A four-pole induction machine with following parameters is controlled in the rotor flux linkage-oriented vector control mode by a PWM inverter with an ideal current regulation loop. The machine is running in the steady state, ieds= 7 A. The frequency of the stator current is 55 Hz. At t = 0 s, when the direction of the rotor flux linkage coincides with that of the magnetic axis of the "a"-phase winding, the input contactor of the machine is opened as shown in figure below. After t=0+, find the line-to line voltage between the "a" and "b" phase of the machine by using the following procedures. The current to the machine is immediately zero after the opening of the contactor.

Rs= 0.55Ω
Rr= 0.36Ω
Lls= 1.8mH
Llr= 1.8mH
Lm=59mH
Jm= 0.04kg. m^2

The rated power of the induction machine is 5Hp, and the inertia of the load is nine times the machine inertia, JM. And the friction coefficient, BM+L, of the drive system is 0.1 N-m/(rad/s).

a. Just after the opening of the contactor, find the rotor angular speed, ωr (0+), and the d-q axis stator flux.
linkage, λrds(0+) and λrqs(0+) in the rotor reference frame.

b. Find the rotor angular speed, ωr (t), t > 0+, in electric angle.
c. Find the "a" phase voltage, Vas(t), t > 0+
d. Find the "b" phase voltage, Vbs(t), t > 0+
e. Find line-to-line voltage, Vab(t), t > 0+