Ripple shows up because there’s a 5th harmonic in the motor’s flux linkage (and therefore back-emf). From the perspective of the field-oriented control, these harmonics at the phases show up as AC disturbances on the D/Q voltages. The two current loops will try to squash these disturbances, but it’s ability to do so depends on the current loop bandwidth and the magnitude of the disturbances.
The post goes in-depth about causes and introduces Adaptive Feedforward Cancellation. This is a weird technique which has the seemingly magical property of giving your controller infinite gain at a specific frequency – i.e. it will perfectly track a signal at that frequency, or perfectly reject a disturbance at that frequency.
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