A,B,C,D matrices. I will check and get back to you for further support if needed
The question remains is how to deal with the constants in the state equations, i.e.
dx/dt=Ax+Bu+constant.
How to include the constant in the equation: G(s) = C*(s*I-A)*B ?
Hi Basim,
I think your system is invariant (LTI) so the matrices A, B, C and D are made up of the constants so in the equation of state or that of the observation there can be no free constant, either the constant is related to the vector state 'x' or at input 'u'.
Regards
Dear Mr. Lafifi,
The system indeed is LTI, hence I will consider the the constants as additional inputs and select finally two inputs to build two inputs two outputs system model.
Thank you for your contribution which added a lot to my knowledge.
Thanks & regards,
Basim Touqan
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