Since the synchronous motors are part of a machine, I make the assumption that they are not the wound rotor, DC excited, slip ring motor described by PLucas. Rather, they are probably smaller permanent magnet synchronous motors. They are generally used when precise speed regulation is needed and there is no precision inverter involved.
Rather than magnetize their rotors indirectly by slipping as in an induction motor, these expensive little rascals have a rare earth permanent magnet rotor. There is no need for slip since the rotor is always fully magnetized. As a result, the motor rotor will turn at exactly the same speed as the spinning stator field which is determined by the number of poles and the frequency the same as in an induction motor. From no load to full rated load, the rotor turns at exactly the same speed. If the torque exceeds the rated torque of the motor, my understanding is that the motor essentially gives up and stalls. I have never seen a torque-speed curve for a permanent magnet sync motor but I am quite sure that there is no useable torque anywhere except when the rotor and the stator are properly "hooked up" in sync. For this reason, there is no way to start a purely synchronous motor across the line. When fed by an inverter, however, a stationary motor can be supplied near zero frequency and the speed can be increased synchronously up to desired running speed (as long as the rated torque is not exceeded).
PLucas describes a wound rotor synchronous motor which is old technology and in my experience is generally found on compressors or other machines that run continuously in a plant operation. It is started by separate windings built in that convert it to an induction motor of just enough torque to get the rotor up to speed unloaded. Once up to sync speed, it converts to synchronous operation and the load is applied to the shaft. One of the primary purposes of these motors was to provide power factor correction for the facility. This is done by varying the excitation. If underexcited, the power factor lags and if overexcited, it leads. Most are therefore overexcited to offset inductive loads elsewhere in the facility. Some of the exciters were designed to monitor p.f. and automatically change the excitation to hold the p.f. constant. These machines are getting rather scarce.
Returning to permanent magnet motors on inverters, control has to be very delicate because very small changes in inverter output frequency translate into instant attempts by the motor to match the change. Large torque and current spikes can result with the drive tripping or the motor exceeding its rated torque and "unhooking". I would expect that the accel/decel ramp rates would be critical and a current limit function that automatically modifies the accel ramp would be essential too.
I must confess that I have had limited experience with these motors. Since I have available a fine precision speed regulating drive at competitive pricing, I would have very little need to use such expensive motors. If anyone has more experience with these motors, I would sure welcome their input. Anybody out there?