> how do you vary the voltage so you can keep a constant current?
You don't.
Electric motors are not resistors. They are a small resistor plus a big generator.
When they run at FULL speed (no load, no drag, no friction), current goes to ZERO.
When working anywhere near full speed (most motors), current is essentially proportional to Torque.
Check it. That high-milage table-saw with broken-in bearings? Take off the belt, blow the sawdust (added air drag) out of the windings, connect an ammeter. Sure it pulls big current while pulling its inertia up to speed. But when the speed settles, the current goes very low, less than 1/10th the nameplate amperage. The friction and drag is less than 1/10th the total work available. A tablesaw motor probably has a fan; bust the blades off and current will drop even lower.
Locked-rotor conditions are different. So is full torque at low-low RPM. You know how that tablesaw will dim the lights when it starts, and when it hits a tough knot. But this is not Leslie turf so I'll skip it.
Feed a common "60Hz 3600RPM" motor 60Hz and it tries to reach 3600 RPM (60 cycles per second times 60 seconds per minute). An induction motor must lag to work, so maybe it gets to 3,550RPM idle, 3,400 RPM hard work. Feed it 30Hz and it aims for 1,800RPM. At 1Hz it wants to do 60RPM (altho a thousands-RPM motor probably won't like that).
What is the current? Assuming you have enough motor to approach target speed, current is only enough to pull the load plus drag. If your load is the same at any speed (pure friction), the current is the same at any speed. If your load is a propeller, torque and current rise with RPM. Since a raw motor has air-drag, and a Leslie's load may have a significant air-drag component, you don't want to over-speed a Leslie's motor much. (Anyway you can fling-off the windings.)
Low Hz and low RPM with a light load, the current will stay in check. Probably reduce due to lower air-drag losses.
There is no "maximum" current. All motors pull short-term surges 2X to 10X their nominal current. The nominal current can be based on many things, but is essentially the current that flows when doing the most real work it can do safely. The same motor frame can be rated 2HP 20A for intermittent (shop-saw) duty but 1HP 10A for 8 hour/day constant (sawmill) work. Or even 20HP 200A for short bursts (electric car spends 90% of time at <25% power, and the battery goes flat before a big motor gets fully over-heated).
So why do AC motors have voltage numbers? That's to cover the high torque low-RPM situation. A "115V" motor will probably run on 24V. Or it may need a flip to get going against static friction. And it will accelerate poorly, and stall at very slight load. You want 100V-150V to get good starting and short-term torque. The 115V motor will run on 240V too, and at nominal load it may run just fine. But the start-up surge will be brutal, and if you hit a tough knot it may overheat quite quickly.
Oh, many DC motors, the no-load speed is proportional to voltage. They run twice as fast at 12V as at 6V.