The main difficulty is isolation, as the coil is at mains voltage. If you don't mind putting an isolation transformer in there, you could do that, and then have a common ground side that's easy to work with; a microcontroller can read the current and feed back to set the phase angle or whatever, using a PID loop. Or if you don't mind that the MCU is riding on mains voltage, you can put it there directly; this can be a bit of a pain for development though, plus whatever kind of interfacing you're looking for (digital control e.g. serial port? just a plain on/off switch and potentiometer?).
For example, your typical plug-in power monitor (Kill-a-Watt and clones) uses an MCU riding on mains voltage, reading the load voltage and current, and calculating the stats displayed. This works out because its interface is well insulated, just plastic buttons and an LCD, real simple. If you wanted to, say, log values from a similar thing though -- you'd need some kind of port connection, and you can't just attach a serial port to mains voltage, you need isolation. Digital isolators are a heck of a lot easier than isolation transformers, so that'd be a typical solution in that case. But if you need to have a programmer attached to it as well (as for development), you'll at least need an isolator for that interface as well; which can be about as simple as a serial port isolator, but it might not be as standard as a serial port, so you might have to cook up something by hand, say. At which point just using an isolation transformer might be more attractive. So that's all that drives such a choice, really.
There are other ways -- you can isolate the sense signal itself, say with a Hall effect sensor (though these aren't great at low currents -- they aren't very sensitive, generally), or with an analog-digital converter and digital isolator. (Pure analog isolators happen to be rather tricky to make, so it's usually actually better to convert it first.) Or even sense the magnetic field directly (something a Hall effect sensor is adept at -- the advantage is all the turns on the magnetic core, versus sampling the current through a tiny (usually one-turn hairpin) winding). Though sensing field has the downside of also being sensitive to the effect of the brake disc itself, the directionality of magnetic fields, and needing calibration.
Tim