I intend to implement field oriented control of PM synchronous and Induction motor in Simulink. I started with the synchronous motor and was trying to find its linearized state space model.
I read that I should equate the following three equations to zero and find an equilibrium point.
(di_d)/dt=Vd/Ld – (Rsid)/Ld+(weLq*iq)/Ld = 0
(di_q)/dt=Vq/Lq – (Rsiq)/Lq-w_e(Ld*id+ƛ_PM)/Lq = 0
J*(dw_m)/dt=T_e – B*wm
where T_e = 1.5*Pƛ_PMiq
Since, there 5 unknowns, namely Vd, Vq, id, iq, and wm (we=p*wm, p= pole pairs) and three equations, I am unable to solve the above equations.
I tried to read few papers online but they did not explain it properly.
If you have any tips or suggestions to proceed further, it would be great!