Ok, I moved it over with a basic title; you can edit the first post's title to change the thread title.
Now to define a few things about your system to be sure you get the right recommendations:
Summary of what it sounds like you are after; anything that's incorrect please note it for us:
48v 20A controller (1000w to match the motor and what your battery can probably handle) with throttle input.
Sensorless (no halls) for simple motor wiring (this may make for rough startups from a stop on simple cheap controllers)
No display connector or option. (if it has the option, it may not provide full power, etc., without the display for you to choose settings in it).
No PAS input. (if it has one, it may require the sensor and you to be pedalling for it to operate, with no display to choose a throttle-only assist level).
"Tough" controller...what specifically do you mean? Some controllers are potted against water intrusion and vibration problems. If you need some other kind of toughness, you'll need to define that as precisely as possible.
Any of them are probably going to come with ebrake wires but you can cut them off or tape them up if you aren't using that function. Note that you probably won't get plug and play with the other cables you still need; you're likely to have ot figure out which wires go where in each cable, as it can be difficult to find matching-connector setups that also have matching wiring.
Depending on your usage and the actual motor you have, and if your battery can handle it (any specs you can post for it may help us figure that out; pics of the labels might help), you mgiht be able to use a controller up to 40A, for doulbe the power for short bursts (for instance, one of the motors on the SB Cruiser trike is only a "500w" motor but I put 2000w into it for a few seconds starting up from a stop...dropping back to the rated power for cruising at 20mph, so it gets hot, but not overheated). Your motor and/or battery might not handle that much for sustained runs, hillclimbs, etc., though.
Some questions:
What happened that caused the controller failure; and what were the symptoms it had? (may help ensure it's *just* a controller problem so you can get all the stuff you need at once if possible).
What job do you need the bike to do for you, under what conditions? Did it already do the work needed with the original controller? (and what controller did it have before; a pic of it's label may give useful info to make sure you have what's needed to run a new one).
There are several ways for a controller to drive the motor, some (like FOC) more complex than others to setup, and more expensive, but simple in actual operation, and can be more efficient. The most common cheap way is trapezoidal (trap) / square wave; it's anywhere from a bit noisy to very noisy depending on the motor it's driving and the load on it. The next most common sometimes a bit more expensive is sinewave, but is nearly silent. Some sinewave controllers only do that in sensored mode, and in sensorless they fallback to trap drive.
If you just want the system to connect up and go, those two are better options than FOC; the only thing you have to do with them (assuming you use the hall sensors for better startup from a stop) is to figure out the right phase/hall wiring combo, or run the autolearn function the controller has (if it has one).
Throttle response varies between different simple cheap controllers, but they'll all be controlling the speed of the motor via the throttle, rather than it's torque.
FOC is also sinewave, but doesn't use a simple "force the motor to go" type of drive like the cheap sine / trap controllers--it has to know all about the motor's characteristics to drive it correctly, and can take some serious patience and time to tune it to work with your system under your conditions, using a computer (or phone) based program via a cable to the controller for setup (but nothing connected while actually riding). Since FOC directly controls the current in the motor, controlling it's torque via the throttle, it's the smoothest control type. (note that not every FOC controller actually implements this, but almost all do--there is one series of Kelly FOC controller that does not, which doesn't make sense but that's Kelly for you).
