Lionel:
I agree with you in part, but disagree in part as well. There are several interesting issues, so it is worth breaking them apart.
I concur that AC motors are fundamentally continuous, not discrete. This includes both asynchronous induction motors and synchronous motors like brushless servo motors and even stepper (yes!) motors. The windings on these motors produce at least approximately sinusoidal torque functions as the motor (or just rotor field) spins. With multiple phases, you can get very low torque variations if you put in sinusoidal waveforms.
Of course, higher harmonics from the windings, and reluctance/cogging torque in the magnetics will limit how low you can get your torque variations, but many AC motors are designed to minimize these effects, and it is possible to compensate for these in the controls.
You may be surprised that I included stepper motors in this class. But most stepper motors (I will exclude cheap VR steppers) are AC synchronous motors. With either open-loop microstepping control or closed-loop control (treating it as a high-pole-count brushless servo motor), you can get very smooth control with sinusoidal command waveforms to the phases.
But I fundamentally disagree with your assertion that "the root problem is that the vector control algorithm is not applying an AC current waveform to the motor." We've been doing vector control for almost 30 years now, and we have always applied AC current waveforms to the motor, which are sinusoidal functions of time in the steady state. The power stage for a vector control drive is really the same as for an open-loop VFD. Both synthesize AC waveforms from a DC bus by a modulation scheme, usually PWM. The differences are in the control schemes for synthesizing the waveforms.
Roughly speaking, there are three classes of control schemes (focusing now on induction motors):
1. Open-loop VFDs ("Volts per Hertz" drives): These command AC waveforms with no knowledge of what the motor is actually doing, relying on the electromagnetic feedbacks in the motor to make the motor (roughly) follow the command signals. As their nickname suggests, the output frequency and magnitude are at least roughly proportional. These are cheap and simple, but have the lowest performance. They have a lot of trouble at low speeds, because they have no capability to resolve the magnetization and torque component interactions as a vector drive would.
2. "Sensorless vector" drives: In the technical literature, these are called "shaft-sensorless" drives, because they do rely on voltage and current sensors inside the drive to try to figure out what the rotor is doing. Fundamentally, they attempt to back out the back EMF voltage component on the phases to compute rotor velocity and angle. This works well at high speeds when the back EMF is large, but is much more difficult at low speeds, when it is a small component of the overall values, and the signal-to-noise ratio is horrible. Still, it is significantly superior to open-loop control.
3. Full vector drives: These employ a high-resolution feedback device on the drive that directly measures rotor angle. This provides excellent performance all the way down to zero speed. In fact, it has been common for over 20 years now to use this to make induction motors operate as positioning servo motors. If a machine tool has a spindle that is capable of "hard tapping", it is almost invariably an induction motor under full vector control. And smooth motion at low speed is vital for this function.
I know of no performance disadvantages of full vector control compared to sensorless vector or Volts/Hertz drives. Of course, they are more complex and expensive.
Curt Wilson
Delta Tau Data Systems