Wow. There is not much to go on here. Is this an application or an academic exercise? I would request that some more specific information be given.
It has been my experience that less than 10% of all motor control applications needed vector control and about 1% needed an encoder or other sensor. Jeff is right - I have never heard of a single phase vector control drive. There are just too many ways to solve this with 3 phase motors.
A little rule I use for Vector Control: 1) Do you need 100:1 speed control? Yes-Open loop vector, No- CT is fine 2) Do you need 100% torque at zero speed? (this is 1000:1 speed control or better) Yes-Closed loop vector, No- Open loop vector is fine.
Many of today's VFDs provide very good torque control at low speeds even in CT mode. To save costs, a single phase in / 3 phase out
VFD will usually not have Closed Loop Vector support. I have seen some that just use a very good Voltage Boost and call it Vector!