How do large power supplies work? (VFD's etc.)
You don't want to control a "rail voltage". You want to control current. Why? Because the fundamental connections between electrical and mechanical world are

$$P_\mathrm{el} = I \cdot U = M \cdot \omega = P_\mathrm{mech}$$

and, in addition:

$$U \sim \omega$$

$$M \sim I$$

It's as great as it is simple.

For your crane example this means, depending on the load on the hook, your motor needs a certain torque – a certain current – to keep that load at an equilibrium of constant speed.

That's why you want to measure and control the current. The current depends directly on the load applied. Speed doesn't, voltage doesn't.