Control Systems, State space to Transfer Function

[k87]

Hi guys,

Need a little help with an example my tutor and I are trying to work through.

We're converting a dynamics system from a state space representation to a transfer function.

This is where we are at so far...

[s^2 + (C/Mb)S + (K1/Mb), -((C)S + K1)/Mb; -((C)S + K1)/Mw, S^2 + (C/Mw)S + (K1+K2)/Mw] [X3;X4] = [0; k2/mW]*Zr(.)

Zr(.) being the differential of Zr which in this case is velocity.

We have what we think is the next step but I'm still not entirely certain so would appreciate some help

 

[k87]

This is it in pictoral form and the corresponding transfer functions, I don't understand how to get the numerators though