Need to control an AC motor so that it can rotate in one direction and then rotate in another direction?

The AC motor needs to rotate from 0deg to 60deg in one direction and the rotate from -60deg to 60deg in another direction straight after the first motion is completed. Can this be done? So the motor would never complete a full circle rotation, also a stepper motor would not be suitable as the motion needs to be fast and the motor needs to be small and lightweight, and this program of motor motion would need to be programmed onto a chip. Can this be done?