The only requirement for open loop control is to maintain proper voltage current and frequency to the motor. Motor is run in closed loop where you need controlling. For example in a 3d printer you need continuous control of motor rotation, so you need to provide feedback to know the motor position.
A pressure transducer driving a VFD driving a motor driving a pump to provide a set pressure would be a closed control loop. The motor itself is operated open loop, as part of a closed process loop.
A VFD can provide closed loop control of a motor by adding encoder feedback. This can provide speed, torque and position control. The basic requirements are to understand the load profile, and choose components that are compatible with each other and will stay within their safe operating regions.