Suppose we have an AC motor which needs to lower an object at a set speed. We use a PID loop to determine and correct positional errors. Presumably the PID loop will keep the current low as most of the work will be done by gravity. By lowering or stopping the current, will the motor be able to maintain the set speed, or will gravity take over and descend the object at its own will?
You will need variable frequency drive (VFD) with "regenerative braking" or a "braking resistor"(the cheaper option) for this application. "Braking" is not necessarily a standard feature (especially on small VFDs) so you will have to specify it.
A common configuration is to have the VFD output a frequency proportional an input(0-10v or 4-20mA). They can also be controlled via digital protocols(ethernet, modbus, canbus) and many even have PID controllers built into them. For your application all you should need to do is put the drive in constant velocity mode and send it a speed input or manually set that speed.
The frequency is what controls the speed of the 3 phase AC motor(single phase will not work). When an external load like gravity exceeds the target speed the VFD will divert the energy to resistors or put it back on to the grid depending on your configuration.
For example, this Saftronics C102005-1 specifies that it has a "Built-in braking transistor". Others may say "Built in dynamic braking" or the like. The resistor will usually be external. You will have to read the user manual or contact the manufacturer to determine the required power capacity and ohms of the resistor bank.