How to deal with the constants' Matrix of state space model?

Dear colleagues,

I am currently developing an HVAC multivariable mathematical model.

The modeling technique I follow is state space

I managed to identify 12 state equations

Part of the 12 equations are 4 with non linearity terms ( the 4 equations are attached where a1, a2, ... are constant coefficients or A matrix elements ), the non linearity is established in the terms where the mass flow of supplied air (qsa) [kg/sec] is multiplied with the following temperature states in individual terms of the relevant state equation:

Tcc: Temperature of the cooling coil [oC]

Tao: Temperature of the output blown air[oC]

Tsa: temperature of the supplied air [oC]

Tz: temperature of the zone [oC]

Tra: Temperature of the recirculated air [oC]

I have followed the methodology of Taylor expansion series linearization around normal operating points to linearise the non linear terms individually, but I ended to have series of new sate equations with additional constants' matrix:

[dx/dt] =[Ax] + [Bu] +[Constants]

Now I need to derive the 2x2 transfer function matrix based on [ tf=B* (s*I-A)*C] equation.

Kindly advise and support how to deal with the constants' matrix [Constants] in order to derive the transfer function matrix, what is your experience in such situation. Is the work I am doing correct?

Thanks & regards,

Basim Touqan

[Paul]

In the model, are the a_i terms constant and are the q_ao and q_sa terms the inputs to the system?

[Basim Touqan]

Dear Mr. Paul

Sincerely apologise, qao is the same qsa, i corrected already the model in the attachment, qsa is one of the states, the two inputs are not shown in the 4 equations attached.

The tw inputs are shown in the remaining linear state equations, I did not show all equations because i focused only on the non linear equations.

a1, a2, ...., a16 are constants.

Best regards,

Basim Touqan