Dear colleagues,
I am developing an HVAC MIMO model, through writing the state equations I am facing the attached state equation where in the third term, two states are multiplied in one term which creates a non-linearity in the system. The equation (part of eleven state equations) is attached
a,b,c and d are constants while (Tcc) is the cooling coil temperature, (Trfrgnt) is the temperature of the refrigerant (qsa) is the mass flow rate of the blown air, (Tra) is the temperature of the recirculated air and (To) is the ambient temperature
Now I face a problem of how to establish the A matrix (11 x 11), what is the best way of linearization of this particular equation? Do I need to linearize only the nonlinear term in the equation? Once linearized, does the linearized process effect the other state equations?
Kindly support and advise
You have to integrate and get the constant of integration.Then apply boundary conditions.
While not being aware of the entire physics of what you are attempting to do, let me provide you with a simple way to do the linearization:
The third term can be represented as [(q_sa)_0 T_ra + q_sa (T_ra)_0]/2 where the 0-subscripted quantities are earlier approximations to these quantities. Yiu can compute the results and keep iterating with the results on 0-subscprited quatities till the values remain unchanged. At that stage you can take that the full equation has been solved properly.
Dear Mr. Makunda,
Thank you for your valuable answer and contribution, i will follow this linearization technique in my project, but do you call this linearization technique? I need to mention it in writing up the work and cite it as well.
Thanks & regards
It is linearization and one approach to linearization. You are welcome to term it so - hsm
I tried it using MATLAB loop but without success to converge the loops, can you please write me the first 5 equations iterations, it might be that I am doing a mistake in building the iterations.
Please suggest the first assumed values, the first state is the refrigerant mass flow which should range between 0.01 kg/sec to 1.8 kg/s
The Recirculated air temperature should range between 1 Celsius to 38 Celsius .
I can help if you write an explanation of what you are intending to solve and also send me your MATLAB code. Without this background, I cannot be of help. You can send these to me at [email protected]
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